Patent Publication Number: US-10785650-B2

Title: Processing module and associated method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the priority under 35 U.S.C. § 119 of European Patent application no. 17158979.9, filed on Mar. 2, 2017, the contents of which are incorporated by reference herein. 
     FIELD 
     This disclosure relates to a processing module for a communication device and a method of estimation of a propagation channel model. 
     BACKGROUND 
     Wideband Radio Frequency (RF) applications have been developed that are capable of accurate distance measurement between two or more wireless devices. These measurements are based on Time-of-Flight (ToF) calculations which are derived by accurate determination of departure and arrival times of RF packets between two devices. RF packets travel at the speed of light and thus a calculated ToF allows determination of the distance between devices. Such a procedure is commonly called ‘Ranging’. One practical application of Ranging is ‘Distance Bounding’ whereby ToF calculations are used to verify whether the distance between two devices is less than a predefined threshold, such as used for automotive Passive Keyless Entry (PKE) systems and other access control systems, as well as for contactless electronic payment systems. 
     A receiving device is able to derive a channel estimate in relation to a transmitting device using known patterns within a received packet from the transmitting device. For example, in IR-UWB (Impulse Radio-Ultra-WideBand) systems, such as defined in IEEE 802.15.4, a preamble comprising repeating synchronization symbols and a Start-of-Frame Delimiter (SFD) is placed in front of a payload segment. In IR-UWB receivers, the repeating synchronization symbols within the preamble of a received packet are typically used to realise time and frequency synchronization and to derive a channel estimate for the received packet. A channel estimate consists of an estimate of arrival times of multipath components, the first arrived multipath component represents the shortest radio path and is therefore important for the ToF calculations. 
     Significantly, since the synchronisation symbols are in many cases used for deriving the channel estimate within a receiving device, an attacking device only requires knowledge of the synchronisation symbol pattern and symbol period to employ an attack that influences the channel estimation process and therefore the ToF calculations. 
     SUMMARY 
     The disclosure provides a processing module for a receiver device, a corresponding receiver device, a processing module for a transmitter device, a corresponding transmitter device and associated methods and computer program products, as described in the accompanying claims. 
     According to a first aspect of the disclosure, we provide a processing module for a receiver device configured to provide for processing of a signal received by the receiver device from a transmitter device, the signal comprising a secure training sequence divided into a plurality of time spaced blocks, the secure training sequence comprising a non-repeating pattern of symbols, and wherein one of:
         a) at least a first block is transmitted from a first antenna and a second block is transmitted from a different second antenna of the transmitter device;   b) at least a first block is received by a first antenna and a second block is received by a different second antenna of the receiver device;   wherein the processing module is configured to:   based on a plurality of repeating, predetermined synchronization symbols of the signal, provide for determination of a phase of a carrier wave of the signal received at the first antenna of the receiver device or transmitted from a first antenna of the transmitter device;   derive a secure training sequence corresponding to the secure training sequence of the signal based on predetermined secure information known to both the transmitter and receiver device, the secure training sequence comprising a non-repeating pattern of symbols;   perform cross correlation between the first block from the first antenna and a first part of the derived secure training sequence to obtain a first phase marker defining a phase of the signal from the first antenna relative to the determined phase of the carrier wave;   perform cross correlation between the second block from the second antenna and a second part of the derived secure training sequence to obtain a second phase marker defining a phase of the signal from the second antenna relative to the determined phase of the carrier wave;   based on the first phase marker and the second phase marker defining a phase difference of the signal between the first and second antennas and a known spacing of the first antenna relative to the second antenna, determine an angle of arrival of the signal relative to the receiver device.       

     In one or more examples, the signal comprises one or more frames comprising data transmission units, the frames comprising the blocks. 
     In one or more embodiments, the blocks are time-spaced by a guard interval of predetermined length. 
     In one or more embodiments, the receiver device comprises a IR-UWB (Impulse Radio-Ultra-WideBand) receiver device. 
     In one or more embodiments, the blocks are transmitted time consecutively (but may be time spaced). 
     In one or more embodiments, the first and/or second phase markers are based on channel estimate information of the cross correlation that defines a Line-of-Sight multipath component. 
     In one or more embodiments, the first block of the signal is transmitted by only the first antenna of the transmitter device and the second block, subsequent to the first block, is transmitted by only the second antenna of the transmitter device, and the receiver device receives the first block and the second block at a single antenna. 
     In one or more embodiments, the first block and the second block are transmitted by the same antenna but the first block as received by the first antenna is cross correlated by the processing module and the second block as received by the second antenna is cross correlated by the processing module. 
     In one or more embodiments, the first block of the signal is transmitted by the first antenna of the transmitter device and the second block, subsequent to the first block, is transmitted by the second antenna of the transmitter device, and a third block, subsequent to the second block is transmitted by the first antenna of the transmitter device and a fourth block, subsequent to the second block, is transmitted by the second antenna of the transmitter device; and
         the receiver device comprises two receive antennas, the processing module configured to receive one of the first block and the third block from the first receive antenna and one of the second and fourth block from the first receive antenna; and the processing module configured to receive the other of the first block and the third block from the second receive antenna and the other of the second and fourth block from the second receive antenna.       

     In one or more embodiments, the processing module is configured to:
         for the blocks received from the first receive antenna, perform cross correlation between the parts of the secure training sequence and the blocks received from the first and second antennas of the transmitter device and determine a phase difference therebetween to determine a first angle of arrival of the signal relative to the receiver device using the known spacing of the first antenna relative to the second antenna of the transmitter device; and   for the blocks received from the second receive antenna, perform cross correlation between the parts of the secure training sequence and the blocks received from the first and second antennas of the transmitter device and determine a phase difference therebetween to determine a second angle of arrival of the signal relative to the receiver device using the known spacing of the first antenna relative to the second antenna of the transmitter device;   the angle of arrival based on one or more of one of the first and second angles of arrival, an average thereof or a function thereof.       

     According to a second aspect of the disclosure, we provide a method comprising
         in respect of a signal received by the receiver device from a transmitter device, the signal comprising a secure training sequence divided into a plurality of time spaced blocks, the secure training sequence comprising a non-repeating pattern of symbols, and wherein one of:   a) at least a first block is transmitted from a first antenna and a second block is transmitted from a second antenna of the transmitter device;   b) at least a first block is received by a first antenna and a second block is received by a second antenna of the receiver device;   wherein the processing module is configured to:   based on a plurality of repeating, predetermined synchronization symbols of the signal, provide for determination of a phase of a carrier wave of the signal received at the first antenna of the receiver device or transmitted from a first antenna of the transmitter device;   deriving a secure training sequence corresponding to the secure training sequence of the signal based on predetermined secure information known to both the transmitter and receiver device, the secure training sequence comprising a non-repeating pattern of symbols;   performing cross correlation between the first block from the first antenna and a first part of the derived secure training sequence to obtain a first phase marker defining a phase of the signal from the first antenna relative to the determined phase of the carrier wave;   performing cross correlation between the second block from the second antenna and a second part of the derived secure training sequence to obtain a second phase marker defining a phase of the signal from the second antenna relative to the determined phase of the carrier wave;   based on the first phase marker and the second phase marker defining a phase difference of the signal between the first and second antennas and a known spacing of the first antenna relative to the second antenna, determining an angle of arrival of the signal relative to the receiver device.       

     According to a third aspect of the disclosure, we provide a processing module for a transmitter device configured to provide for generation of a signal comprising at least one frame for transmission by the transmitter device to a receiver device, the processing module configured to provide for time-division of a secure training sequence into blocks, each block provided for transmission from only one of a plurality of antennas of the transmitter device, the processing module configured to provide for transmission of consecutive blocks from different antennas of the plurality of antennas, the secure training sequence comprising a non-repeating sequence of symbols based on one or more of an agreed symbol sequence and an agreed reference for generation of such a symbol sequence agreed between the transmitter device and receiver device. 
     According to a fourth aspect of the disclosure, we provide a method comprising:
         providing for generation of a signal comprising at least one frame for transmission by the transmitter device to a receiver device, by time-division of a secure training sequence into blocks, each block provided for transmission from only one of a plurality of antennas of the transmitter device,   providing for transmission of consecutive blocks from different antennas of the plurality of antennas, the secure training sequence comprising a non-repeating sequence of symbols based on one or more of an agreed symbol sequence and an agreed reference for generation of such a symbol sequence agreed between the transmitter device and receiver device.       

     According to a fifth aspect of the disclosure, we provide a system comprising at least one receiver device controlled by the processing module according to the first aspect and at least one transmitter device controlled by the processing module according to the third aspect. 
     In one or more embodiments, the system comprises at least one of:
         an access control system for a building;   a passive keyless entry and/or start system for an automobile;   a contactless payment terminal; and   an automatic teller machine.       

     According to a sixth aspect of the disclosure, we provide a processing module for a transmitter device configured to provide for generation of a signal comprising at least one frame for transmission by the transmitter device to a receiver device, the processing module configured to provide for modulation of an input bitstream to form at least part of the frame, the processing module configured to;
         provide for convolutional encoding of an input bitstream, the convolutional encoding providing for generation of a first code bit g 0  and a second code bit g 1  for each bit of the input bitstream;   determine a position bit based on the equation g 0 +g 1  mod 2;   determine a polarity bit based on the second code bit g 1 ;   determine a BPPM-BPSK symbol, the BPPM-BPSK symbols forming the at least part of the frame, based on the mapping;       

                                                 Position   Polarity   BPPM-BPSK           bit   bit   symbol                          0   0   (+√E s , 0)           0   1   (−√E s  ,0)           1   1   (0, −√E s )           1   0   (0, √E s )                        
where E s  represents signal energy.
 
     In one or more embodiments, the convolutional encoding has a constraint length of 7. 
     In one or more embodiments, the input bitstream is encoded with a Reed-Solomon code prior to convolutional encoding. 
     In one or more embodiments, the input bitstream represents at least part of the frame. 
     In one or more embodiments, the convolutional encoding is defined as follows;
         denoting the input bit stream for encoding with x(n) then first code bit g 0 (n)=x(n)+x(n−2)+x(n−3)+x(n−5)+x(n−6) mod 2, and second code bit g 1 (n)=x(n)+x(n−1)+x(n−2)+x(n−3)+x(n−6) mod 2, in which x(n) comprises the input bit of the input bitstream at time n, having a value 0 or 1.       

     According to a seventh aspect of the disclosure, we provide a processing module for a receiver device configured to provide for processing of a signal comprising at least one frame received by the receiver device from a transmitter device, the processing module configured to:
         provide for identification of BPPM-BPSK symbols in the signal, the BPPM-BPSK symbols selected from (+√E s ,0), (−√E s ,0), (0, −√E s ) and (0, √E s ) where E s  represents signal energy;   provide for demodulation of each BPPM-BPSK symbols to obtain two code bits comprising g 0  and g 1  based on the mapping;       

     
       
         
           
               
               
               
               
             
               
                   
                   
               
               
                   
                 BPPM-BPSK 
                   
                   
               
               
                   
                 symbol 
                 g0 
                 g1 
               
               
                   
                   
               
             
            
               
                   
                 (+√E s , 0) 
                 0 
                 0 
               
               
                   
                 (−√E s  ,0) 
                 0 
                 1 
               
               
                   
                 (0, −√E s ) 
                 1 
                 1 
               
               
                   
                 (0, √E s ) 
                 1 
                 0 
               
               
                   
                   
               
            
           
         
       
         
         
           
             provide for determination of an output bitstream based on decoding of the code bits based on a convolutional code. 
           
         
       
    
     In one or more embodiments, the convolutional code has a constraint length of 7. 
     In one or more embodiments, the processing module is further configured to provide for determination of the output bitstream based on decoding a Reed-Solomon code post decoding the convolutional code. 
     In one or more embodiments, the output bitstream represents at least part of the frame. 
     In one or more embodiments, the convolutional encoding is defined as follows; 
     denoting the input bit stream for encoding with x(n) then first code bit g 0 (n)=x(n)+x(n−2)+x(n−3)+x(n−5)+x(n−6) mod 2, and second code bit g 1 (n)=x(n)+x(n−1)+x(n−2)+x(n−3)+x(n−6) mod 2, in which x(n) comprises the input bit of the input bitstream at time n, having a value 0 or 1. 
     According to an eighth aspect of the disclosure, we provide a method comprising providing for generation of a signal comprising at least one frame for transmission by a transmitter device to a receiver device, by providing for modulation of an input bitstream forming at least part of the frame, the method comprising;
         providing for convolutional encoding of an input bitstream, the convolutional encoding providing for generation of a first code bit g 0  and a second code bit g 1  for each bit of the input bitstream;   determining a position bit based on the equation g 0 +g 1  mod 2;   determining a polarity bit based on the second code bit g 1 ;   determining a BPPM-BPSK symbol, the BPPM-BPSK symbols forming the signal, based on the mapping;       

                                                 Position   Polarity   BPPM-BPSK           bit   bit   symbol                          0   0   (+√E s , 0)           0   1   (−√E s , 0)           1   1   (0, −√E s )           1   0   (0, √E s )                        
where E s  represents signal energy.
 
     According to a ninth aspect of the disclosure, we provide a method comprising providing for processing of a signal comprising at least one frame received by a receiver device from a transmitter device, the method comprising:
         providing for identification of BPPM-BPSK symbols in the signal, the BPPM-BPSK symbols selected from (+√E s ,0), (−√E s ,0), (0, −√E s ) and (0, √E s ) where E s  represents signal energy;   providing for demodulation of each BPPM-BPSK symbols to obtain two code bits comprising g 0  and g 1  based on the mapping;       

     
       
         
           
               
               
               
               
             
               
                   
                   
               
               
                   
                 BPPM-BPSK 
                   
                   
               
               
                   
                 symbol 
                 g0 
                 g1 
               
               
                   
                   
               
             
            
               
                   
                 (+√E s , 0) 
                 0 
                 0 
               
               
                   
                 (−√E s , 0) 
                 0 
                 1 
               
               
                   
                 (0, −√E s ) 
                 1 
                 1 
               
               
                   
                 (0, √E s ) 
                 1 
                 0 
               
               
                   
                   
               
            
           
         
       
         
         
           
             providing for determination of an output bitstream based on decoding of the code bits based on a convolutional code. 
           
         
       
    
     According to a tenth aspect of the disclosure, we provide a system comprising at least one receiver device controlled by the processing module according to the seventh aspect and at least one transmitter device controlled by the processing module according to the sixth aspect. 
     In one or more embodiments, the system comprises at least one of:
         an access control system for a building;   a passive keyless entry and/or start system for an automobile;   a contactless payment terminal; and   an automatic teller machine.       

     The communication receiver device comprises at least one of: an Impulse Radio Ultra-WideBand (UWB) receiver device; and a light/laser ranging receiver device. 
    
    
     
       Further details, aspects and examples will be described, by way of example only, with reference to the drawings. In the drawings, like reference numbers are used to identify like or functionally similar elements. Elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. 
         FIG. 1  shows a current standard frame format for Ultra-Wideband (UWB) based ranging, as defined in IEEE 802.15.4-2015; 
         FIG. 2  shows an example of a first device and a second device which may comprise transmitter devices and receiver devices for communication therebetween; 
         FIG. 3  shows an example embodiment of a frame format, such as an UWB frame format; 
         FIG. 4  shows an example reduced frame format, reduced in temporal length in comparison to the frame format of  FIG. 2 ; 
         FIG. 5  shows a part of the frame format with two or more pilot symbols interleaved therein; 
         FIG. 6  shows the synchronisation field of the frame including repeated synchronisation symbols and is labelled with parameters thereof; 
         FIG. 7  shows an example representation of a de-spreaded synchronisation field for ternary encoded synchronisation symbols; 
         FIG. 8  shows an example representation of a de-spreaded synchronisation field for binary encoded synchronisation symbols; 
         FIG. 9  shows example channel estimate information of an example channel comparing the use of binary and ternary encoded synchronisation symbols; 
         FIG. 10  shows an example autocorrelation function of the signal; 
         FIG. 11  shows an example cross-correlation between the start of frame delimiter symbols and the synchronisation symbols of the synchronisation field; 
         FIG. 12  shows an example cross-correlation, similar to  FIG. 11 , between the start of frame delimiter symbols and the synchronisation symbols of the synchronisation field, using synchronisation symbols and start of frame delimiter symbols as specified in the IEEE standard; 
         FIG. 13  shows an example non-repeating series of bit, such as output from a CSPRNG, and their mapping to a spreading sequence, which is divided into segments, for a first peak repetition frequency; 
         FIG. 14  shows an example non-repeating series of bit, such as output from a CSPRNG, and their mapping to a spreading sequence, which is divided into segments, for a second peak repetition frequency; 
         FIG. 15  shows an example modulation of the segments of the spreading sequence; 
         FIG. 16  shows a first and second example frame format for transmitting from two or four antennas or receiving by two or four antennas; 
         FIG. 17  shows an example data-rate selection field; 
         FIG. 18  shows an example convolutional encoder; 
         FIG. 19  shows a graph of word error rate versus Es/N0 to compare error correction performance of the convolutional encoding proposed herein and the encoding defined in the IEEE standard; 
         FIG. 20  shows a graph of bit/packet error rate versus Es/N0 to compare error correction performance of the convolutional encoding proposed herein and the encoding defined in the IEEE standard; 
         FIG. 21  shows an example diagrammatic depiction of an encoding scheme for bits of a physical layer (PHY) service data unit (PSDU) for containing arbitrary data transferred between the transmitter device and receiver device; 
         FIG. 22  shows a butterfly section of an encoder/decoder trellis for the proposed encoder; 
         FIG. 23  shows an example QPSK modulation Gray mapping; 
         FIG. 24  shows an example semi-full quadrature modulator for QPSK modulation; 
         FIG. 25  shows an example of dummy pulse insertion; 
         FIG. 25A  shows an example method of dummy pulse insertion; 
         FIG. 26  shows an example block diagram illustrating the process for dummy pulse insertion; 
         FIG. 27  shows the format of a BPPM-BPSK symbol according to the IEEE standard; 
         FIG. 28  shows an example format of a BPSK symbol in which no position modulation is applied, only BPSK modulation; 
         FIG. 29  shows an example illustration for ranging between a first device comprising a tag and a second device comprising an anchor; 
         FIG. 30  shows an example illustration of ranging between multiple anchors and multiple tags; 
         FIG. 31  shows an example configuration of symbols divided into subsymbols; 
         FIG. 32  shows a top view of a device having two antennas; and 
         FIG. 33  shows a side view of the device of  FIG. 32 . 
     
    
    
     Examples herein are described with reference to a radio frequency (RF) communication device e.g. transmitter device and a receiver device and the processing modules thereof. However, it is contemplated that examples are not limited to being implemented solely within RF communication devices and examples may be applicable to any system in which ToF measurements are required to be determined, and is particular applicable to any system in which a Time-of-Flight (ToF) distance measurement is a specified function, such as IR-UWB (Impulse Radio-Ultra WideBand) radio frequency (RF) transceivers, pulse radars at 60 GHz and higher frequencies, and pulse-based light/laser ranging transceivers. Thus it is contemplated that examples may be implemented within a range of different communication systems including, but not limited to, RF communication systems, and optical (e.g. light/laser) communication systems, etc. The applications may range from automotive Passive Keyless Entry (PKE) systems and other access control systems to (contactless) electronic payment systems, and in particular to any application where ranging and distance bounding is performed. 
     In IR-UWB RF systems, it may be desirable to maximize security and link budget while minimizing current consumption, latency, and system cost. 
     The IR-UWB physical layer is defined in IEEE Standards Association, IEEE Standard for Low-Rate Wireless Personal Area Networks (WPANs), IEEE Std 802.15.4™-2015 (hereinafter “IEEE standard”). The specification of the physical layers in the standard may have drawbacks for particular use cases. However, we describe herein a plurality of aspects of the physical layer specification that may provide one or more technical effects for one or more particular use cases. One or more of the aspects herein may provide a technical effect over what is disclosed in the standard, for particular use cases. 
     Accordingly, one or more of the aspects described herein are described as changes to or improvements on the IR-UWB physical layer IEEE standard and accordingly terms and concepts used herein may be equivalent to terms used and concepts defined in the IEEE standard. Additionally, processes or definitions of the IEEE standard may be combined with the features defined herein. 
     In the sections that follow we describe different aspects of a frame format definition (PHY). One or more of the aspects may be implemented in a processing module for a receiver device arranged to receive a signal transmitted by a transmitter device. One or more of the aspects may be implemented in a processing module for a transmitter device arranged to transmit a signal for receipt by a receiver device. The disclosure is split into the section as follows for ease of understanding and it will be appreciated that features disclosed in one section may be combined with features of other sections, in particular as they relate to the same, proposed, physical layer definition. 
     The current standard frame format  100  for Ultra-Wideband (UWB) based data communication and ranging, as defined in IEEE 802.15.4-2015, is shown in  FIG. 1 . 
     The frame consists of a preamble  101 , which may include at least a portion for synchronization, and a payload  102  for the transmitted data. The preamble  101  is further divided into a portion comprising a plurality of synchronization symbols, termed “SYNC”, and a Start-of-Frame Delimiter, termed “SFD”. The plurality of synchronization symbols may include a repeating pattern of one or more synchronization symbols. The plurality of synchronization symbols at the start of the preamble may enable a receiver device to synchronize, such as in terms of time and/or frequency, with an incoming frame. The SFD signals the end of the plurality of synchronization symbols. The synchronization symbols have special properties to provide for easy synchronization by a receiver device. The synchronization symbols may be used by a receiver device for making an estimation of the Channel Impulse Response (CIR). The synchronization and/or the estimation of the CIR may be achieved by a plurality of repetitions of the synchronization symbols. 
     The payload  102  comprises a plurality of parts comprising a physical layer (PHY) header  103 , termed “PHR” and a physical layer (PHY) service data unit  104 , termed a “PSDU”. The physical layer header  103  may comprise information defining frame properties, such as the data-rate of one or more parts of the frame or the length of the PSDU  104 . The PSDU may contain arbitrary information to be exchanged between transmitter and receiver devices. 
     For ranging purposes, the IEEE standard suggests to use the transition from the preamble  101  to the PHY header  103  as a time marker, i.e. the marker to base a time of arrival estimate on. 
     Although this frame format may enable an efficient hardware implementation of the receiver device for ranging applications, it may also be open to several vulnerabilities from adversaries who want to shorten the measured distance. This may be a problem if the UWB frame format is used for secure distance bounding where only a distance below a certain threshold enables certain privileges like opening a door for example. 
     In one or more situations, the IEEE standard defined frame format described above may not be well suited for short frames and/or for tracking of the CIR in a secure way. 
     In one or more situations or use cases the frame format definition of the above-mentioned IEEE standard may have one or more of the following drawbacks.
         Preamble injection vulnerability: in the IEEE standard a channel estimate is generated based on the preamble  101  and the IEEE standard specifies no method for verification of the channel estimate. The security of the system may be compromised as attackers may perform preamble injection attacks which could reduce the measured distance, as described in Marcin Poturalski, Manuel Flury, Panos Papadimitratos, Jean-Pierre Hubaux, and Jean-Yves Le Boudec. Distance Bounding with IEEE 802.15.4a: Attacks and Countermeasures. In IEEE Transactions on Wireless Communications, Year: 2011, Volume: 10, Issue: 4.   Early Detect, Late Commit (EDLC) vulnerability: The IEEE standard specifies the use of burst position modulation (BPM) and known scrambling sequences. However, burst position modulation, and, to a certain degree, use of known scrambling sequences within a burst may allow an attacker with high available signal to noise ratio (SNR) to detect a symbol&#39;s polarity early and therefore perform EDLC attacks.   The IEEE standard provides support for non-coherent receivers: The IEEE standard specifies ternary coding of the preamble and SFD, as well as a header/payload coding scheme that allows reception using only the BPM information. For an implementation in which the receivers are of coherent type, this support in the frame design for non-coherent receivers may result in loss of link budget and/or frame efficiency (length of frame, time used for the medium to exchange messages).   The IEEE standard provides support for long channels: For 1 μs and 4 μs preamble lengths, the standard supports radio channel lengths of 300 m and 1200 m, respectively. For implementations that do not require such a long channel, the frame may be designed more efficiently with a tighter bound on the radio channel length. In addition, tighter bounds may prevent certain types of distance reduction attacks. Accordingly, for some use cases, there may be drawbacks in terms of security and link budget.   The IEEE standard only provides for coarse granularity in adjusting link budget per frame phase: The number of synchronization preambles (a pattern of synchronisation symbols) in the preamble, as well as the payload data rate, cannot be adjusted in fine steps.   The IEEE standard may be sub-optimal for short frames in terms of Forward Error Correction (FEC): While the length of the payload data can be scaled from 0 to 127 octets, always 48 parity bits are added. This may not be efficient, especially for short payloads, and may be improved by using a different coding scheme.   Symbol design: When using pulses that comply with FCC/ETSI/ARIB spectral masks (as specified in ETSI EN 302 065-1 (V2.1.1) (11-2016): “Short Range Devices (SRD) using Ultra Wide Band technology (UWB); Harmonised Standard covering the essential requirements of article 3.2 of the Directive 2014/53/EU; Part 1: Requirements for Generic UWB applications”), a peak pulse repetition frequency (PRF) of 499.2 MHz may lead to a ˜2 dB increase of peak power used by a RF power amplifier of an IR-UWB transmitter which may result from constructive inter-pulse interference. This would lead to extra current consumption. In addition, the burst scrambling sequences, as defined in the IEEE standard, may lead to unnecessarily high peak power as measured by FCC/ETSI. Furthermore, the use of Binary Pulse Position Modulation (BPPM) of bursts leads to opportunities for attackers to mount EDLC attacks, especially considering the FEC scheme that is defined. Finally, the use of long bursts at low data rates could lead to a need for a large energy storage capacitance for the RF power amplifier of an IR-UWB transmitter, thereby increasing the system cost.   Long non-optional header: Since the header is of a fixed length and always transmitted using 110 or 850 kbit/s, it will occupy at least 20 μs of air time, which may be undesirable for short frames, resulting in excessive battery drain and reduction of short frame gain (due to regulations, e.g., the ETSI specification mentioned above, the total amount of energy in a short frame must be below a certain value).   The IEEE standard requires a tight crystal tolerance: The reference frequency tolerance is specified to be ±20 ppm, which may mean, in practice, that a sufficiently accurate, and therefore possibly expensive, crystal must be used.   The IEEE standard does not provide for use of multiple antennas: There are no provisions in the existing PHY definition that standardize the use (function definition) of multiple antennas at the transmitter device.       

     As mentioned above, the different aspects of the frame format definition described below may be suited to secure ranging applications and, in particular although not exclusively, suited to automotive Passive Keyless Entry (PKE) applications. In these applications, one or more fobs (transmitter/receiver devices) which might be in proximity to the automobile should be identified and eventually localized. The low frequency (LF) spectrum may be utilized to achieve these tasks in systems termed LF-PKE. In such systems, the localization of the fobs may be based on subsequent measurements of the received signal strength indicator (RSSI) with different antenna orientations. 
     In addition to the proposed frame format, one or more of the sections below propose a UWB secure ranging protocol suitable for secure ranging such as automotive PKE applications. The proposed protocol may overcome none, one or more of the following disadvantages associated with LF-PKE systems:
         Localization in LF-PKE may be based on RSSI measurements which is prone to so-called relay attacks.   On the automobile side for example, large and expensive copper coils may be used as antennas. Substantial currents of approximately 1A may be required to flow for tens of milliseconds to build up required LF fields.   Current Passive Keyless Entry (PKE) protocols require around 70 ms to identify which fobs are within reach, and to perform localization.       

       FIG. 2  shows a first device  201  and a second device  202 . Each device  201 ,  202  may be configured to transmit signaling to the other device (and thus may be considered a transmitter device) or receive signaling from the other device (and thus may be considered a receiver device) through a channel  203 . Each device  201 ,  202  includes one or more antennas  204 ,  205 . Each device  201 ,  202  includes a processing module  206 ,  207  configured to provide for generation of at least part of the signaling transmitted by the device  201 ,  202  and/or configured to provide for processing of at least part of the signaling received by the device  201 ,  202 . It will be appreciated that in some examples separate processing modules  206 ,  207  may be provided for generating the signaling and processing the signaling. 
     Definition of a Full Frame Format 
       FIG. 3  shows an example embodiment of a frame format  300 . The frame format includes a preamble  301 , which comprises a plurality of synchronization symbols  305 , termed “SYNC”, and one or more symbols that define a Start-of-Frame Delimiter  306 , termed “SFD”. The plurality of synchronization symbols may include a repeating pattern of one or more synchronization symbols that are known to the receiver device  201 ,  202  and the transmitter device  201 ,  202 . The plurality of synchronization symbols at the start of the preamble may enable the receiver device to synchronize with an incoming frame  300 . The Start-of-Frame Delimiter  306  may comprise a known pattern of symbols that designate the end of the synchronization symbols  305 . 
     The frame format  300  may include one or more guard intervals  307 A,  307 B,  307 C, which may be absent of transmitted symbols, to provide resistance against interference due to multi-path propagation. 
     The frame format may include a Secure Training Sequence (STS)  308 . The STS  308  is a non-repeatable sequence, such as generated by a Cryptographically Secure Pseudo-Random Number Generator (CSPRNG). The STS  308  may be known by or derivable by both the transmitter device and receiver device but not by an attacker. In one or more examples, a STS reference or “seed” is required to be known by both the transmitting device and the receiving device. The seed can then be applied to respective CSPRNGs such that the same STS can be generated independently by the transmitter device for generating the frame  300  and by the receiver device for processing the frame  300 . The STS may be sufficiently long to avoid guessing attacks and to provide good auto-correlation properties. In one or more examples, to avoid guessing attacks, it may be important to have a very large set of sequences from which the STS is formed. 
     Accordingly, in one or more examples, we provide a processing module for a transmitter device configured to provide for generation of a frame for transmission by the transmitter device to a receiver device, the frame having a first Secure Training Sequence comprising a non-repeating sequence of symbols based on one or more of an agreed symbol sequence and an agreed reference for generation of such a symbol sequence agreed between the transmitter device and receiver device, the Secure Training Sequence provided for channel impulse response estimation and/or verifying channel impulse response estimate determined by the receiver device using a repeating pattern of predetermined synchronisation symbols. 
     A channel estimate based on the synchronisation symbols, which may be defined on a standard, may be considered to be insecure. However, determination or verification of a channel estimate using the secure training sequence which is securely known between the transmitter and receiver devices, may provide for a secure channel impulse response determination. 
     In one or more examples, we provide a processing module for a receiver device configured to provide for processing of a signal comprising at least one frame received by the receiver device from a transmitter device, the processing module configured to:
         derive a secure training sequence for the frame based on predetermined secure information, the secure training sequence comprising a non-repeating pattern of symbols;   identify at least a section of the frame containing a secure training sequence provided by the transmitter device; and   perform cross-correlation between at least a part of the secure training sequence in the frame with the derived secure training sequence for the frame to determine channel estimate information and/or verify channel estimate information determined based on the performance of cross-correlation between at least a part of a synchronization section of the frame comprising a repeating pattern of known synchronization symbols and one or more of the known synchronization symbols.       

     In one or more examples, the processing module may obtain channel estimate information using this method to identify a line-of-sight multipath component of the signal and, based on the line-of-sight component, determine a marker at which to measure the phase of the signal for determining the angle of arrival of the signal, as will be described in more detail below. 
     Thus, the determination of a predetermined correlation between at least a part of the first secure training sequence for the frame and secure training sequence provided by the transmitter, may indicate the determination of a secure channel estimate information comprising the time of arrival of the frame from multiple paths of a channel through which the signal propagates between the transmitter device and the receiver device. The processing module may be configured to use the secure channel estimate information for ranging. The process for use of a channel estimate, in general, for ranging will be familiar to those skilled in the art. 
     In one or more examples, the secure training sequence comprises a non-repeatable sequence of symbols, which may be generated by a Cryptographically Secure Pseudo-Random Number Generator (CSPRNG) based on the predetermined secure information comprising a seed value. 
     In one or more examples, the determination of the channel estimate may include identification of the first tap of the cross correlation having a corresponding tap value having a magnitude above a predetermined CIR threshold. For example, the first tap within the channel estimate may be indicative of a Line of Sight path, which may be used for distance bounding. 
     In one or more examples, the frame comprises a second STS  310 , temporally, spaced from the STS  308 . The second STS  310  may provide for verification of the channel estimate information based on the first STS  308 . 
     The provision of the optional second STS, after a payload section  311 , may be signalled in a physical layer (PHY) header  312 , termed “PHR”, of the payload section  311 . The payload section  311  may further include a physical layer (PHY) service data unit  313 , termed a “PSDU”, to contain arbitrary data transferred between the transmitter device and receiver device  201 ,  202 . The physical layer header  312 , similar to the equivalent part in the IEEE standard may comprise information defining frame properties, such as the data-rate of one or more parts of the frame or the length of the PSDU  313 . 
     In one or more examples, the processing module of the transmitter device is configured to provide for generation of the frame comprising a reference pattern of synchronization symbols known to both the transmitter device and receiver device for synchronization of one or more of the frequency of a carrier wave for modulation by the symbols of the frame and a symbol frequency comprising the frequency at which symbols of the frame are provided. In one or more examples, the processing module of the receiver device is configured to provide for processing of the frame by cross correlation between the reference pattern of the frame and a predetermined reference pattern. 
     In one or more examples, we provide a processing module of the transmitter device configured to provide for generation of a frame with a Data-Rate Selection (DRS) field  314 . The properties of the DRS field will be described in a subsequent section. 
     In one or more examples, the DRS field  314  is adaptively coded using an adaptive coding scheme. The use of an adaptive coding scheme may minimize overhead while providing more flexibility than the IEEE scheme. 
     The DRS  314  and PHR  312  may be omitted if the parameters of the frame defined in those sections are already known by the processing modules  206 ,  207  of the transmitter device and receiver device  201 ,  202 . In one or more examples, the PSDU section  313  may be omitted if no arbitrary data needs to be transmitted. 
     In one or more examples, the processing module provides for modulation of an arbitrary data stream of the transmitter device with one or more symbols of the secure training sequence. In one or more examples, the processing module provides for processing of a section of a received frame from a transmitter device containing arbitrary data modulated with one or more symbols of the secure training sequence, the receiver configured to derive a secure training sequence for the frame based on predetermined secure information, the secure training sequence comprising a non-repeating pattern of symbols and demodulate the arbitrary data using the derived secure training sequence. 
     The IEEE standard provides for spreading of one or more of the PHR  312  and PSDU  313  based on a linear feedback shift register technique (LFSR). In one or more examples, the processing module of the transmitter device  201 ,  202  may provide for spreading of one or more of the physical layer header  312  and the arbitrary data of the PSDU based on a third Secure Training Sequence comprising a non-repeating sequence of symbols based on one or more of an agreed symbol sequence and an agreed reference for generation of such a symbol sequence agreed between the transmitter device and receiver device  201 ,  202 . The third STS may be based on the output from the same Cryptographically Secure Pseudo-Random Number Generator (CSPRNG) as the first STS. 
     Definition of a Reduced Frame Format 
     A reduced frame format is shown in  FIG. 4 . Corresponding reference numerals have been used for like parts. The reduced frame format may be absent one or more of the SYNC portion  305 , the SFD  306  and the DRS  314 . Thus, if synchronization is not required (e.g. if already provided by a previous frame), the SYNC and SFD fields  305 ,  306  in the preamble can be omitted. 
     In one or more examples we provide a transmitter device having a processing module configured to provide for generation of a frame for transmission to a receiver device, wherein based on synchronization between the transmitter device and receiver device being provided by a previously sent frame, the processing module is configured to provide for generation of a subsequent frame without the reference pattern of synchronisation symbols but with the secure training sequence comprising a different non-repeatable sequence of symbols. 
     The STS  308  of the reduced format may present to provide for acquisition comprising one or more of detection of frame, timing synchronization, frequency offset estimation, Channel Impulse Response estimation (e.g. the channel might be changed compared to previous frame exchange). For ranging a secure time of flight (ToF) calculation may have to be done again. 
     The generation of a reduced frame format frame by a processing module of a transmitter and the processing of such a frame by a processing module of a receiver may require a tight frequency and a timing alignment between the devices within ±0.5 T sym , where T sym  defines a preamble symbol period comprising the period of a symbol of the preamble  301  of the previously sent frame. 
     Pilot-Symbol Insertion 
     To allow a tracking of the channel impulse response (e.g. for mobile channels), the PSDU  313  may be interleaved with two or more pilot symbols  501 ,  502 ,  503 , as shown in  FIG. 5 . 
     The pilot symbols  501 ,  502 ,  503  may be considered to separate the PSDU  313  into a plurality of PSDU segments  504 ,  505 . The presence of the pilot symbols in the PSDU  313  may be indicated in the PHR field  312 . In one or more examples, the processing modules of the transmitter and receiver devices have predetermined information to determine the location of the pilot symbols. However, in one or more examples, their location may be indicated in the PHR field  312 . In one or more examples, the pilot symbols are modulated based on the same modulation scheme as the rest of the PSDU  313  but always use a symbol having a predefined modulation. The predefined modulation may be specific to whatever modulation scheme is employed such as BPSK, BPPM-BPSK and QPSK. Accordingly, the pilot symbols may not need to be demodulated. In one or more examples, the pilot symbols are spread (in terms of time and/or frequency) amongst the symbols of the PSDU  313  based on a non-repeating pattern, such as derived from a CSPRNG. Each pilot symbol by itself may not provide optimum auto-correlation properties, and in one or more examples, the second channel estimate information may be based on an average of several of these pilot symbols. 
     Accordingly, following determination of channel impulse response information based on the synchronisation symbols and/or the secure training sequence described above, the processing module of the receiver device may be configured to provide for cross-correlation between parts of a received frame containing pilot symbols, a predetermined pilot symbol pattern defining the location in terms of time in the frame of a plurality of pilot symbols, and one or more known pilot symbols; and based on said cross-correlation determine second channel impulse response information. In one or more examples, the processing module may update its record of the channel impulse response with the second channel impulse response information or combine the channel impulse response information and the second channel impulse response information. The pilot symbols may be of a predetermined pattern known to both the processing module of the transmitter device and the processing module of the receiver device or may be based on a secure training sequence comprising a non-repeating sequence of symbols based on one or more of an agreed symbol sequence and an agreed reference for generation of such a symbol sequence agreed between the transmitter device and receiver device. 
     In one or more examples, we provide a processing module for a receiver device configured to provide for processing of a signal comprising at least one frame received by the receiver device from a transmitter device, the processing module configured to:
         based on the predetermined pilot symbol pattern defining the location in terms of time in the frame of a plurality of pilot symbols, identify the plurality of pilot symbols present in the frame within the received signal;   based on an average of two or more of the identified plurality of pilot symbols, provide for determination of channel estimate information.       

     Thus, in one or more examples, the use of pilot symbols may provide for tracking of the channel estimate at least for frames absent a block comprising a plurality of consecutive symbols of a known pattern for deriving channel estimate information. 
     Accordingly, the apparatus may provide for determination of a first channel estimate information based on a block of synchronization symbols  305  and/or the secure training sequence  308 ,  310  and then, subsequently, provide for determination of channel estimate information based on the first channel estimate information and the channel estimate information that is based on the average of two or more of the identified plurality of pilot symbols. 
     In one or more examples, the predetermined pilot symbol pattern is based on a non-repeatable sequence of symbols, such as generated by a Cryptographically Secure Pseudo-Random Number Generator (CSPRNG) based on a seed value, the seed value or sequence previously agreed between the transmitter device and receiver device. 
     Synchronization Symbols (SYNC) 
     The IEEE standard block of synchronisation symbols SYNC  305  comprises a certain number of synchronisation symbols, which are transmitted consecutively. A single synchronisation symbol is constructed using a certain ternary spreading sequence, taken from a set of available sequences, which are defined in the IEEE standard. During the transmission of the SYNC  305  by a transmitter device, the synchronisation symbol does not change. Accordingly, the receiver device is configured to cross-correlate an unchanging, repeating pattern of synchronisation symbols. This allows the receiver to retrieve timing information, to estimate carrier and symbol frequency offset and, optionally, obtain a channel estimate. The SYNC field  305  including the repeated synchronisation symbols labelled with parameters thereof are shown in  FIG. 6 . 
       FIG. 6  shows the SYNC field  305  in more detail comprising a first synchronisation symbol  601 , a second synchronisation symbol  602  comprising a repeated symbol of the first synchronisation symbol  601 , the symbols continuing to repeat until the total number of synchronisation symbols, N sync    603 , at the end of the SYNC field  305 . The symbol duration T PSYM  is also shown in  FIG. 6 . N sync  and T PSYM  may be important parameters for the design of a UWB frame. In particular, the symbol duration may limit the length of the estimated channel because the length of the individual synchronisation symbols determines the length of the correlator. When the channel length is larger than Tpsym, parts of the CIR will be folded back in the correlator results, i.e. different multipath components will end up at the same correlator bin and may therefore be indistinguishable. The symbol duration may influence allowed crystal tolerance. The number of preamble symbols N sync    603  may determine the SNR of the channel estimate and hence the ranging precision. In addition, the acquisition performance depends on the overall duration of the synchronisation field  305  i.e. N×T PSYM . 
     In the IEEE standard, for one or more applications, the range for the number of preamble symbols is too coarsely grained for the construction of optimal frames, especially for short frame lengths. Therefore, we disclose the following range for the number of preamble symbols:
 
 N   SYNC =1.5 k *16*2 l  with  k∈{ 0,1} and  l∈{ 0,1,2,3,4,5,6,7}  (Eq 1)
 
     Further, we provide a special treatment of the case k=1 and l=7, where N SYNC  is set to 4096 instead of 3072, which the equation Eq 1 suggests. 
     It some situations it may be considered that there is little flexibility in the IEEE standard to match the preamble symbol duration to the channel length. Only two values of N×T PSYM  are provided comprising 1 μs and 4 μs. Thus, this results in a channel lengths of 300 m and 1200 m, respectively. For one or more applications, the expected channel lengths of interest may be significantly shorter. A frame can be designed more efficiently with a tighter bound on the radio channel length. In addition, tighter bounds may prevent certain types of distance reduction attacks. Another advantage of shorter preamble symbols (i.e. shorter T PSYM ) is the improved tolerance to frequency variations of the reference clock. Therefore, we disclose the following approximate preamble symbol durations:
 
 T   PSYM ={0.25μ s, 0.5μ s, 1μ s} 
 
     The symbol duration both depends on the length of the spreading sequence and the peak pulse repetition frequency, which may be set to 124.8 MHz in the present example. To arrive at the specified values for T PSYM , we propose an additional set of length-31, length-63, and length-127 sequences. 
     Alternatively, the ternary sequences specified in the standard can be used, although there are no sequences with a length of 63 specified. Hence, a symbol duration of 0.5 μs is not possible when using the IEEE standard (ternary) sequences. 
     In one or more examples, we propose synchronisation symbols that comprise sequences that use binary symbols instead of ternary symbols. The use of binary symbols is to overcome the loss in transmitted energy caused by the zero symbols in ternary sequences. This may result in a higher mean-PRF (pulse repetition frequency) for a given symbol rate, and therefore in a channel estimate with higher SNR compared to the case when ternary sequences are used. 
     The new set of synchronisation sequences was selected for good cross-correlation and autocorrelation properties. The IEEE standard-compliant sequences are listed in Table 1, Table 2 and are referenced with preamble-IDs 1-24. A new set of binary sequences are listed in Table 3, Table 4, Table 5 and are referenced with preamble-IDs 25-54. Thus, in one or more examples, a processing module for a transmitter may be configured to select one of the synchronisation symbols from tables 3, 4 and 5 and provide for generation of a frame containing said selected synchronisation symbol repeated N sync  times to form a synchronisation field of the frame. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Length-31 ternary preamble codes (optional) 
               
               
                 Length-31 
               
            
           
           
               
               
               
            
               
                   
                 ID 
                 Code 
               
               
                   
                   
               
               
                   
                 1 
                 −0000+0−0+++0+−000+−+++00−+0−00 
               
               
                   
                 2 
                 0+0+−0+0+000−++0−+−−−00+00++000 
               
               
                   
                 3 
                 −+0++000−+−++00++0+00−0000−0+0− 
               
               
                   
                 4 
                 0000+−00−00−++++0+−+000+0−0++0− 
               
               
                   
                 5 
                 −0+−00+++−+000−+0+++0−0+0000−00 
               
               
                   
                 6 
                 ++00+00−−−+−0++−000+0+0−+0+0000 
               
               
                   
                 7 
                 +0000+−0+0+00+000+0++−−−0−+00−+ 
               
               
                   
                 8 
                 0+00−0−0++0000−−+00−+0++−++0+00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Length-127 ternary preamble codes 
               
               
                 Length-127 
               
            
           
           
               
               
            
               
                 ID 
                 Code 
               
               
                   
               
               
                  9 
                 +00+000−0−−00−−+0+0+00−+−++0+0000++−000+00−00−−0−+0+0−−0−+++0++000+−0+00− 
               
               
                   
                 0++−0+++00−+00+0+0−0++−+−−+000000+00000−+0000−0−000−−+ 
               
               
                 10 
                 ++00+0−+00+00+000000−000−00−−000−0+−+0−0+−0−+00000+−00++0−0+00−−+00++− 
               
               
                   
                 +0+−0+0000−0−0−0−++−+0+00+0+000−+0+++000−−−−+++0000+++0−− 
               
               
                 11 
                 −+−0000+00−−00000−0+0+0+−0+00+00+0−00−+++00+000−+0+0−0000+++++−+0+−−0+− 
               
               
                   
                 0++−−0−000+0−+00+0+−−−−000−000000−+00+−0++000++−00++−0−0 
               
               
                 12 
                 −+0++000000−0+0−+0−−−+−++00−+0++0+0+0+000−00−00−+00+−++000−+−0−++0−  
               
               
                   
                 0++++0−00−0++00+0+00++−00+000+−000−0−−+0000−0000−−0+00000+−− 
               
               
                 13 
                 +000−−0000−−++0−++++0−0++0+0−00−+0++00++−0++0+−+0−00+00−0−−000−+−  
               
               
                   
                 00+0000−0++−00000+−0−000000−00−+−++−+000−0+0+0+++−00−−00+0+000 
               
               
                 14 
                 +000++0−0+0−00+−0−+0−00+0+0000+0+−0000++00+0+++++−+0−0+−0−−+0++−−000−−−  
               
               
                   
                 0+000+0+0−+−000000+−+−0−00++000−00+00++−00−−++−00−00000 
               
               
                 15 
                 0+−00+0−000−++0000−−−++000+0+−0−+00−+000−−0−00−−0−+++−+0−++00+−  
               
               
                   
                 ++0+00000+0−0+++−00+00+000−0000+00−−+0++0+0+0−00−0−+−0+0++00000 
               
               
                 16 
                 ++0000+000+00+−−0+−++0−000−−00+−0+00++000+++00+0+0−0−+−0−0+00+00+0++−−−  
               
               
                   
                 −+00++−−+0+−0−−+000000−0−0000−+0−−00+00000+−++000−0−+0+0 
               
               
                 17 
                 +−−000−0−0000+−00000+000000+−−+−++0−0+0+00+−00+++0−++0−00+0−+000++0+++−  
               
               
                   
                 0−−0+0+−0−−00−00+000−++0000+0++−+−00+0+0+−−00−−0−000+00+ 
               
               
                 18 
                 −−0+++0000+++−−−−000+++0+−000+0+00+0+−++−0−0−0−0000+0−+0+−++00+−−00+0−  
               
               
                   
                 0++00−+00000+−0−+0−0+−+0−000−−00−000−000000+00+00+−0+00++ 
               
               
                 19 
                 −0−++00−++000++0−+00+−000000−000−−−−+0+00+−0+000−0−−++0−+0−−+0+−  
               
               
                   
                 +++++0000−0+0+−000+00+++−00−0+00+00+0−+0+0+0−00000−−00+0000−+−0 
               
               
                 20 
                 −−+00000+0−−0000−0000+−−0−000−+000+00−++00+0+00++0−00−0++++0−0++−0−+− 
               
               
                   
                 000++−+00+−00−00−000+0+0+0++0+−00++−+−−−0+−0+0−000000++0+− 
               
               
                 21 
                 +0+00−−00−+++0+0+0−000+−++−+−00−000000−0−+00000−++0−0000+00−+−000−−0− 
               
               
                   
                 00+00−0+−+0++0−++00++0+−00−0+0++0−0++++−0++−−0000−−000+000 
               
               
                 22 
                 0−00−++−−00−++00+00−000++00−−0−+−+000000−+−0+0+000+0−−−000−−++0+−−0−+0−0+− 
               
               
                   
                 +++++0+00++0000−+0+0000+0+00−0+−0−+00−0+0−0++000+0000 
               
               
                 23 
                 000++0+0−+−0−00−0+0+0++0+−−00+0000−000+00+00−+++0−0+00000+0++−+00++− 
               
               
                   
                 0+−+++−−0−−00−0−−000+−00+−0−+0+000++−−−0000++−000−0+00−+000 
               
               
                 24 
                 +0+−0−000++−+00000+00−−0+−0000−0−000000+−−0−+0+−−++00+−−−−++0+00+00+0−0−+− 
               
               
                   
                 0−0+0+00+++000++00+0−+00−−000−0++−+0−−+00+000+0000++0 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Length-31 binary preamble codes (optional) 
               
               
                 Length-31 
               
            
           
           
               
               
               
            
               
                   
                 ID 
                 Code 
               
               
                   
                   
               
               
                   
                 25 
                 −+−+−+++−++−−−+++++−−++−+−−+−−− 
               
               
                   
                 26 
                 −++−−+−−+++++−+++−−−+−+−++−+−−− 
               
               
                   
                 27 
                 −++−+−+−−+−−−+−+++++−++−−+++−−− 
               
               
                   
                 28 
                 −+−−+−++−−+++++−−−++−+++−+−+−−− 
               
               
                   
                 29 
                 −+++−−++−+++++−+−−−+−−+−+−++−−− 
               
               
                   
                 30 
                 −+−++−+−+−−−+++−+++++−−+−−++−−− 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Length-63 binary preamble codes (optional) 
               
               
                 Length-63 
               
            
           
           
               
               
            
               
                 ID 
                 Code 
               
               
                   
               
               
                 31 
                 −++++++−+−+−++−−++−+++−++−+−−+−−+++−−−+−++++−−+−+−−−++−−−−+−−−− 
               
               
                 32 
                 −+−−−−++−−−+−+−−++++−+−−−+++−−+−−+−++−+++−++−−++−+−+−++++++−−−− 
               
               
                 33 
                 −+++−−−−+−−+−−−++−++−−+−++−+−+++−++++−−++−−−+−+−+−−++++++−+−−−− 
               
               
                 34 
                 −++−+++−−++−−−+++−+−++++++−++−+−−−+−−−−+−++−−+−+−+−−+−−++++−−−− 
               
               
                 35 
                 −+−++++++−−+−+−+−−−++−−++++−+++−+−++−+−−++−++−−−+−−+−−−−+++−−−− 
               
               
                 36 
                 −++++−−+−−+−+−+−−++−+−−−−+−−−+−++−++++++−+−+++−−−++−−+++−++−−−− 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Length-127 binary preamble codes 
               
               
                 Length-127 
               
            
           
           
               
               
            
               
                 ID 
                 Code 
               
               
                   
               
               
                 37 
                 −+++++++−+−+−+−−++−−+++−+++−+−−+−++−−−++−++++−++−+−++−++−−+−−+−−−+++−−−−+− 
               
               
                   
                 +++++−−+−+−+++−−++−+−−−+−−++++−−−+−+−−−−++−−−−−+−−−−− 
               
               
                 38 
                 −+−−+−−++−+−−++++−+++−−−−+++++++−−−+++−++−−−+−+−−+−+++++−+−+−+−−−−+−++− 
               
               
                   
                 ++++−−+++−−+−+−++−−++−−−−−++−++−+−+++−+−−−++−−+−−−+−−−−− 
               
               
                 39 
                 −++−−++−++−−−+++−−+++−+−+++−−−−+−−++−−−−−+−+−+−++−+−−+−−+−+−−++++−−+−−−++−+− 
               
               
                   
                 +−−−−+++++++−+++−++−++++−+−−−+−++−−+−+++++−−−+−−−−− 
               
               
                 40 
                 −++−+++++−−−−−+−++−−−−+−−−−+++−+−−−++−−−+−−+++−−+−+−−++−+−−+−++++−+−+++−+++−− 
               
               
                   
                 −++++−−++−−+−−+−−−+−+−+−++−++−−+++++++−++−+−+−−−−− 
               
               
                 41 
                 −++−−−−+−−+−−+++++++−+++++−−−+++−+−+−+−−+−+−++++−+−−++−−+++−−++−+−++−−−+−−− 
               
               
                   
                 +−+++−++−−+−−−−++++−−+−++−+++−−−−−+−+−−−++−++−+−−−−− 
               
               
                 42 
                 −++++−++−−++−−−+−−+−−+++−−+++++−−+−−−−−+−−−++−+−+−+−−++−++−+−−+−+−−−−+−++−−−− 
               
               
                   
                 ++−−+−+++++++−+−++−+++−++++−−−+++−+−−−+−+−+++−−−−− 
               
               
                 43 
                 −+−−−+−−++−−−+−+++−+−++−++−−−−−++−−++−+−+−−+++−−++++−++−+−−−−+−+−+−+++++−+−− 
               
               
                   
                 +−+−−−++−+++−−−+++++++−−−+++−++++−−+−++−−+−−+−−−−− 
               
               
                 44 
                 −+−++−−−−−+++−+−−−−+−−+++−−−++−+−−+−−+−+++−++−+++−−++−++−−+−+−++−+−+++++− 
               
               
                   
                 ++++−−−−++−−−+−−−+−+−−++−−++++−+−+−+−−−+++++++−−+−−−−− 
               
               
                 45 
                 −+++−++−+++++−−+++++++−+−−+−−+−+−+++−+−+−+−−+++−−−++−−+−++−−++−−−+−++++− 
               
               
                   
                 +++−−+−−−+−−−−++−+−++−+−−−++++−−−−−+−−++−++−−−−+−+−−−−− 
               
               
                 46 
                 −+−−+++++++−−−+−+−+−++++−−++−−+−+−−−+−−−++−−−−++++−+++++−+−++−+−+−−++−++−− 
               
               
                   
                 +++−++−+++−+−−+−−+−++−−−+++−−+−−−−+−+++−−−−−++−+−−−−− 
               
               
                 47 
                 −+−−−−−++−−−−+−+−−−++++−−+−−−+−++−−+++−+−+−−+++++−+−−−−+++−−−+−−+−−++−++−+−++− 
               
               
                   
                 ++++−++−−−++−+−−+−+++−+++−−++−−+−+−+−+++++++−−−−− 
               
               
                 48 
                 −+++−+−+−−−+−+++−−−++++−+++−++−+−+++++++−+−−++−−−−++−+−−−−+−+−−+−++−++−−+− 
               
               
                   
                 +−+−++−−−+−−−−−+−−+++++−−+++−−+−−+−−−++−−++−++++−−−−− 
               
               
                 49 
                 −+−+−−−++−++−−+−−−−−++++−−−+−++−+−++−−−−+−−−+−−+++−++++−+−−−++−−++−+−−++−−− 
               
               
                   
                 +++−−+−+−+−+++−+−+−−+−−+−+++++++−−+++++−++−+++−−−−− 
               
               
                 50 
                 −+−+−++−+++++++−−++−++−+−+−+−−−+−−++−−++++−−−+++−+++−+−++++−+−−+−++−−+− 
               
               
                   
                 +−−+++−−+−−−++−−−+−+++−−−−+−−−−++−+−−−−−+++++−++−−−−− 
               
               
                 51 
                 −++−−+−+−−−+++−−−−+++++−−−+−++−++−−++−−−++−+−−++−+++++++−+++−−++++−+−−−−−+− 
               
               
                   
                 +−++++−−+−−+−−−+−−−−+−−+++−++−+−+−+−−+−+++−+−++−−−−− 
               
               
                 52 
                 −+−−−+++++−+−−++−+−−−+−++++−++−+++−+++++++−−−−+−+−++−−−+−−++++−−+−+−−+−−+− 
               
               
                   
                 ++−+−+−+−−−−−++−−+−−−−+++−+−+++−−+++−−−++−++−−++−−−−− 
               
               
                 53 
                 −++−+−+++−+−−+−+−+−++−+++−−+−−−−+−−−+−−+−−++++−+−+−−−−−+−++++−−+++−+++++++− 
               
               
                   
                 ++−−+−++−−−++−−++−++−+−−−+++++−−−−+++−−−+−+−−++−−−−− 
               
               
                 54 
                 −+−++−++−−−+−+−−−−−+++−++−+−−++++−−−−+−−++−+++−+−−−+−−−++−+−++−−+++−−++−−+− 
               
               
                   
                 ++++−+−+−−+−+−+−+++−−−+++++−+++++++−−+−−+−−−−++−−−−− 
               
               
                   
               
            
           
         
       
     
     The binary sequences listed in tables 3, 4 and 5 are configured such that the autocorrelation functions of a repeating pattern of the same sequence are impulse-like, but not perfect in a sense that all out-of-phase components are zero. However, as the resulting error is constant throughout the whole autocorrelation sequence (the sequences are configured such that an autocorrelation sequence thereof has a slight offset in the out-of-phase components), the resulting de-spreading error can easily be corrected. 
     In  FIG. 7  and  FIG. 8 , received samples of UWB-frame  300  after de-spreading with the preamble codes is shown, for both the ternary sequences  700  and the binary sequences  800 . The x-axis shows the index of the received samples and the y-axis shows the cross-correlation between the received signal and the respective one of the synchronisation symbols. Every sharp impulse marks a de-spreaded synchronisation symbol. Comparing the height of these impulses for both figures, there is roughly a 3 dB SNR improvement when using the binary sequence. So, the cross-correlation function determined by the processing module of the receiver using the proposed binary synchronisation symbols in the sync field  305  has a greater SNR  305  than using the ternary sequence synchronisation symbols of the IEEE standard, making synchronisation and channel estimation more reliable. 
     In one or more examples, we provide a processing module for a receiver device configured to provide for processing of a signal comprising at least one frame received by the receiver device from a transmitter device, the processing module configured to:
         perform cross-correlation on at least a part of the received frame comprising a synchronization field of the frame, the synchronization field comprising a plurality of repeating predetermined synchronization symbols, the cross-correlation performed with one of the predetermined synchronization symbols known to the processing module to obtain a cross correlation function thereof;   provide for determination of a corrected cross-correlation function based on application of an error removal function to the cross-correlation function, the error removal function configured to remove the effect of a periodic offset of constant period due to non-zero out-of-phase autocorrelation components of binary code sequences that form the synchronization symbols and up-sampling performed at the transmitter device or the error removal function is configured to remove an offset to the cross-correlation function based on a mean average of said cross-correlation function when up-sampling is not performed at the transmitter device; and   based on the corrected cross-correlation function provide for determination of one or more of:   a) an estimate of a carrier frequency offset compared to a carrier frequency used by the transmitter device;   b) an estimate of the channel impulse response;   c) detecting the presence of a valid signal.       

     In one or more examples, the repeated predetermined synchronization symbols are binary coded. In one or more examples, the repeated predetermined synchronization symbols provide non-zero out-of-phase autocorrelation components. 
     In one or more examples, the (noise-less) auto-correlation result provides a template for subtracting correlation results for the out-of-phase components. This error removal can be done iteratively, starting with the largest cross-correlation result. The iterative process may work as follows: search for the largest cross-correlation result. Using the auto-correlation function it can be estimated which out-of-phase interference is caused to the other cross-correlation results of the cross-correlation function. This estimate is subtracted from the cross-correlation function. Then the 2nd largest cross-correlation result can be searched for etc. 
     In one or more examples, the repeated predetermined synchronization symbols comprise one of the symbols recited in tables 3, 4 and 5 above. 
       FIG. 9  shows a realization of a Channel Impulse Response estimate based on correlating with synchronization symbols comprising a ternary sequence and synchronization symbols comprising binary sequences.  FIG. 9  shows on the x-axis cross-correlation or time index and on the y-axis an example of a cross-correlation results for a given channel realization.  FIG. 9  shows the cross-correlation (de-spreading error)  901  resulting from the use of the IEEE ternary sequences and the cross-correlation (de-spreading error)  902  resulting from the use of the binary sequences defined above with and without the error removal function. 
     At the transmitter device, an oversampling procedure may be used to generate the frame of the UWB waveform from the synchronization symbol sequences. The oversampling leads to the periodic non-perfect autocorrelation properties of the binary sequences and thereby the occurrence of a periodic error in the autocorrelation function. 
     It is this periodic error that is compensated for by the error removal function. 
     Thus, in one or more examples, the error removal function is based on a known up-sampling factor applied by the transmitter device, which may be predetermined. 
     For the error removal function, an estimate of the error caused by the binary codes of the synchronization symbols must be obtained. If no oversampling is performed by the transmitter device, the error caused by the use of binary sequences is visible to the processing module of the receiver device as a constant offset of the cross-correlation function obtained during de-spreading of the synchronization symbols. If oversampling is performed by the transmitter device, the offset visible to the processing module of the receiver device is different for each up-sampling phase, but periodic based on the up-sampling factor. 
     In one or more examples, where no up-sampling is performed by the transmitter device, the error correction function may be based on an estimation of the mean value of the obtained cross-correlation function, which may be subtracted therefrom. In one or more examples, where up-sampling is performed by the transmitter device, an estimation of the mean value is determined for each up-sampling phase, the number of up-sampling phases may be known to the processing module of the receiver device based on predetermined information, the error correction function based on the mean values for each up-sampling phase which may be applied to the cross-correlation function separately for each up-sampling phase, due to the periodicity of the error. 
       FIG. 10  shows an example cross-correlation function  1000  of the received signal impaired by transmission channel  203  with the binary code sequence synchronization symbols and where the transmitter device has provided for up sampling. The part of the signal that yields the channel estimate is shown as section  1001  and a part of the signal in the time-domain that is absent of wanted signal is shown as section  1002 . The section  1002  includes, in the main, only the periodic error that may influence the determination of channel estimate information. Inlay  1003  shows a magnified portion of the graph. In one or more examples, the processing module is configured to determine the part of the cross-correlation function absent the channel estimate information based on a minimum energy measure. 
     In this example the up-sampling factor applied to the signal transmitted by the transmitter device is four. Accordingly, four repeating offset values  1004 ,  1005 ,  1006  and  1007  may be identified. The cross-correlation function is sampled at a rate such that the tap index of consecutive repeating offset values has a separation equal to the up-sampling factor. The sampling rate of the cross-correlation function may be based on information contained in the frame or a previous frame that specifies the up-sampling applied by the transmitter device. The factor delta-L specified in relation to the SHR part of the IEEE standard may fulfill such a purpose. 
     Accordingly, the first offset value  1004  has a value −3.299 for tap index  162  (and periodic taps 162+/−N·UPS, where UPS=up-sampling factor and N=an indexing value). The second offset value  1005  has a value 0.2258 for tap index  163  (and periodic taps 163+/−N·UPS, where UPS=up-sampling factor and N=an indexing value). The third offset value  1006  has a value 4.173 for tap index  164  (and periodic taps 164+/−N·UPS, where UPS=up-sampling factor and N=an indexing value). The fourth offset value  1007  has a value −1.315 for tap index  165  (and periodic taps 165+/−N·UPS, where UPS=up-sampling factor and N=an indexing value). 
     The determination of the error correction function may be as follows and accordingly the processing module of the receiver device may be configured to perform the following method: 
     The cross correlation function may be considered a circular cross-correlation signal R_xy[n], n∈(0,N−1) between received signal y[n] and the one or more synchronization symbols sequence x[n] is obtained by de-spreading the SYNC field  305 . 
     Considering an oversampling factor K, R_xy[n] is down-sampled multiple times with different down-sampling phases k=0, 1, . . . K−1, obtaining K sequences R_xy_k[m], m∈(0,N/K−1) 
     For each down-sampled component R_xy_k[m], a novel estimation procedure for the mean value may be applied, which automatically rejects the wanted signal  1001  from being included in the mean value. 
     The circular convolution EN_k[m] of squared signal R_xy_k 2 [m] and a moving average filter h[m]=1/L with Length L&lt;N/K is obtained as a measure of the energy in the cross-correlation signal. 
     In addition, the circular convolution DC_k[m] of signal R_xy_k[m] and same filter h[m] is obtained as a measure of the mean value in the cross-correlation signal. 
     We search for the index m_s related to the global minimum of EN_k[m] and read out DC_k[m] at this index to obtain an estimate of the error signal err_k of the current phase. 
     This estimate is using mostly samples from noise signal  1002  and is not impaired by the wanted signal  1001 
 
 m _ s=arg min{ EN _ k [ m ]}
 
 err _ k=DC _ k [ m _ s ]
 
     This procedure is done for each downsampling phase k∈(0,K−1). The periodic error signal Err[n] is composed of M=N/K repetitions of the vector [err 1, err_2, . . . , err_k] 
     To complete the error correction, Err[n] is subtracted from R_xy[n]. 
     Start-of-Frame Delimiter (SFD) 
     In the IEEE standard the one or more symbol sequences of the SFD  306  are ternary coded. The use of ternary coding is convenient for non-coherent transmitter/receiver devices for reasons that will be apparent to those skilled in the art. In one or more examples, for a coherent receiver device, the use of ternary coding may not be necessary and may, in practice, cause a 3 dB loss in energy for the same symbol power. This 3 dB loss is caused by half of the symbols being 0 (e.g. the short, 8 symbol IEEE standard SFD looks like this: [0+0−+00−].) 
     The process of SFD detection at the processing module  206 ,  207  of the receiver may be performed only after a signal (e.g. synchronisation symbols of the preamble) is detected and thus its purpose is to distinguish the preceding part of the synchronization (SYNC)  305  against the actual SFD  306 . Accordingly, in one or more examples, it may be advantageous for the SFD to have low cross-correlation with the synchronization symbols of the sync field  305 . 
     According to an aspect of the disclosure, we provide a processing module for a receiver device configured to provide for processing of a signal comprising at least one frame received by the receiver device from a transmitter device, the at least one frame comprising a plurality of repeating predetermined synchronization symbols for providing synchronization between the processing module and the transmitter device and, subsequent to the synchronization symbols, one or more start-of-frame symbols defining the end of the synchronization symbols, the processing module configured to:
         perform cross correlation to obtain a cross-correlation function on
           i) at least a part of the received frame; with   ii) a predetermined modulation sequence used to modulate the one or more start-of-frame symbols and not the synchronization symbols; and   
           determine the location of a start of the one or more start-of-frame symbols based on an increase, above a threshold increase, in the cross-correlation function from a negative cross-correlation with the synchronization symbols to a greater cross-correlation with the part of the received frame containing the start-of-frame symbols.       

     The provision of start-of-frame symbols that are modulated with a particular modulation sequence that negatively cross-correlates with the synchronization symbols may provide for improved detection of the start of the one or more start-of-frame symbols. The effective identification of parts of a frame, comprising a data transmission unit, may be achieved due to a greater distance in correlation value between a peak identifying a correlation with the start-of-frame symbols and a negative cross-correlation with the synchronization to symbols. 
     In one or more embodiments, the receiver device comprises a IR-UWB (Impulse Radio-Ultra-WideBand) receiver. In one or more embodiments the start-of-frame symbols are binary encoded. In one or more embodiments, the start-of-frame symbols comprise synchronization symbols that are binary modulated. 
     In one or more examples, the repeated predetermined synchronization symbols comprise one of the symbols recited in tables 3, 4 and 5 above. 
     In one or more examples, the processing module is configured to identify a peak correlation result  1103  from the cross-correlation and based on a predetermined offset from the peak correlation result, identify the temporal location  1102  of the start and/or end of the one or more start-of-frame symbols in the frame. There are numerous algorithms to identify peaks within a data set which may be known to those skilled in the art. 
     In one or more examples, the one or more start-of-frame symbols defining the end of the synchronization symbols comprise a plurality of (N sym ) synchronization symbols that are modulated by Binary Phase-shift keying based on a modulation sequence selected from one or more of the sequences in the following table, where N sym  comprises the number of repeated synchronization symbols present in the SFD: 
     
       
         
           
               
               
               
               
             
               
                   
                   
               
               
                   
                 ID 
                 Pattern 
                 N sym   
               
               
                   
                   
               
             
            
               
                   
                 0 
                 −−+− 
                  4 
               
               
                   
                 1 
                 −−−−++−+ 
                  8 
               
               
                   
                 2 
                 −−−+−+−−+−++−−−+ 
                  16 
               
               
                   
                 3 
                 −−−−−+−−−+++−−+−−+−+−+−−+−− 
                  32 
               
               
                   
                   
                 ++−− 
                   
               
               
                   
                 4 
                 −−−−−+−−−+−−+−−−−+−++−−−+−+− 
                  64 
               
               
                   
                   
                 +−−−−−−−++−−−++−+−++−−+−−−−− 
                   
               
               
                   
                   
                 ++++−−+− 
                   
               
               
                   
                 5 
                 −−−+−−−−−−−+−+++−−−+−−−−+−−− 
                 128 
               
               
                   
                   
                 +++++−−+−+−−−−−++−−−−−+−− 
                   
               
               
                   
                   
                 ++−+−+−−+−+++++−−−−−+−+−−− 
                   
               
               
                   
                   
                 +−−++−−−+−++−−+−+−++−−−++− 
                   
               
               
                   
                   
                 +−++++−−+−−++−++−+−−++ 
               
               
                   
                   
               
            
           
         
       
     
     These “modulation sequences” indicates how the individual N sym  4, 8, 16, 32 etc synchronization symbols are modulated using BPSK modulation e.g. ID 0 refers to a sequence of length 4: −1 −1 +1 −1. Hence the SFD  306  consists of 4 synchronization symbols that are multiplied with −1 −1 +1 −1 respectively. 
     The IEEE standard defines the SFD field up to a length of 64 synchronisation symbols. For low data-rates (e.g. 106 kBit/s) such an SFD modulated with a faster symbol rate (e.g 1 Msym/s) is challenging to detect reliably. Thus, in one or more examples, the SFD field of 128 symbols is provided. 
     The provision of binary encoded SFDs symbols, the binary modulation sequence having negative cross-correlation with the synchronisation symbols, may be advantageous. In particular, symbols with such a cross-correlation property increases distance (i.e., decreases probability of “false lock”) between the symbols of the SFD field  305  and symbols of the SYNC field  305 . 
     An example of the cross-correlation of one of the binary modulated SFD symbol sequences with the synchronisation symbols of tables 3, 4 or 5 followed by the symbols of the SFD field can be seen in  FIG. 11 . The x-axis shows the sequence symbol index position in the frame and the y-axis shows the magnitude of the cross-correlation. In region  1100  there is the negative cross-correlation with the synchronization symbols. From this it may be determined that the synchronization field is in this region. In region  1101  there is an increased correlation, which may comprise an upward step change in the magnitude of the cross-correlation. Accordingly, the increase at  1102  from the region  1100  to region  1101  may define the end of the repeating synchronization symbols and the start of the start-of-frame symbols. The peak  1103  defines the main peak of the correlation which may designate the detection of the SFD field. This point may be used as a marker, as described below, in a protocol for ranging between lock and key devices. Region  1104  may represent auto-correlation side lobes, as will be appreciated by those skilled in the art. 
     In  FIG. 12  a comparison to an IEEE SFD with twice the number of symbols is given. Corresponding reference numerals with  FIG. 11  have been provided for corresponding regions but beginning 12xx. As can be seen the energy in the main auto-correlation tap/peak  1203  is still the same as the shorter binary SFD used in  FIG. 11 . The cross correlation region  1200  between the SFD and the synchronization symbols is zero when using the SYNC and SFD symbols of the IEEE standard. The cross correlation between the SFD symbol of the frame and SYNC symbols shown in region  1201  varies around zero. In the presence of noise, correlation results in region  1200  and  1201  may be confused with peak  1203  and therefore may point  1202  more difficult to determine. However, in comparison to  FIG. 11 , the negative correlation in regions  1100  and  1101  may make peak  1103  easier to identify over noise and therefore the position of  1102  may be determined therefrom. 
     Thus, the binary SFD symbols provided herein gives a greater distance (in terms of the difference in magnitude between the cross correlation value between the SYNC and SFD fields) which may make it possible to differentiate between SYNC  305  and SFD  306  at lower power levels. Noise can decrease the distance between the correlation results at the point between the synchronisation field and the SFD field and therefore, the suggested symbols may improve noise resilience. 
     Secure Training Sequence (STS) 
     The STS may consists of one non-repeatable CSPRNG generated sequence. In one or more examples, which may reduce reconfiguration minimum, the STS may comprise an integer multiple of an STS segment length. 
     As mentioned previously, the STS  308  does not contain repeated symbols and therein, for clarity, we will refer to parts of STS as “segments”. 
     In one or more examples, the secure training sequence comprising a non-repeating pattern of symbols, the pattern of symbols grouped into segments each segment comprising a same predetermined number of symbols, wherein the processing module of the receiver device is configured to identify the start and/or end of the secure training sequence based on detection of a guard interval comprising an absence of signaling having a length equal to a segment. 
     We disclose three different segment lengths N cps_sts ∈{128, 256, 512} are possible, where only 512 is mandatory. N cps_sts  defines the number of chips per segment. The number of pulses per segment N pps_sts  depend on the mean pulse repetition frequency PRF. We disclose the use of two different mean PRFs of 62.4 MHz, N pps_sts  {16, 32, 64} and 124.8 MHz, N pps_sts  ∈{32, 64, 124}. We disclose that the peak PRF during the transmission of the secure training sequence is the same as during the SHR field  301  (at 124.8 MHz→an up-sampling factor δL=4 is applied at the transmitter device). For each segment N bps_sts  ∈(32, 64, 128) bits need to be generated by the CSPRNG. For a mean PRF=124.8 MHz each bit defines the polarity of one pulse. 
     We disclose that the mapping from bit to polarity is done using the function pol(n)=1−2×bit(n). In one or more examples, the processing module of the transmitter device may be configured to generate signalling based on said mapping and a non-repeatable sequence of bits, such as from the CSPRNG of the transmitter device. In one or more examples, the processing module of the receiver device may be configured to process a signal received from the transmitter device based on said mapping and a non-repeatable sequence of bits for the received signal, such as from the CSPRNG of the receiver device. 
       FIG. 13  shows an example for mapping for CSPRNG output  1301  to STS segment spreading  1302  for this case. The CSPRNG to STS segment spreading is shown for PRF=124.8 MHz and N pps           sts =32. A first segment  1303  and a second segment  1304  of the non-repeating STS symbols is shown. 
     We propose that for a mean PRF=62.4 MHz, the CSPRNG output is split into two bit nibbles  1405 . Each two bit nibble  1405  corresponds to position (first bit) and polarity (second bit) of one pulse. An example is shown in  FIG. 14 , which similar to  FIG. 13  shows the mapping for CSPRNG output  1401  to STS segment spreading  1402  and a first segment  1403  and a second segment  1404 . In  FIG. 14 , CSPRNG to STS segment spreading is shown for PRF=62.4 MHz and N pps           sts =16. 
     In addition to the spreading described above, the segments  1304 ,  1305 ,  1404 ,  1405  may be binary phase shift keying (BPSK) modulated. 
       FIG. 15  shows an example of modulated segments  1503 ,  1504  of a secure training sequence for transmittal  1505  with PRF=124.8 MHz. Accordingly, the processing module of the transmitter device may be configured to provide spreading of the output of a CSPRNG, comprising a stream of non-repeatable n bits by pol(n)=1−2×bit(n) and, optionally, additionally modulate the spread bits on a per segment basis. The modulation may comprise BPSK such that in first modulation state  1507  (shown over segment  1503 ) the polarity of the spread bits  1502  are maintained and in a second modulation state  1508  (shown over segment  1504 ) the polarity of the spread bits  1502  are reversed. 
     In one or more examples, the processing module for a receiver device configured to provide for processing of a signal comprising at least one frame received by the receiver device from a transmitter device, the processing module configured to:
         based on the received frame, provide for demodulation of per segment BPSK modulated secure training sequence followed by dispreading based on a spreading function of pol(n)=1−2×bit(n) to recover the bits n of a secure training sequence, the processing module configured to provide for cross correlation of the recovered secure training sequence with a known secure training sequence of the receiver device.       

     In one or more examples, we provide no additional encoding on top of the BPSK modulation described above. In the reduced frame format, modulation shall only be used on the STS  310  after the payload  311 , to allow the receiver to derive channel estimate information and chip-accurate timing in the STS  308  before the DRS field  314 . 
     The STS  308  modulation may be described by following two formulas: 
     
       
         
           
             
                 
             
             ⁢ 
             
               PRF 
               = 
               
                 62.4 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 MHz 
                 ⁢ 
                 
                   : 
                 
               
             
           
         
       
       
         
           
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 [ 
                 
                   1 
                   - 
                   
                     2 
                     · 
                     
                       m 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
                 ] 
               
               · 
               
                 
                   ∑ 
                   
                     n 
                     = 
                     0 
                   
                   
                     
                       N 
                       pps_sts 
                     
                     - 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     [ 
                     
                       1 
                       - 
                       
                         2 
                         · 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             
                               
                                 k 
                                 · 
                                 
                                   N 
                                   bps_sts 
                                 
                               
                               + 
                               
                                 2 
                                 ⁢ 
                                 n 
                               
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     ] 
                   
                   · 
                   
                     p 
                     ⁡ 
                     
                       ( 
                       
                         t 
                         - 
                         
                           
                             s 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   k 
                                   · 
                                   
                                     N 
                                     bps_sts 
                                   
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   n 
                                 
                               
                               ) 
                             
                           
                           · 
                           
                             T 
                             c 
                           
                         
                         - 
                         
                           2 
                           ⁢ 
                           
                             n 
                             · 
                             δ 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             L 
                             · 
                             
                               T 
                               c 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
       
         
           
             
                 
             
             ⁢ 
             
               RPF 
               = 
               
                 124.8 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 MHz 
                 ⁢ 
                 
                   : 
                 
               
             
           
         
       
       
         
           
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 [ 
                 
                   1 
                   - 
                   
                     2 
                     · 
                     
                       m 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
                 ] 
               
               · 
               
                 
                   ∑ 
                   
                     n 
                     = 
                     0 
                   
                   
                     
                       N 
                       pps_sts 
                     
                     - 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     [ 
                     
                       1 
                       - 
                       
                         2 
                         · 
                         
                           s 
                           ⁡ 
                           
                             ( 
                             
                               
                                 k 
                                 · 
                                 
                                   N 
                                   
                                     p 
                                     ⁢ 
                                     ps_sts 
                                   
                                 
                               
                               + 
                               n 
                             
                             ) 
                           
                         
                       
                     
                     ] 
                   
                   · 
                   
                     p 
                     ⁡ 
                     
                       ( 
                       
                         t 
                         - 
                         
                           
                             n 
                             · 
                             δ 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             L 
                             · 
                             
                               T 
                               c 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     Where m (k)  is the modulated bit for segment k, and s is the CSPRNG generated bit sequence. 
     The maximum number of modulated bits is equal to the number of segments N sts . If less than N sts  are used, then the remaining segments may be modulated with ‘0’. 
     Antenna Switched STS for Angle-of-Arrival Estimation 
     With reference to  FIG. 2 , an angle-of-arrival estimation may be made based on an estimated carrier wave phase difference between demodulated sections of a secure training sequence that is either;
         a) transmitted from at least two separate and spaced antennas  205 ,  206  at the transmitter device  202  and received by at least one antenna  204  at the receiver device  201 ; or   b) transmitted from a single antenna  204  at the transmitter device  201  and received by at least two separate and spaced antennas  205 ,  206  at the receiver device  202 .       

     Thus, depending on the example embodiment set out in (a) and (b) above the devices  201 ,  202  may act as receiver devices or transmitter devices. 
     With reference to  FIG. 16  two example frames are shown comprising a first frame  1601  and a second frame  1602 . The first frame  1601  includes a secure training which is divided into time separated blocks  1603 ,  1604  and, for the second example frame  1602  is divided into time separated blocks  1605 ,  1606 ,  1607  and  1608 . The blocks  1603 - 1608  are separated by guard intervals  1609  comprising an absence of the secure training sequence, which may comprise periods in which no signal is transmitted. 
     The first frame  1601  may be for use in systems that have two antennas at either the transmitter/receiver devices. The second frame  1602  may be for use in systems that have four antennas at either the transmitter/receiver devices. 
     In a first example, we consider the transmitter device  202  having two antennas  205 ,  208  and the receiver device  201  having one antenna  204 . Thus, the processing module  207  at the transmitter may provide for generation of the secure training sequence, such as from a CSPRNG. The secure training sequence is then divided into the blocks  1603   1604  and the processing module provides for transmitting of the blocks from alternate antennas  205   206 . Thus, blocks of the secure training sequence designated STS_A  1603  provided for transmittal from the first antenna  205  with the second antenna  208  not transmitting and the blocks of the secure training sequence designated STS_B  1604  are provided for transmittal from the first antenna  205  with the first antenna  205  not transmitting. 
     Accordingly, in one or more examples, the processing module for a transmitter device configured to provide for generation of a signal comprising at least one frame for transmission by the transmitter device to a receiver device, the processing module configured to provide for time-division of a secure training sequence into blocks, each block provided for transmission from only one of a plurality of antennas of the transmitter device, the processing module configured to provide for transmission of consecutive blocks from different antennas of the plurality of antennas, the secure training sequence comprising a non-repeating sequence of symbols based on one or more of an agreed symbol sequence and an agreed reference for generation of such a symbol sequence agreed between the transmitter device and receiver device. 
     In one or more examples the blocks are time-spaced by a guard interval. 
     In one or more examples, we provide a processing module for a receiver device configured to provide for processing of a signal received by the receiver device from a transmitter device, the signal comprising a secure training sequence divided into a plurality of time spaced blocks, the secure training sequence comprising a non-repeating pattern of symbols, and wherein one of:
         a) at least a first block is transmitted from a first antenna and a second block is transmitted from a second antenna of the transmitter device;   b) at least a first block is received by a first antenna and a second block is received by a second antenna of the receiver device;   wherein the processing module configured to:   based on a plurality of repeating, predetermined synchronization symbols of the signal, provide for determination of a phase of a carrier wave of the signal received at the first antenna of the receiver device or transmitted from a first antenna of the transmitter device;   derive a secure training sequence corresponding to the secure training sequence of the signal based on predetermined secure information known to both the transmitter and receiver device, the secure training sequence comprising a non-repeating pattern of symbols;   perform cross correlation between the first block from the first antenna and a first part of the derived secure training sequence to obtain a first phase marker defining a phase of the signal from the first antenna relative to the determined phase of the carrier wave;   perform cross correlation between the second block from the second antenna and a second part of the derived secure training sequence to obtain a second phase marker defining a phase of the signal from the second antenna relative to the determined phase of the carrier wave;   based on the first phase marker and the second phase marker defining a phase difference of the signal between the first and second antennas and a known spacing of the first antenna relative to the second antenna, determine an angle of arrival of the signal relative to the receiver device.       

     In one or more examples, the first and/or second phase markers are derived based on channel estimate information of the cross correlation that defines a Line-of-Sight multipath component. 
     Thus, the synchronisation symbols and/or a secure training sequence may be used to provide synchronisation between a particular antenna pair of the transmitter device and the receiver device. The synchronisation may provide for determination of a carrier frequency offset of the signal relative to a local frequency reference and/or a phase offset of the signal relative to the local frequency reference. The processing module of the receiver device expects that the second block is transmitted by or received by a specific different antenna. As the second antenna has a different physical position to the first antenna and the signalling provided to the antennas is provided by the same processing module of the transmitter and is therefore relative to the same local frequency reference at the transmitter, a phase difference may be determined. The phase difference in the carrier wave between the parts of the secure training sequence from one antenna compared to the parts of secure training sequence from the other antenna, can be used to determine an angle of arrival based on the frequency of the carrier wave and the known positions of the antennas. 
     For time interleaved AoA measurement the STS can be divided into 2 (STS_A, STS_B) or 4 streams (STS_A, STS_B, STS_C, STS_D) provided to separate 2 or 4 antennas respectively. The antenna separation can be provided on transmitter device or receiver device side. Thus, a single antenna may transmit time spaced STS blocks which are received by two antennas or two antennas may transmit time spaced separate parts of the STS, which is received by a single antenna. For the four streams, there may be two antennas at the transmitter and two antennas at the receiver. The transmitter configured to transmit two of the four blocks from a first antenna and the other two of the four blocks from the other antenna. A block from each transmit antenna is then received at each receiver antenna, and a similar process may be followed. 
     In one or more examples, for time-interleaving the STS is divided into 2 d     sts    blocks, where each block is 2 k     sts     +3−d     sts    segments longs. A segment is defined in the secure training sequence section above. In one or more examples, for 2 antenna streams, the minimum d sts =1 and for 4 streams d sts =2. 
     In one or more examples, only these minimum interleaving options are mandatory. All other block-sizes, down to only 1 segment may be optional. In one or more examples, the time spaced blocks are separated by a guard interval of one segment in length where the segment may comprise a predetermined length. 
     In one or more examples, the secure training sequence may be divided into two, three, four, five, or any plurality of time spaced blocks and each block may be configured to be transmitted by or received by a corresponding number of antennas. Accordingly, the phase difference between different pairs or groups of the antennas may be derived and the phase difference may thus be indicative of the angle of arrival of the signal to those pairs or groups of antennas. Subsets of the plurality of antennas may be arranged along different axes to determine a direction of arrival of the signal. 
       FIG. 32  defines example relative positions in the horizontal plane of first and second antennas A and B  3201 ,  3202  associated with corresponding Secure Training Sequences in the radio frame. Positions are defined in reference to the intended (primary) direction of radiation of the device. 
       FIG. 33  defines example relative positions along the vertical axis of Antennas C and D  3301 ,  3302  associated with corresponding Secure Training Sequences in the radio frame. Positions are defined in reference to the intended (primary) direction of radiation of the device. 
     It will be appreciated that the phase difference between the phase markers of the secure training sequence blocks may be indicative of the extra distance one signal is required to travel from/to the first and second antennas. A determination of the angle of arrival may be determined based on trigonometry, the frequency of the signal and the known physical configuration of the antennas. A person skilled in the art will be familiar with such calculations. 
     Data-Rate Selection (DRS) 
     Compared to the IEEE standard we disclose a means for more flexible and more robust data-rate selection in the DRS field  314  of the frame  300 . An example form of the DRS field  314  is shown in  FIG. 17 . The data rate selection is based on a k-out-of-N encoding with adaptive symbol lengths. Each symbol is spread in the same manner as the payload  311  and BPSK modulated with decreasing symbol period lengths. If Binary Pulse Position Modulation and Binary Phase Shift Keying (BPPM-BPSK) is used for the payload, the position bit is always set to 0 and only the polarity information is used. The first k drs  symbols  1701  of the DRS field  314  correspond to the slowest supported symbol rate (e.g 122 kSym/s or 4096 chips/symbol). The next k drs  symbols  1702  are modulated with twice the symbol rate (e.g 244 kSym/s) and so on. This continues until the last k drs  symbols  1703  which are modulated with the highest symbol-rate (124.8 MSym/s). The symbol rates may be selected from a predetermined set of symbol rates. Only one k drs  symbol data-rate segment must be set to ‘1’. In  FIG. 17  the DRS field  314  is shown. It consists of several symbol-rate selector elements  1701 ,  1702 ,  1703 . All elements except one are modulated with a symbol “0”. To indicate which symbol-rate is used after the DRS field, the corresponding symbol-rate selector element  1701 ,  1702 ,  1703  is modulated with a symbol “1”. The segment  1701 ,  1702 ,  1703  modulated with symbol “1” that appears first in the DRS field, may define what data-rate is used for the payload  311 . The DRS field  314  may include a predetermined termination pattern  1704  at its end. 
     By default, the maximum symbol period may comprise max(T sym )=4096 chips and a repetition factor k drs =4. In the default case the DRS may occupy 32768 chips or 65 μs. This mode supports dynamic selection of symbol-rates from 122 kSym/s up to 124.8 Msym/s. For less overhead for use-cases with fast symbol-rate, the minimum selectable symbol-period can be defined to be any power of 2 between 4 and 4096 chips. 
     Furthermore, the repetition factor k drs  may be changed to the value 1, 2 or 4. e.g. for max(T sym )=512 (975 kSym/s) and k drs =2, the DRS field is 2048 chips or 4 μs long. 
     Packet Header (PHR) 
     The packet header  312 , in one or more examples, is encoded via k=7 convolutional code only. Six tailing bits may be added for termination before the PSDU  313  starts again from the all-zero state. Thus, the initial starting data for convolutional encoding of the PSDU  313  will be zero symbols. An example encoder  1800  is shown in  FIG. 18 , the delay elements  1801 - 1806  receive the data to be encoded at input  1807  and may initially contain all binary zeros (defining an all zero-state). 
     In one or more examples the processing module at the receiver device or at the transmitter device may provide for generation of a frame with one of the following 3 different variants for the PHR: 
     1) No PHR
         Header  312  is not part of the frame  300 . The PSDU  313  therefore follows the DRS field  314  directly.       

     2) Short PHR
         The form of the short PHR is shown in the table below in which;
           a. Frame length: Specifies a number of decoded bytes in the PSDU  313 .   b. d sub : Sub symbol division. One symbol is divided into 4 d     sub    sub symbols   c. RS: defines use of reed Solomon encoding where 0— No Reed Solomon is used in PSDU  313 ; 1—Reed Solomon used in PSDU  313 .   d. r sts : Defines the segment length of the secure training sequence.
 
 N   cps_sts =128·2 r     sts    
   e. k sts : The STS length specifier is given in N sts =16×2 k     sts     −1  STS segment periods. For k sts =0 no STS field is sent after the PSDU. E.g. for r sts =1 and k sts =3, the STS is 16384 chips long.   
               

     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Bit 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 0 
                 Frame Length [Bytes] 
                 d sub   
                 RS 
                 r sts   
                 k sts   
               
               
                   
               
            
           
         
       
     
     3) Extended PHR (Optional) 
     The form of the optional extended PHR is shown in the table below; Contains extended frame length specifier and additional pilot spacing specifier.
         a. p r : The number of consecutive pilot symbols is given with the factor 2 P     r   .   b. p s : The pilot spacing is given with 2 P     s     +P     r     −1  symbols. p s =0 does not insert pilot tones.       

     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                   
               
             
            
               
                 Bit 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 Frame Length [Bytes] 
                 d sub   
                 RS 
                 r sts   
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Bit 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
                 23 
               
               
                   
                   
               
            
           
           
               
               
               
            
               
                 k sts   
                 p r   
                 p s   
               
               
                   
               
            
           
         
       
     
     The provision of pilot symbols in the PDSU  311  may be defined in the PHR  312 . An example for p r =1, p s =2 is given in the table below, which represents a part of the PDSU in accordance with the pilot symbol insertion parameters pr and p s . 
                         
Inner Encoding (Convolutional)
 
     In one or more examples, we provide a processing module for a transmitter device configured to provide for generation of a signal comprising at least one frame for transmission by the transmitter device to a receiver device, the processing module configured to: provide for encoding of one or more of a physical layer header and a PSDU with convolutional encoding, the physical layer header defining one or more frame properties, such as the data-rate of one or more parts of the frame or the length of the PSDU. The PSDU may contain arbitrary information to be exchanged between transmitter and receiver devices. 
     In contrast to that defined in the IEEE standard, a convolutional code with a constraint length, K, of 7 may be used. In a preferred embodiment, generator polynomials G=(133,171) are used. This notation is an octal representation of the outputs that are used in the encoder to produce 2 code bits for every input bit. 
     In  FIG. 18 , a diagrammatic illustration of the encoder  1800  is shown. 
     In this example, after encoding the PHR, the encoder  1800  is configured to an all-zero state by appending 6 tailbits to the bits of the PHR  312 , equal to the number of delay elements of the convolutional encoder  1800 . Thus, in one or more examples, the convolutional encoding of the PHR and the PDSU is separated into two, independent convolutionally encoded sections, one for the PHR and one for the PDSU, by the provision of the tailbits. 
     The termination of the trellis of the encoder provides for an independent decoding of the PHR  312  and the PSDU  313 . Independent decoding of the PHR  312  and PSDU fields  313  means that because of the trellis termination, the Viterbi decoder at a processing module of the receiver device can be reset after the PHR is decoded and no decoder state from the PHR has to be preserved for proper decoding of the PSDU. 
     The IEEE standard does not specify an operation in which the encoder is forced to the all-zero state, such that independent decoding of PHR and PSDU can only be done at the expense of a poor decoding performance of the PHR. The larger constraint length of the convolutional code 7 (versus K=3 in the IEEE standard) proposed provides a stronger protection than the protection used in the IEEE standard, where the concatenation of Single Error Correction Double Error Detection (SECDED) block-code of length 19 with a constraint length K=3 convolutional code is prescribed. Such a concatenated scheme can be decoded sequentially or as a joint coding scheme. In the sequential scheme, first the convolutional code is decoded by a Viterbi decoder followed by SECDED decoder. Because of a lack of termination, by way of the tailbits, in the encoder after the PHR, the decoding depth of the Viterbi decoder delays the availability of SECDED coded bits to the SECDED decoder. In a joint coding scheme the properties of the convolutional code and the SECDED code are exploited simultaneously leading to optimal decoding performance at the expense of a decoder with state complexity  256 . In one or more examples, the processing module is configured to use a K=7 convolutional code, which requires a decoder with state complexity  64 . 
     As an example, the protection of a 13 bits PHR (as used in IEEE standard) using both the IEEE standard schemes and the scheme described above is demonstrated in  FIG. 19 .  FIG. 19  shows word error rate versus Es/N0. Es/N0 is a metric for the SNR. Es represents symbol energy, NO represents spectral density of the noise and therefore Es/N0 is a measure for the signal-to-noise ratio. Plot  1901  shows the IEEE standard scheme comprising sequential Viterbi with K=3 and HD SECED. Plot  1902  shows the scheme proposed herein comprising Viterbi only with K=7. Plot  1903  shows the IEEE standard scheme of joint Viterbi and SECED. The proprietary PHR protection has a similar protection level as the most advanced standard compliant PHR decoder, while its complexity is only ¼. Moreover, compared to the sequential decoding of the standard scheme an SNR gain of more than 1.5 dB is achieved. 
     The PSDU is protected with the same K=7 convolutional code. Termination of the encoder with 6 tailbits at the end of the PHR bits takes care that the encoder at the beginning of the PSDU starts in the all-zero state. At the end of the PSDU, the encoder may again be terminated to the all-zero state with 6 tailbits. 
     In  FIG. 20  the performance difference in terms of bit error rate (BER) between the IEEE convolutional code  2001  and the proprietary convolutional code  2002  is shown. Also the performance in terms of packet/frame error rate (PER) is shown in which plot  2003  shows the proposed scheme. Plot  2004  shows the proposed scheme with optional outer encoding (Reed-Solomon) and plot  2005  shows the IEEE standard scheme. 
     Outer Encoding (Block) 
     In contrast to the IEEE standard, we propose the use of an optional Reed-Solomon (RS) outer code. For small payloads (e.g. 20 bytes), the K=7 convolutional code described above provides sufficient error correction protection. The use of the optional RS coder may be signalled in the PHR  312 . In one or more examples, the RS code used may be as defined in the IEEE standard, i.e. a RS code with parameters [63,55,9] over GF(2 6 ). When the PSDU size exceeds 55 “6-bit” symbols (i.e. 330 bits or 41.25 bytes), several codewords are sent sequentially. 
       FIG. 21  shows an example of a diagrammatic depiction of the encoding scheme for the PSDU  313 . The input bit stream  2101  may be optionally encoded with the Reed-Solomon coding shown at  2102 . The parameters of the Reed-Solomon coding may comprise [k+8,k,9]. Thus, K symbols, each consisting of 6 bits are encoded by a Reed-Solomon encoder. The Reed-Solomon encoder adds 8 parity symbols (again each 6 bits). In total the encoder provides a codeword of k+8 symbols. Every different pair of codewords will differ in at least 9 symbol positions, which defines the distance of the code. Accordingly, [k+8,k,9] represents the parameters of a code as [n,k,d]: n being the length of the codewords, k the number of information or payload symbols per codeword and d the minimum distance between 2 different codewords. The stream is then encoded with the convolutional encoder  1800  shown in  FIG. 18 . The code bits g 0 (n) and g 1 (n) are modulated with one of BPPM-BPSK, BPSK or QPSK modulation at  2103 . The mapping from codebits to modulation symbols is discussed in the subsequent section. 
     Modulation 
     After convolutional encoding the processing module for the transmitter may provide for modulation of the coded bits. The processing module may use one of the following three modulation methods:
         BPPM-BPSK   BPSK   QPSK       

     Accordingly, we provide a processing module for a receiver device configured to provide for processing of a signal received by the receiver device from a transmitter device, the processing module configured to:
         demodulate the signal, optionally using one of the following modulation methods
           BPPM-BPSK   BPSK   QPSK   
           perform convolutional decoding.       

     The mapping from coded bits at the output of the convolutional encoder  2102  to modulation symbols provided at the output of modulator  2103  may be performed such that Euclidean distance on the channel  203  high, such as above a threshold, or maximized. 
     The three modulation schemes will now be described in turn. 
     BPPM-BPSK 
     With BPPM-BPSK modulation, the convolutional encoding described above provides two code bits g 0  and g 1  for modulation in to one BPPM-BPSK symbol. In this example, one code bit determines the position of the BPSK symbol and the second code bit determines the phase of the BPSK symbol. 
     A preferred mapping can be realized by using (g 0 +g 1 ) mod 2, equivalent to (g 1   (k) ⊕g 0   (k) ) used in the symbol construction equation, as the position bit and g 1  as the polarity bit. With this mapping the Euclidean distance between code sequences may be maximized. 
     The table below shows the code bits g 0  and g 1  based on convolutional encoding of each bit of an input bitstream. Based on the code bits the table shows the determination of a position bit and a polarity bit. Based on the position bit and the polarity bit, the table shows the mapping to a BPPM-BPSK symbol comprising a burst of pulses that are modulated using (binary) position and (binary) phase of the magnitude and polarity defined, in which E s  comprises the signal energy of a BPPM-BPSK symbol. 
     
       
         
           
               
               
               
               
               
               
             
               
                   
               
               
                   
                   
                 Position bit =  
                 Polaritybit =  
                 BPPM-BPSK 
                 Euclidean 
               
               
                 g 0   
                 g 1   
                 g 0  + g 1  mod 2 
                 g 1   
                 symbol 
                 distance 
               
               
                   
               
             
            
               
                 0 
                 0 
                 0 
                 0 
                 (+√E s , 0) 
                 2√E s   
               
               
                 1 
                 1 
                 0 
                 1 
                 (−√E s , 0) 
                   
               
               
                 0 
                 1 
                 1 
                 1 
                 (0, −√E s ) 
                 2√E s   
               
               
                 1 
                 0 
                 1 
                 0 
                 (0, √E s ) 
               
               
                   
               
            
           
         
       
     
     In one or more examples, we provide a processing module for a transmitter device configured to provide for generation of a signal comprising at least one frame for transmission by the transmitter device to a receiver device, the processing module configured to provide for modulation of an input bitstream forming at least part of the frame, the processing module configured to;
         provide for convolutional encoding of an input bitstream, the convolutional encoding providing for generation of a first code bit g 0  and a second code bit g 1  for each bit of the input bitstream;   determine a position bit based on the equation g 0 +g 1  mod 2;   determine a polarity bit based on the second code bit g 1 ;   determine a BPPM-BPSK symbol based on the mapping;       

     
       
         
           
               
               
               
               
             
               
                   
                   
               
               
                   
                 Position 
                 Polarity 
                 BPPM-BPSK 
               
               
                   
                 bit 
                 bit 
                 symbol 
               
               
                   
                   
               
             
            
               
                   
                 0 
                 0 
                 (+√E s , 0) 
               
               
                   
                 0 
                 1 
                 (−√E s , 0) 
               
               
                   
                 1 
                 1 
                 (0, −√E s ) 
               
               
                   
                 1 
                 0 
                 (0, √E s ) 
               
               
                   
                   
               
            
           
         
       
     
     In one or more examples, the convolutional encoding has a constraint length of 7. 
     In one or more examples, the input bitstream is encoded with a Reed-Solomon code prior to convolutional encoding. 
     In one or more examples, the input bitstream represents at least part of the frame. In one or more examples, the input bitstream represents arbitrary data to be exchanged between the transmitter device and the receiver device. 
     In one or more examples, the convolutional encoding is defined as follows;
         denoting the input bit stream for encoding with x(n) then first code bit g 0 ( n )=x(n)+x(n−2)+x(n−3)+x(n−5)+x(n−6) mod 2, and second code bit g 1 ( n )=x(n)+x(n−1)+x(n−2)+x(n−3)+x(n−6) mod 2. x(n) being input bit of the input bitstream at time n, having a value 0 or 1.       

     In one or more examples, we provide a processing module for a receiver device configured to provide for processing of a signal comprising at least one frame received by the receiver device from a transmitter device, the processing module configured to:
         provide for identification of BPPM-BPSK symbols in the signal, the BPPM-BPSK symbols selected from (+√E s ,0), (−√E s ,0), (0, −√E s ) and (0, √E s );   provide for demodulation of each BPPM-BPSK symbols to obtain two code bits comprising g 0  and g 1  based on the mapping;       

     
       
         
           
               
               
               
               
             
               
                   
                   
               
               
                   
                 BPPM-BPSK 
                   
                   
               
               
                   
                 symbol 
                 g0 
                 g1 
               
               
                   
                   
               
             
            
               
                   
                 (+√E s , 0) 
                 0 
                 0 
               
               
                   
                 (−√E s , 0) 
                 0 
                 1 
               
               
                   
                 (0, −√E s ) 
                 1 
                 1 
               
               
                   
                 (0, √E s ) 
                 1 
                 0 
               
               
                   
                   
               
            
           
         
       
         
         
           
             provide for determination of an output bitstream based on decoding of the code bits based on a convolutional code. 
           
         
       
    
     In one or more examples, the convolutional code has a constraint length of 7. 
     In one or more examples, the processing module is further configured to provide for determination of the output bitstream based on decoding a Reed-Solomon code post decoding the convolutional code. 
     In one or more examples, the output bitstream represents at least part of the frame. In one or more examples, the output bitstream represents arbitrary data to be exchanged between the transmitter device and the receiver device. 
     In one or more examples, the code bits g 0 +g 1  may be used to define the position of the burst and the code bits g 0  for the polarity. 
     This mapping may be considered optimum based on a corresponding encoding trellis of the code. It will be appreciated that an encoder trellis is a graphical representation that indicates with arrows which encoder states can be reached as function of the current encoder state and the value of the input bit. Along the arrows one can place labels designating the value of the input bit and the values for the corresponding code bits g 0  and g 1 . 
     For the example K=7 encoder, there are 64 states and for each state there are 2 possible information bits: 0 or 1. One trellis section consists of the 64 possible starting states, 2 outgoing edges from each state and 64 next states. A trellis section can be decomposed into 32 butterfly sections. A butterfly section  2200  of the encoder/decoder trellis is shown in  FIG. 22 . In this drawing s x  represents a 5-tuple of bits and together with 0 or 1 a 6-tuple is formed representing an encoder (based on the six positions labelled “D” to receive the input stream of  FIG. 18 ) or decoder state. 
     Being in state (s x ,0), the encoder arrives at state (0,s x ) when an input bit with value 0 is provided to the encoder. However, when the encoder is in state (s x ,1) it also ends up in state (0,s x ) when an input bit with value 0 is provided. Hence, in the Viterbi decoder two paths merge in state (0,s x ). Similarly two paths merge in state (1,s x ). Both end states (0,s x ) and (1,s x ) have the same originating states (s x ,0) and (s x ,1). Along the edges in the butterfly, three values are indicated. Before the slash the value of the input bit is shown. After the slash the values of the code bits g 0  and g 1  are represented by a,b (a,b being 0 or 1). In case the transition from state (s x ,0) to (0,s x ) (input bit should have value 0) leads to code bit with values g 0 =a and g 1 =b, the transition from state (s x ,0) to (1,s x ) (input bit should have value 1) should have code bits with values g 0 =ā and g 1 = b  (not a and not b, respectively). Hence the code bits have opposite values compared to the other branch. Similarly, the branches that merge into one state will have opposite code bit values. Since a Viterbi decoder accumulates Euclidean distances and make decisions on base of accumulated distances, it is important to have an as large as possible accumulation of Euclidean distance. With the bit-mapping from code bits to modulation symbols as shown in the table above, the Euclidean distance between two outgoing branches or to merging branches is 2√E s . Choosing for the position bit g 0 , and the polarity bit equal to g 1  leads for the same transitions to an Euclidean distance of only √2√E S . 
     BPSK 
     In case of BPSK mapping, the code bits g 0  and g 1  must be distributed over 2 BPSK symbols. In this example, no mapping is required to maximize the Euclidean distance. Code bits g 0  can be mapped to the even BSPK symbols and code bits g 1  to the odd BPSK symbols. 
     QPSK 
     In one or more examples a Gray mapping is used for mapping the code bits g 0  and g 1  to the QPSK symbols. It should be noted that the constellation points “00” and “11” have maximum Euclidean distance. This also holds for “01” and “10”. In that case code bits can be mapped directly on the QPSK symbols. 
     It may be noted that a non-Gray mapping of QPSK has a similar constellation as a BPPM-BPSK constellation (in-phase corresponds with 1 st  position, quadrature phase corresponds with 2 nd  position). 
       FIG. 23  illustrates QPSK modulation Gray mapping  2300 , as will be familiar to those skilled in the art, for mapping code bit combinations g 0 g 1 =00, 11, 01 and 10 to I and Q components. 
     Since the modulation is based on bursts of pulses (also termed chips) and that within the burst only BPSK modulation is applied, the QPSK modulation may be realized with a semi-full quadrature modulator  2400 , as shown in  FIG. 24 . The modulator  2400  receives an input stream  2405  and provides a modulated output to a power amplifier  2401  and on to the antenna  204 ,  205 ,  208 . 
     In  FIG. 24 , the concept of the QPSK modulator is illustrated. The BPSK modulation is realized with a +1/−1 multiplier, where the +/−1 value is derived from the code bit according to the formula (1−2g 0 ). In one or more examples, the selection between the inphase (I, cos ω c t) carrier and the quadrature carrier (Q, sin ω c t) is done with a switch  2402  that is controlled by the Boolean g 0 +g 1  mod 2, labelled  2403 . The in phase carrier and the quadrature carrier are different phases of a carrier frequency. In a clock generation unit (not shown) a carrier frequency 4ω c  is realised and after a frequency divider by 4, 4 phases of the carrier with frequency ω c  are available. For the QPSK modulator  2400 , the 2 phases that have a phase difference of π/2 are selected for modulating the signal to an RF frequency fc (ω c =2πf c ). 
     Spreading 
     Dummy Pulse Insertion 
     A pulse stream comprising a plurality of pulses may be representative of data for transmission as at least part of the at least one frame. Each pulse of the pulse stream may have one of two states comprising a positive polarity and a negative polarity, the polarity of the pulse defining the phase with which a carrier wave is modulated during the pulse for transmission by the transmitter device. The receipt, by the transmitter device, of a pulse stream containing many consecutive pulses of the same polarity may induce a DC offset in the transmitter device. 
     Accordingly, we disclose a processing module  206 ,  207  for a transmitter device  201 ,  202  configured to provide for generation of a signal comprising at least one frame for transmission by the transmitter device to a receiver device, the processing module configured to provide for processing of an input pulse stream  2500 , the input pulse stream comprising a stream of pulses e.g.  2501 ,  2502  representative of data of at least part of the at least one frame, to provide for generation of an output pulse stream for transmitting to the receiver device as part of the signal, each pulse of the pulse streams having one of two states comprising a positive polarity e.g. pulse  2501  and a negative polarity e.g. pulse  2502 . 
     The processing module  206 ,  207  may be configured to;
         divide the input pulse stream into consecutive groups  2503  of pulses, each group of pulses containing the same number of pulses. In this example each group comprises three pulses (those outside the dashed line box).       

     The processing module  206 ,  207  may be configured to provide for insertion of a dummy pulse, those pulses in box  2504 , for each of the example groups of pulses  2505 ,  2506 ,  2507 ,  2508 . In particular, based on determination that the first two or more consecutive pulses of the group have the same polarity (shown in example groups  2505  and  2506 ) the processing module may be configured to provide for addition of at least one dummy pulse to the group directly after the first two or more consecutive pulses. Accordingly, the dummy pulse is inserted between the 2 nd  and 3′ pulse of the group of three pulses. Considering the example groups  2505 ,  2506 , the at least one dummy pulse has an opposite polarity to the first two or more consecutive pulses. Thus, in example group  2505  the first two pulses are positive and thus the dummy pulse provided is negative. In example group  2506 , the first two pulses are negative and the dummy pulse provided is positive. The output bit stream provided by the processing module therefore includes the consecutive groups of pulses including the added dummy pulses. 
     For example groups  2507  and  2508 , the first two pulses in the group are of an opposite polarity. In case of unequal polarities of the first two pulses, two strategies can be followed. 
     Strategy 1: To reduce measured peak power as much as possible, the dummy pulse is set to polarity opposite of the pulse preceding it. Thus, the processing module may be configured to provide for addition of at least one dummy pulse to the group directly after the first two or more consecutive pulses, the at least one dummy pulse having a polarity opposite to a final pulse in the first two or more consecutive pulses. 
     Strategy 2: To reduce DC content in the frame, the dummy pulse can be set opposite of the accumulated DC value (possibly only beyond a certain DC threshold, e.g., 4 pulses offset, following the other strategy otherwise or making the pulse amplitude zero otherwise). Thus, the processing module may be configured to provide for addition of at least one dummy pulse to the group directly after the first two or more consecutive pulses, the at least one dummy pulse having a polarity opposite to an aggregate polarity of all the (three) pulses in the group of pulses, wherein the number of pulses in the group is odd. 
     While in this example the number of pulses per group is three, the group size could be larger. Accordingly, a different number of consecutive pulses of the same polarity may result in the addition of more than one dummy pulse (consecutively arranged or not). 
     In one or more examples, all of the groups  2505 - 2508  have a dummy pulse inserted therein but in some examples, the provision of a dummy pulse may be conditional on the group having two consecutive pulses of the same polarity. 
     For QPSK modulation, two such bit streams are implemented, each operating across an axis in the complex plane. Thus, the input bit stream may comprise a first input bit stream and a second input bit stream, the first input bit stream representing in-phase components for Quadrature Phase Shift Keying modulation and the second input bit stream representing quadrature-phase components for Quadrature Phase Shift Keying modulation. 
     With reference to  FIG. 25A , we also disclose a method of generation, from an input pulse stream, of an output pulse stream comprising a plurality of pulses for controlling the phase with which a carrier wave is modulated during each pulse for transmission by a transmitter device, the input pulse stream comprising a stream of pulses representative of data of at least part of at least one frame for transmitting as part of a signal by the transmitter device, each pulse of the pulse streams having one of two states comprising a positive polarity and a negative polarity, the polarity of the pulse defining the phase with which the carrier wave is modulated; the method comprising: 
     a first step  2550  comprising dividing the input pulse stream into consecutive groups of pulses, each group of pulses containing the same number of pulses, where the number of pulses comprises at least three; and a second step  2551 , for each group of pulses, based on determination that the first two or more consecutive pulses of the group have the same polarity, providing for addition of at least one dummy pulse to the group directly after the first two or more consecutive pulses, the at least one dummy pulse having an opposite polarity to the first two or more consecutive pulses, the groups of pulses, including the added dummy pulses, comprising the output pulse stream. 
     The method may be embodied as computer program code for execution by a processing module of the transmitter device. The code may be provided as a firmware or software, such as on a memory of the processing module. 
     Turning to the receiver device, the dummy pulses may require removal prior to further processing of the bit stream. Accordingly, the processing module at the receiver device may be configured to;
         divide the input pulse stream into consecutive groups of pulses, each group of pulses containing the same number of pulses, where the number of pulses comprises at least three and the position of the groups in the input bit stream determined based on predetermined data; and   for each group of pulses, based on determination that the first two or more consecutive pulses of the group have the same polarity, provide for discarding of one or more dummy pulses in the group directly after the first two or more consecutive pulses, the at least one dummy pulse having an opposite polarity to the first two or more consecutive pulses, the groups of pulses without the discarded dummy pulse or pulses comprising the output pulse stream.       

     The positioning of the groups within the bit stream obtained from the signal may be:
         i) agreed in advance of the signal being received by the receiver device; or   ii) determined from information in a header field of the at least one frame  300 .       

     Polarities of non-dummy pulses may be generated from a non-repeating sequence of pulses, such as generated from a CSPRNG. 
     For bursts of length 3 using rectangular pulses and peak PRF of 499.2 MHz, the provision of a dummy pulse at position  2  in the group may reduce measured peak power acc. FCC/ETSI by ˜5 dB as compared to an IEEE-compliant burst of N cpb =2, while adding only ˜1.8 dB average power. These numbers vary with burst length and number of dummy pulses per burst, peak PRF, and somewhat with pulse shape. 
     For longer bursts, multiple peak power “cancellation blocks” of multiple consecutive dummy pulses may be inserted in between the pulses containing the payload. 
     As the polarities of the dummy pulses only depend on previous data and are not used for distance bounding purposes in the receiver, they cannot be exploited by an attacker to mount an EDLC attack. 
       FIG. 26  shows a block diagram of the processing module for insertion of dummy pulses. In particular, the input bitstream may be provided by main frame generator  2600 . A burst polarity counter  2601  may be configured to keep a tally of the polarity of consecutive pulses and a frame polarity counter  2602  to keep a tally of the aggregate polarity of a group. It will be appreciated that depending on the strategy applied, only one of the counters  2601 ,  2602  may be present. Accordingly, a cancellation modulator  2603  may be configured to determine the dummy pulses to be inserted. The output bit stream may be created by the frame combiner  2604  by inserting the dummy pulses into the original groups of the input bitstream. A pulse shaper  2604  may then determine the shape of the pulses based on the output bitstream which may then be provided to a power amplifier  2605  for transmitting. 
     Symbol Construction 
     In one or more examples, the following techniques for symbol construction are provided. 
     The data symbol duration T dsym  ranges from 4 to 4096 chips (i.e., T dsym =T c *2{circumflex over ( )}(N+2), where N=0, 1, . . . ,10 and T c  comprises the chip duration time. Tc=1/499.2 MHz):
         4 chips/symbol=symbol rate 124.8 MHz
           data rate BPPM-BPSK, BPSK-with-FEC, &amp; QPSK ˜110 Mbit/s   data rate BPSK-without-FEC 124.8 Mbit/s   
           4096 chips/symbol=symbol rate 121.875 kHz
           data rate BPPM-BPSK, BPSK-with-FEC, &amp; QPSK ˜110 kbit/s   data rate BPSK-without-FEC 121.875 kbit/s   
               

     A random number generator, such as a CSRNG, produces a stream of bits s n ∈ {0,1}, n=0, 1, . . . , N bits −1 related to number of transmitted data octets, data rate, modulation scheme, and PRF. N bits  is equal to N octets *8*(N cpb +log 2 (N hop ))*4 d     sub   . In case more bits are produced by the AES encoder, the unused bits at the end of the stream are discarded and not made available for any purpose whatsoever. 
     The stream of bits s n  is then modulated according to the data stream from a Forward Error Correction (FEC) encoder g {0,1}   (k) ∈{0,1}, k=0, 1, . . . , 8*N octets −1 into a stream of output chips which is described in the time domain as follows. 
     In case of BPSK-only modulation, only one bit can be encoded per symbol, so the default mode of operation is uncoded, directly using the incoming data bits, possibly in combination with error-tolerant crypto on the receiver side. FEC may be supported in BPSK-only mode with use of subsymbols. 
       FIG. 27  shows the format of a BPPM-BPSK symbol  2700  according to the IEEE standard. A burst of pulses is either present in the first  2701  or the third part  2703  of the symbol (this modulates the first bit), on top of that the burst is BPSK modulated (second bit). In order to facilitate spectrum shaping, hopping of the burst is applied in the first and third parts  2701 ,  2703  of the symbol  2700  (depending on whether the burst is in the first or third part). In which of the N hop  positions  2701 ,  2703  the burst is placed is determined by a predetermined “PRN” sequence. 
     BPPM-BPSK 
     For BPPM-BPSK (62.4 MHz nominal mean PRF and δL=1) the symbols, in one or more examples, are modulated by default as follows: 
     
       
         
           
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 [ 
                 
                   1 
                   - 
                   
                     2 
                     · 
                     
                       g 
                       1 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
                 ] 
               
               · 
               
                 
                   ∑ 
                   
                     n 
                     = 
                     0 
                   
                   
                     
                       N 
                       cpb 
                     
                     - 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     [ 
                     
                       1 
                       - 
                       
                         2 
                         · 
                         
                           
                             m 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                   · 
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           t 
                           - 
                           
                             
                               ( 
                               
                                 
                                   g 
                                   1 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⊕ 
                                 
                                   g 
                                   0 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                             · 
                             
                               T 
                               BPM 
                             
                           
                           - 
                           
                             
                               h 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             · 
                             
                               T 
                               burst 
                             
                           
                           - 
                           
                             
                               n 
                               · 
                               δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               L 
                               · 
                               
                                 T 
                                 c 
                               
                             
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
     In this mode, the number of hopping positions N hop  is defined as T dsym /(4*T burst ). The symbol, in terms of available chip positions and time, is shown in  FIG. 27 . A pulse burst can be placed in one of the N hop  possible burst positions  2701 ,  2703 . Hopping is already part of the IEEE standard and its purpose is to reduce the presence of spurs in the frequency domain representation of the signal. It will be appreciated that hopping the burst is a provision for taking care that the transmitted signal has proper spectral properties to avoid spectral spurs. 
     BPSK 
     For BPSK without FEC (124.8 MHz nominal mean PRF and δL={1,2}) the symbols, in one or more examples, are modulated by default as follows: 
     
       
         
           
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 [ 
                 
                   1 
                   - 
                   
                     2 
                     · 
                     
                       d 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
                 ] 
               
               · 
               
                 
                   ∑ 
                   
                     n 
                     = 
                     0 
                   
                   
                     
                       N 
                       cpb 
                     
                     - 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     [ 
                     
                       1 
                       - 
                       
                         2 
                         · 
                         
                           
                             m 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                   · 
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           t 
                           - 
                           
                             
                               h 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             · 
                             
                               T 
                               burst 
                             
                           
                           - 
                           
                             
                               n 
                               · 
                               δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               L 
                               · 
                               
                                 T 
                                 c 
                               
                             
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
     In this mode, the number of hopping positions N hop  is defined as T dsym /(2*T burst ). Note that T burst  is proportional to δL and therefore larger δL directly reduces the number of available hopping positions. Note that the data stream d (k)  is modulated directly onto the symbols without FEC. The symbol  2800 , in terms of available chip positions and time, is shown in  FIG. 28 . 
     For BPSK with FEC (124.8 MHz nominal mean PRF and δL={1,2}) the symbols are modulated by default into two subsymbols as follows: 
     
       
         
           
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 [ 
                                 
                                   1 
                                   - 
                                   
                                     2 
                                     · 
                                     
                                       g 
                                       0 
                                       
                                         ( 
                                         
                                           ⌊ 
                                           
                                             k 
                                             / 
                                             2 
                                           
                                           ⌋ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 ] 
                               
                               · 
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   
                                     
                                       n 
                                       cpb 
                                     
                                     - 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     [ 
                                     
                                       1 
                                       - 
                                       
                                         2 
                                         · 
                                         
                                           
                                             m 
                                             
                                               ( 
                                               k 
                                               ) 
                                             
                                           
                                           ⁡ 
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   · 
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                           
                         
                       
                       
                         
                           
                             p 
                             ⁡ 
                             
                               ( 
                               
                                 t 
                                 - 
                                 
                                   
                                     h 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   · 
                                   
                                     T 
                                     burst 
                                   
                                 
                                 - 
                                 
                                   
                                     n 
                                     · 
                                     δ 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     L 
                                     · 
                                     
                                       T 
                                       c 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         for 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         k 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         is 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         even 
                       
                       , 
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               
                                 [ 
                                 
                                   1 
                                   - 
                                   
                                     2 
                                     · 
                                     
                                       g 
                                       1 
                                       
                                         ( 
                                         
                                           ⌊ 
                                           
                                             k 
                                             / 
                                             2 
                                           
                                           ⌋ 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 ] 
                               
                               · 
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   
                                     
                                       n 
                                       cpb 
                                     
                                     - 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     [ 
                                     
                                       1 
                                       - 
                                       
                                         2 
                                         · 
                                         
                                           
                                             m 
                                             
                                               ( 
                                               k 
                                               ) 
                                             
                                           
                                           ⁡ 
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                   · 
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                           
                         
                       
                       
                         
                           
                             p 
                             ⁡ 
                             
                               ( 
                               
                                 t 
                                 - 
                                 
                                   
                                     h 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   · 
                                   
                                     T 
                                     burst 
                                   
                                 
                                 - 
                                 
                                   
                                     n 
                                     · 
                                     δ 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     L 
                                     · 
                                     
                                       T 
                                       c 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       for 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       k 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       is 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         odd 
                         . 
                       
                     
                   
                 
               
             
           
         
       
     
     In this mode, the number of hopping positions N hop  is defined as T dsubsym /(2*T burst ). Note that T burst  is proportional to δL and therefore larger δL directly reduces the number of available hopping positions. The subsymbol definition is otherwise similar to the subsymbol definitions below. 
     QPSK 
     For QPSK (62.4 MHz nominal mean PRF and δL=2) the symbols, in one or more examples, are modulated by default as follows: 
     
       
         
           
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 [ 
                 
                   1 
                   - 
                   
                     2 
                     · 
                     
                       g 
                       1 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
                 ] 
               
               · 
               
                 j 
                 
                   ( 
                   
                     
                       g 
                       1 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     ⊕ 
                     
                       g 
                       0 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                   ) 
                 
               
               · 
               
                 
                   ∑ 
                   
                     n 
                     = 
                     0 
                   
                   
                     
                       n 
                       cpb 
                     
                     - 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     [ 
                     
                       1 
                       - 
                       
                         
                           2 
                           · 
                           
                             m 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         ⁢ 
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                     ] 
                   
                   · 
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           t 
                           - 
                           
                             
                               h 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             · 
                             
                               T 
                               burst 
                             
                           
                           - 
                           
                             
                               n 
                               · 
                               δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               L 
                               · 
                               
                                 T 
                                 c 
                               
                             
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
     The intended constellation is precisely along the I and Q axes of the modulator, resulting in the constellation diagram of  FIG. 23 . 
     In this mode, the number of hopping positions N hop  is defined as T dsym /(2*T burst ). The symbol timing diagram is the same as for BPSK. 
     Cryptographically Secure Random Number Generator (CSPRNG) 
     In one or more examples, the transmitter device and the receiver device  206 ,  207  may include a Cryptographically Secure Random Number Generator. The CSPRNG may be used for spreading of the STS  308 , PHR  312  and PSDU  313 . In one or more examples a NIST SP 800-90A based CSPRNG is used. 
     The core of the CSPRNG is an AES128 encryption unit which creates 128 bit blocks of pseudo-random numbers. Before ranging starts, all communicating devices (transmitter device and receiver device  201 ,  202 ) need to agree on a common 256 bit seed comprising an example of secure information that may be used to generate a secure training sequence (key and data of the AES core). This agreement is handled by a higher level protocol and is not part of the operation of the CSPRNG block itself. 
     General Definitions 
     Note that the three equations above describe the time-continuous pulse shape p(t) placed in the correct chip positions and phase modulated for each chip position of length T c . For BPPM-BPSK and BPSK the pulse shape is multiplied with {−1,0,1} for each chip position, while for QPSK (requiring a complex modulator) the pulse shape is multiplied with {−1,−j,0,j,1} for each chip position. 
     For N hop =1, h (k)  is an empty set, but for N hop &gt;1, the hopping sequence h (k)  ∈{0,1, . . . , N hop −1} is a subset of s n  defined as: 
     
       
         
           
             
               h 
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   n 
                   = 
                   0 
                 
                 
                   
                     
                       log 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       
                         N 
                         hop 
                       
                       ) 
                     
                   
                   - 
                   1 
                 
               
               ⁢ 
               
                 
                   2 
                   n 
                 
                 · 
                 
                   
                     s 
                     
                       n 
                       + 
                       
                         k 
                         · 
                         
                           ( 
                           
                             
                               N 
                               cbp 
                             
                             + 
                             
                               
                                 log 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   N 
                                   hop 
                                 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   . 
                 
               
             
           
         
       
     
     The equation shows that a group of bits is selected from s n  to encode, in LSB-first binary way, the hopping positions used for each transmitted symbol k. 
     In all cases, the scrambling sequence m (k) (n)∈{0,1}, k=0, 1, . . . , 8*N octets −1, n=0, 1 . . . , N cpb −1 is a subset of s n  defined as:
 
 m   (k) ( n )= s   n+log     2     (N     hop     )+k·(N     cpb     +log     2     (N     hop     )) .
 
     The equation shows that bits are reserved to encode both the scrambling sequence and the hopping position used for each transmitted symbol k, and also grouped per symbol k. It should be noted that the scrambling sequence is encoded in s n  after the hopping position. 
     T burst  is defined as:
 
 T   burst   =N   cpb   ·δL·T   c .
 
     Note that according to this definition, the empty (δL−1) chips following the last active pulse in a burst are considered to be part of the burst. 
     Dummy Pulses 
     For dummy pulse generation, no additional random bits, such as generated by a CSRNG, are needed, as pulse polarities may be purely determined by the polarities of preceding pulses. 
     An example is given for QPSK modulation with parameters N cps =4, symbol rate=31.2 MHz, T d,sym =32 ns. In this example, the number of pulses per burst before addition of dummy pulses is equal to 2, with spacing δL equal to 2 (i.e., there is always 1 gap chip in between the two pulses within a burst). The symbol construction without dummy pulses then looks as follows, where we have already filled in numerical values for N cpb  and δL:
 
 x   (k) ( t )=[1−2 ·g   1   (k) ]· j   (g     1       (k)     ⊕g     0       (k)     ) ·Σ n=0   1 [1−2 ·m   (k) ( n )]· p ( t−h   (k)   ·T   burst   −n ·2 ·T   c ).
 
To this symbol pattern we add the following dummy pulse pattern x d   (k) (t):
 
 x   d   (k) ( t )=[1−2 ·g   1   (k) ]· j   (g     1       (k)     ⊕g     0       (k)     ) ·[2 ·m   (k) (0)−1]· p ( t−h   (k)   T   burst −1 ·T   c )
 
     This pattern is essentially a copy of the pulse pattern at n=0, but reversed in sign and moved ahead in time by 1·T c , which puts it precisely inside the gaps between the n=0 and n=1 pulses. When the overall frame, assuming T c  equal to 1/(499.2 MHz), is then evaluated using a 50 MHz RBW peak power measurement filter according to ETSI or FCC, the ratio of measured peak power to pulse amplitude will have decreased as a result. For short frames, this fact may increase the available useful link budget, without introducing an EDLC vulnerability (provided the receiver ignores the dummy pulses). 
     This general idea can be extended to different burst designs and optional inclusion of DC cancellation. 
     Subsymbols 
     An example definition of subsymbols is provided. Symbol are divided into 4 d     sub    subsymbols, where d sub  is a 2 bits LSB-first encoded number of the set {0,1,2,3}, where the default value 0 indicates that the subsymbol is equal to the symbol (i.e., no further subdivision). Combinations of modulation parameters and division into subsymbols, that would result in N hop &lt;1 per subsymbol, are forbidden. Symbol timing diagrams show basically a concatenation of subsymbols into one overall symbol, as shown in the example for BPSK (without FEC) and QPSK below. 
       FIG. 31  shows a symbol  3100  divided into a plurality of subsymbols  3101 ,  3102 ,  3103 . Each subsymbol  3101 ,  3102 ,  3103  comprises a possible burst position  3104  and a guard interval  3105 . 
     BPPM-BPSK Sub-Symbols 
     For BPPM-BPSK (62.4 MHz nominal mean PRF and δL=1) the subsymbols are modulated as follows: 
                 x     (   k   )       ⁡     (   t   )       =       [     1   -     2   ·     g   1     (     ⌊       k   /     4   ^       ⁢     d   sub       ⌋     )           ]     ·       ∑     n   =   0         N   cpb     -   1       ⁢       [     1   -     2   ·       m     (   k   )       ⁡     (   n   )           ]     ·       p   ⁡     (     t   -       (       g   1     (     ⌊       k   /     4   ^       ⁢     d   sub       ⌋     )       ⊕     g   0     (     ⌊       k   /     4   ^       ⁢     d   sub       ⌋     )         )     ·     T   BPM       -       h     (   k   )       ·     T   burst       -       n   ·   δ     ⁢           ⁢     L   ·     T   c           )       .                 
BPSK Sub-Symbols
 
     For BPSK without FEC (124.8 MHz nominal mean PRF and δL={1,2}) the subsymbols are modulated as follows: 
     
       
         
           
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 [ 
                 
                   1 
                   - 
                   
                     2 
                     · 
                     
                       g 
                       1 
                       
                         ( 
                         
                           ⌊ 
                           
                             
                               k 
                               / 
                               
                                 4 
                                 ^ 
                               
                             
                             ⁢ 
                             
                               d 
                               sub 
                             
                           
                           ⌋ 
                         
                         ) 
                       
                     
                   
                 
                 ] 
               
               · 
               
                 
                   ∑ 
                   
                     n 
                     = 
                     0 
                   
                   
                     
                       N 
                       cpb 
                     
                     - 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     [ 
                     
                       1 
                       - 
                       
                         2 
                         · 
                         
                           
                             m 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                   · 
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           t 
                           - 
                           
                             
                               h 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             · 
                             
                               T 
                               burst 
                             
                           
                           - 
                           
                             
                               n 
                               · 
                               δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               L 
                               · 
                               
                                 T 
                                 c 
                               
                             
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
     In this mode, the number of hopping positions N hop  is defined as T dsubsym /(2*T burst ). Note that T burst  is proportional to δL and therefore larger δL directly reduces the number of available hopping positions. Note that the data stream d (k)  is modulated directly onto the symbols without FEC. 
     For BPSK with FEC (124.8 MHz nominal mean PRF and δL={1,2}) the symbols are modulated by default into 2·4 d     sub    subsymbols as follows: 
     
       
         
           
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             
                               [ 
                               
                                 1 
                                 - 
                                 
                                   2 
                                   · 
                                   
                                     g 
                                     0 
                                     
                                       ( 
                                       
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                                               k 
                                               / 
                                               2 
                                             
                                             · 
                                             4 
                                           
                                           ⁢ 
                                           
                                             d 
                                             sub 
                                           
                                         
                                         ⌋ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               ] 
                             
                             · 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 
                                   
                                     N 
                                     cpb 
                                   
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   [ 
                                   
                                     1 
                                     - 
                                     
                                       2 
                                       · 
                                       
                                         
                                           m 
                                           
                                             ( 
                                             k 
                                             ) 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           n 
                                           ) 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 · 
                               
                             
                           
                         
                       
                       
                         
                           
                             p 
                             ⁡ 
                             
                               ( 
                               
                                 t 
                                 - 
                                 
                                   
                                     h 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   · 
                                   
                                     T 
                                     burst 
                                   
                                 
                                 - 
                                 
                                   
                                     n 
                                     · 
                                     δ 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     L 
                                     · 
                                     
                                       T 
                                       c 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         for 
                         ⁢ 
                         
                             
                         
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                           ⌊ 
                           
                             k 
                             ⁢ 
                             
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                               sub 
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                         is 
                         ⁢ 
                         
                             
                         
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                         even 
                       
                       , 
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               [ 
                               
                                 1 
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                                     1 
                                     
                                       ( 
                                       
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                                               k 
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                                               2 
                                             
                                             · 
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                                           ⁢ 
                                           
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                                             sub 
                                           
                                         
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                                       ) 
                                     
                                   
                                 
                               
                               ] 
                             
                             · 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 
                                   
                                     N 
                                     cpb 
                                   
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   [ 
                                   
                                     1 
                                     - 
                                     
                                       2 
                                       · 
                                       
                                         
                                           m 
                                           
                                             ( 
                                             k 
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                                         ⁡ 
                                         
                                           ( 
                                           n 
                                           ) 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                 · 
                               
                             
                           
                         
                       
                       
                         
                           
                             p 
                             ⁡ 
                             
                               ( 
                               
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                                 - 
                                 
                                   
                                     h 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   · 
                                   
                                     T 
                                     burst 
                                   
                                 
                                 - 
                                 
                                   
                                     n 
                                     · 
                                     δ 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     L 
                                     · 
                                     
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                                       c 
                                     
                                   
                                 
                               
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                       ⁢ 
                       
                           
                       
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                       ⁢ 
                       
                           
                       
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                       is 
                       ⁢ 
                       
                           
                       
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                         odd 
                         . 
                       
                     
                   
                 
               
             
           
         
       
     
     In this mode, the number of hopping positions N hop  is defined as T dsubsym /(2*T burst ). Note that T burst  is proportional to δL and therefore larger δL directly reduces the number of available hopping positions. 
     QPSK Sub-Symbols 
     For QPSK (62.4 MHz nominal mean PRF and δL=2) the subsymbols are modulated as follows: 
     
       
         
           
             
               
                 x 
                 
                   ( 
                   k 
                   ) 
                 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 [ 
                 
                   1 
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                     2 
                     · 
                     
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                       0 
                       
                         ( 
                         
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                               k 
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                                 4 
                                 ^ 
                               
                             
                             ⁢ 
                             
                               d 
                               sub 
                             
                           
                           ⌋ 
                         
                         ) 
                       
                     
                   
                 
                 ] 
               
               · 
               
                 j 
                 
                   ( 
                   
                     
                       g 
                       1 
                       
                         ( 
                         
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                             k 
                             / 
                             
                               4 
                               ^ 
                               
                                 d 
                                 sub 
                               
                             
                           
                           ⌋ 
                         
                         ) 
                       
                     
                     ⊕ 
                     
                       g 
                       0 
                       
                         ( 
                         
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                             k 
                             / 
                             
                               4 
                               ^ 
                               
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                                 sub 
                               
                             
                           
                           ⌋ 
                         
                         ) 
                       
                     
                   
                   ) 
                 
               
               · 
               
                 
                   ∑ 
                   
                     n 
                     = 
                     0 
                   
                   
                     
                       N 
                       cpb 
                     
                     - 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     [ 
                     
                       1 
                       - 
                       
                         2 
                         · 
                         
                           
                             m 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                     ] 
                   
                   · 
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           t 
                           - 
                           
                             
                               h 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             · 
                             
                               T 
                               burst 
                             
                           
                           - 
                           
                             
                               n 
                               · 
                               δ 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               L 
                               · 
                               
                                 T 
                                 c 
                               
                             
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
             
           
         
       
     
     Default values for d sub  are given in the tables below, with timings related to a nominal chip rate of 499.2 MHz (the chip rate here chosen equal to the one in the IEEE standard). T guard  denotes the length of the guard interval, as labelled in the symbol timing diagrams. 
     BPPM-BPSK (δL=1) 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
               
               
                 N cps   
                 sym_rate [Hz] 
                 T d, sym  [s] 
                 d sub   
                 T d, subsym  [s] 
                 T guard  [s] 
                 Mean PRF [Hz] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 4 
                 124.80E+6 
                 8.01E−9 
                 0 
                  8.01E−9 
                  2.00E−9 
                 124.80E+6  
               
               
                 8 
                  62.40E+6 
                 16.03E−9  
                 0 
                  16.03E−9 
                  4.01E−9 
                 62.40E+6 
               
               
                 16 
                  31.20E+6 
                 32.05E−9  
                 0 
                  32.05E−9 
                  8.01E−9 
                 62.40E+6 
               
               
                 32 
                  15.60E+6 
                 64.10E−9  
                 0 
                  64.10E−9 
                  16.03E−9 
                 62.40E+6 
               
               
                 64 
                  7.80E+6 
                 128.21E−9  
                 0 
                 128.21E−9 
                  32.05E−9 
                 62.40E+6 
               
               
                 128 
                  3.90E+6 
                 256.41E−9  
                 0 
                 256.41E−9 
                  64.10E−9 
                 62.40E+6 
               
               
                 256 
                  1.95E+6 
                 512.82E−9  
                 0 
                 512.82E−9 
                 128.21E−9 
                 62.40E+6 
               
               
                 512 
                 975.00E+3 
                 1.03E−6 
                 0 
                  1.03E−6 
                 256.41E−9 
                 62.40E+6 
               
               
                 1024 
                 487.50E+3 
                 2.05E−6 
                 1 
                 512.82E−9 
                 128.21E−9 
                 62.40E+6 
               
               
                 2048 
                 243.75E+3 
                 4.10E−6 
                 1 
                  1.03E−6 
                 256.41E−9 
                 62.40E+6 
               
               
                 4096 
                 121.88E+3 
                 8.21E−6 
                 2 
                 512.82E−9 
                 128.21E−9 
                 62.40E+6 
               
               
                   
               
            
           
         
       
     
     BPSK (δL={1,2}) 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
               
               
                 N cps   
                 sym_rate [Hz] 
                 T d, sym  [s] 
                 d sub   
                 T d, subsym  [s] 
                 T guard  [s] 
                 Mean PRF [Hz] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 4 
                 124.80E+6 
                 8.01E−9 
                 0 
                  4.01E−9 
                  2.00E−9 
                 249.60E+6 
               
               
                 8 
                  62.40E+6 
                 16.03E−9  
                 0 
                  8.01E−9 
                  4.01E−9 
                 124.80E+6 
               
               
                 16 
                  31.20E+6 
                 32.05E−9  
                 0 
                  16.03E−9 
                  8.01E−9 
                 124.80E+6 
               
               
                 32 
                  15.60E+6 
                 64.10E−9  
                 0 
                  32.05E−9 
                  16.03E−9 
                 124.80E+6 
               
               
                 64 
                  7.80E+6 
                 128.21E−9  
                 0 
                  64.10E−9 
                  32.05E−9 
                 124.80E+6 
               
               
                 128 
                  3.90E+6 
                 256.41E−9  
                 0 
                 128.21E−9 
                  64.10E−9 
                 124.80E+6 
               
               
                 256 
                  1.95E+6 
                 512.82E−9  
                 0 
                 256.41E−9 
                 128.21E−9 
                 124.80E+6 
               
               
                 512 
                 975.00E+3 
                 1.03E−6 
                 0 
                 512.82E−9 
                 256.41E−9 
                 124.80E+6 
               
               
                 1024 
                 487.50E+3 
                 2.05E−6 
                 1 
                 256.41E−9 
                 128.21E−9 
                 124.80E+6 
               
               
                 2048 
                 243.75E+3 
                 4.10E−6 
                 1 
                 512.82E−9 
                 256.41E−9 
                 124.80E+6 
               
               
                 4096 
                 121.88E+3 
                 8.21E−6 
                 2 
                 256.41E−9 
                 128.21E−9 
                 124.80E+6 
               
               
                   
               
            
           
         
       
     
     QPSK (δL=2) 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
               
               
                 N cps   
                 sym_rate [Hz] 
                 T d, sym  [s] 
                 d sub   
                 T d, subsym  [s] 
                 T guard  [s] 
                 Mean PRF [Hz] 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 4 
                 124.80E+6 
                 8.01E−9 
                 0 
                  8.01E−9 
                  4.01E−9 
                 124.80E+6  
               
               
                 8 
                  62.40E+6 
                 16.03E−9  
                 0 
                  16.03E−9 
                  8.01E−9 
                 62.40E+6 
               
               
                 16 
                  31.20E+6 
                 32.05E−9  
                 0 
                  32.05E−9 
                  16.03E−9 
                 62.40E+6 
               
               
                 32 
                  15.60E+6 
                 64.10E−9  
                 0 
                  64.10E−9 
                  32.05E−9 
                 62.40E+6 
               
               
                 64 
                  7.80E+6 
                 128.21E−9  
                 0 
                 128.21E−9 
                  64.10E−9 
                 62.40E+6 
               
               
                 128 
                  3.90E+6 
                 256.41E−9  
                 0 
                 256.41E−9 
                 128.21E−9 
                 62.40E+6 
               
               
                 256 
                  1.95E+6 
                 512.82E−9  
                 0 
                 512.82E−9 
                 256.41E−9 
                 62.40E+6 
               
               
                 512 
                 975.00E+3 
                 1.03E−6 
                 1 
                 256.41E−9 
                 128.21E−9 
                 62.40E+6 
               
               
                 1024 
                 487.50E+3 
                 2.05E−6 
                 1 
                 512.82E−9 
                 256.41E−9 
                 62.40E+6 
               
               
                 2048 
                 243.75E+3 
                 4.10E−6 
                 2 
                 256.41E−9 
                 128.21E−9 
                 62.40E+6 
               
               
                 4096 
                 121.88E+3 
                 8.21E−6 
                 2 
                 512.82E−9 
                 256.41E−9 
                 62.40E+6 
               
               
                   
               
            
           
         
       
     
     The advantage of the use of subsymbols becomes clear in a direct comparison with the IEEE standard for BPPM-BPSK, as shown in the table below. Here we see that for the range of symbol rates supported in the IEEE standard at Mean PRF=62.4 MHz, the proposed format offers finer symbol rate granularity as well as avoiding that the number of pulses per burst (N ppb ) exceeds 64. 
                                                     sym_rate    Mean PRF        N ppb     N ppb          N cps     [Hz]   [Hz]   d sub     proposed   in IEEE                                                        16    31.20E+6   62.40E+6   0   2   2       32    15.60E+6   62.40E+6   0   4   N/A       64    7.80E+6   62.40E+6   0   8   8       128    3.90E+6   62.40E+6   0   16   N/A       256    1.95E+6   62.40E+6   0   32   N/A       512   975.00E+3   62.40E+6   0   64   64       1024   487.50E+3   62.40E+6   1   32   N/A       2048   243.75E+3   62.40E+6   1   64   N/A       4096   121.88E+3   62.40E+6   2   32   512                    
Novel Protocol to Exchange the Secure Preamble Seed with Minimal Overhead
 
     For a secure ranging measurement, based on a secure training sequence it is a prerequisite, that only the genuine sender as well as the intended recipient know the secure information (i.e. seed) to generate corresponding secure training sequence. In one or more examples, a different secure training sequence needs to be used for every frame. This implies a significant protocol overhead. 
     In one or more examples, an AES based cryptographically secure random number generator (CSRNG) is utilised for generation of the secure training sequence. The CSRNG seed, comprising the secure information from which a secure training sequence may be generated comprises, in one or more examples, a key plus a counter value. A challenge response scheme may be utilised to exchange the key plus the initial counter value at the beginning of a ranging protocol. For all subsequent ranging frames the CSRNG sequence is extended over multiple frames. In one or more other examples, the processing modules of transmitter and receiver may be configured to reuse the same key for each secure training sequence required and for every new frame to increment only the counter value by a fixed, agreed, amount. 
       FIG. 29  shows an exemplary protocol exchange, for a so called double sided ranging sequence. In the example, one of the transmitter/receiver devices  201 ,  202  is termed an anchor (labelled anchor 1  in  FIG. 29 ) or “lock device” as it is typically mounted with a secured element (such as a vehicle or building) that is unlocked by completion of the protocol. The other of the transmitter/receiver devices  201 ,  202  is termed a tag (labelled tag 1  in  FIG. 29 ) or “key device” as it is typically a mobile device used to unlock the secured element. The term “secure preamble” where used refers to the secure training sequence described above. 
     The following procedure is executed:
         1. The anchor
           a. derives a cryptographic challenge using a random number and his cryptographic key   b. sends an UWB frame  2901  with the cryptographic challenge in the payload   
           2. The tag
           a. receives the challenge at  2902  and uses his cryptographic key to derive a cryptographic response using a cryptographic algorithm (AES  128  for example) (i.e. the tag effectively uses the cryptographic challenge combined with his cryptographic key as seed for the secure training sequence)   b. uses the cryptographic response as secure training sequence  2903     c. sends this frame  2904  as the beginning of a ranging frame (e.g. a frame from which timing information is determined for use in distance determination between tag and anchor)   d. starts the time measurement when the secure training sequence has been transmitted at  2905     
           3. The anchor
           a. has prior knowledge of the cryptographic key in the tag and computes the expected cryptographic response using the same cryptographic algorithm as the tag   b. correlates the received secure training sequence  2906  against the expected response   c. demodulates the received secure training sequence  2906  to authenticate the sender   d. starts the time measurement when the expected secure training sequence is detected at  2907 . By basing the time measurement on the detection of an expected secure training sequence, comprising a non-repeating sequence, that is known or derivable only by the anchor and the tag, a secure marker for time measurement may be provided. The secure marker may be placed at the start of the expected secure training sequence or at the end or other defined point relative to the detected, expected, secure training sequence.   e. a continuation of the secure training sequence is used to generate the next secure training sequence  2908  for the next ranging frame  2909     f. sends this frame as the next ranging frame   g. records the time when the when the secure training sequence has been transmitted at  2910     
           4. The tag
           a. correlates the received secure training sequence  2911  against the expected response   b. demodulates the received secure training sequence  2911  to authenticate the sender   c. records the time when the secure training sequence is detected. The detection of the expected secure training sequence may there define a secure marker  2912  for timing purposes.   d. a continuation of the secure training sequence is used to generate the next secure training sequence  2913     e. sends this frame as the next ranging frame  2914     f. records the time when the secure training sequence has been transmitted at  2915     
           5. The anchor
           a. correlates the received secure training sequence  2916  against the expected response   b. demodulates the received secure training sequence  2916  to authenticate the sender   c. records the time when the expected secure training sequence is detected at marker  2917 . As the marker  2917  is based on the receipt of the expect secure training sequence, it may be considered a secure marker.   
           6. The tag
           a. encrypts the time measurements and sends them as payload in a separate frame  2917     
           7. The anchor
           a. decrypts the received time measurements  2918  and calculates the distance to the tag based on the anchor&#39;s own time measurements and those received from the tag   
               

     The distance, d, between the tag and the anchor, may be determined from the following equation: 
             d   =       ToF   ·   c     ≈               T   T     ⁡     [   1   ]       ·       T   A     ⁡     [   2   ]         -         T   A     ⁡     [   1   ]       ·       T   T     ⁡     [   2   ]                 T   T     ⁡     [   1   ]       +       T   A     ⁡     [   2   ]       +       T   A     ⁡     [   1   ]       +       T   T     ⁡     [   2   ]           ·     c   .               
where c comprises the speed of light, T A [1] and T A [2] comprise the time between marker  2907  to marker  2910  and marker  2910  to marker  2917  respectively, T T [1] and T T [2] comprise the time between marker  2905  to marker  2912  and marker  2912  to marker  2915  respectively.
 
Novel Protocol to Measure the Shortest Distance Between a Group of Anchors and a Group of Tags with Minimal Overhead
 
     In the automotive PKE context several anchors may be mounted on different locations in and around a lockable element, such as automobile. Possible locations are the roof, the bumper, the mirrors and the driver cabin. A significant number of key fobs (also known as a tag or key device) may also be registered with one car. The challenge is to identify which fobs, if any, are in the proximity of the car, and to establish a tight upper bound for the distance of each fob (key device) to the car (the lock devices of the lockable element). 
       FIG. 30  shows an exemplary protocol exchange, for a so called double sided ranging sequence with multiple anchors and multiple fobs. The terms anchor and lock device are used interchangeably. The terms tag, fob and key device are used interchangeably. The underlying ranging sequence is the same as described in the previous section. There are however none, one or more of the following enhancements:
         1. There is at least one anchor that is visible to all other anchors. It starts the protocol, by synchronising all other anchors.   2. The synchronised anchors transmit the same challenge simultaneously.
           a. For the fob this looks like the transmission from one antenna, spread over a long, diverse multipath.   
           3. Position modulation is used by the anchors and the fobs to identify themselves.
           a. Each anchor and fob has a specific period where only it is allowed to transmit.   b. All other anchors and fobs are quiet during this time   
           4. The anchors notify each fob when it is allowed to transmit the final message with the timing information.   5. Each anchor derives its distance to each fob.   6. A controller or “BCM” in the car retrieves all distance measurements and uses the shortest distance as criteria for opening the car. A BCM comprises a Body Control Module comprising an electronic control unit responsible for monitoring and controlling various electronic accessories in a vehicle&#39;s body.       

     The advantages of this approach may comprise one or more of:
         1. Receive time is minimised, because all anchors and fobs transmit at the same time.   2. Each fob knows which anchors can receive its messages.   3. Each anchor knows which fobs can receive its messages. With the following procedure it can work out which one is the closest.
           a. It estimates the distance based on the timing measurements received from each fob.   b. The fob whose timing measurement results in the shortest distance is the closest one.   
               

     However, the estimated distance may not necessarily be correct, because the fob may start its timing based on the earliest message it receives. The earliest message may however have been transmitted from another anchor which is even closer. 
     A central or distributed controller, or one of the anchors in communication with each of the anchors may work out which fob and which anchor are the closest to each other and what their actual distance is using the following procedure:
         a. The controller reads back from each anchor who the closest fob was and which distance it estimated.   b. The anchor that reports the shortest distance is the closest one to any of the fobs. Its distance estimate to the closest fob is the actual distance.       

     With reference to  FIG. 30 , anchor  1  comprises the lock device that is visible to the others. Accordingly, anchor  1  may be physically positioned relative to anchors  2 ,  3  and  4  such that signaling sent by anchor  1  is received by all the other anchors of the group of anchors  3001 . Accordingly, the anchor  1  may send a synchronization message  3002  to the other anchors with timing information that allows for time synchronization of the group of anchors  3001 . A wake-up signal (labelled WUP in  FIG. 30 ), based on the sending of the synchronization message  3002 , may be sent to the tags to prepare them for the forthcoming exchange of messages. 
     Based on said time synchronization between the anchor  1  and the other anchors of the group  3001 , a challenge message  3003  is sent. The challenge message is to a key group comprising a plurality of key devices, labelled Tag  1  and Tag  4  in  FIG. 30 . It will be appreciated that there may be more key devices although only Tag  1  and Tag  4  happen to be nearby. The challenge message  3003  is transmitted in time synchronization by all of the lock devices labelled anchors  1  to  4 . The challenge message comprises a first common part  3004  comprising the same data transmitted by all of the lock devices at the same time. The challenge message further includes an identifier part  3005 , the identifier part including a unique identifier among the lock devices (anchors  1  to  4 ). The identifier part is provided for transmission by each anchor in a discrete predetermined time slot assigned to said anchor relative to the common part  3004 . Thus, the other anchors may be silent while each anchor transmits its identifier part of the challenge message in it its dedicated time slot. 
     The key devices tag  1  and tag  4  receive the challenge message from only those lock devices/anchors that are in range. Accordingly, tag  1  is shown in receipt of the challenge message at  3006  with only the identifiers of anchor  1  and anchor  3 . Accordingly, tag  4  is shown in receipt of the challenge message at  3007  with only the identifiers of anchor  2 , anchor  3  and anchor  4 . 
     Each key device on receipt of the challenge message at  3006  and  3007 , is configured to provide for transmission of a key response message  3010 ,  3011  at a predefined moment after reception of the challenge message. The key response message  3010 ,  3011  comprising a common part  3012  comprising the same data transmitted by the other key devices at the same time. The common part  3012  may comprise a secure training sequence, as described above, to confirm the identity of the key devices/tags to the lock devices/anchors. The secure training sequence may comprise a non-repeating sequence of symbols based on one or more of an agreed symbol sequence and an agreed reference for generation of such a symbol sequence agreed between the key devices and receiver devices. The key response message  3010 ,  3011  comprises an identifier part  3013 , the identifier part including a unique identifier  3014  among the key devices to identify the tags, the identifier part provided for transmission in a discrete predetermined time slot assigned to each of said key devices relative to the common part  3012  and different to corresponding time slots assigned to the other key devices of the key group. 
     Further, based on the transmission of the key response message  3010 ,  3011 , the key devices may be configured to begin a timer based on a temporal position of a marker  3015  present in the response message. The marker  3015  may be considered a secure marker if its temporal position is based on the temporal position of the secure training sequence, as the secure training sequence comprises data that can be trusted and is verifiable by the lock devices and key devices. 
     It will be appreciated that not all key devices may have received the challenge message from all of the lock devices. Accordingly, based on the received key response message at  3016  from at least some of the key devices of the key group (e.g. tag  1  and tag  4 ), each anchor begins its own timer for timing future message exchanges between it and the key devices from which it received the key response message  3016 . The beginning of the timer is based on a secure marker  3017  present in the received key response message  3016  from that particular key device. The timer may start on the basis of the marker in the shortest multipath component or individual timers may be provided for each key device. The individual timers may be started based on the shortest multipath component of that particular key device based on the identifier. The marker is a secure marker by virtue of the marker being temporally related to the secure training sequence, which may be checked as valid by the lock device based on generation of a corresponding secure training sequence by the lock device. 
     At this point each lock device knows with which key devices it can communicate by virtue of the identifiers sent as part of the response message, received at  3016 . 
     It may be possible for an attacker, say Tag X, to insert a key response message consisting part of a preamble, labelled “P” in the figure, the SFD, and an identifier tag ID (e.g. for tags that happen not to be present, such as. tag 2  or tag 3 ). However, tag X cannot produce the secure training sequence (labelled R 1 ). Thus, in one or more examples, each lock device may be configured to determine channel estimate information for each lock device from which it receives a message based on a valid secure training sequence being detected and using cross-correlation with at least part of secure training sequence of the received key response message and a corresponding secure training sequence generated by the lock device. The channel estimate information may comprise a secure channel estimate information profile for each genuine tag. The secure channel estimate information profile may include characteristic reflections or multi-path components of the channel that may be used for validation of messages from genuine key devices. The lock device may be configured to determine channel estimate information for each subsequent message it receives and based on a comparison with the one or more secure channel estimate information profiles, accept messages from genuine key devices and reject messages from non-genuine key devices. 
     The lock devices then provide for transmission of a lock response message  3019  to the key group in time synchronization with the other lock devices. The lock response message  3019  comprising a second common part  3018  comprising the same data transmitted by all of the lock devices at the same time and the identifier part  3020  provided for transmission in the discrete predetermined time slot assigned to said first lock device relative to the common part. The second common part  3018  may comprise a continuation of the secure training sequence, generated by the lock device. The lock response message  3019  may provide information defining a designated reporting time slot  3021 ,  3022  different for the each of the key devices of the key group to provide timing information measured by the key device, the designated reporting time slot subsequent to the sending of the at least one further key response message  3023 . 
     The lock response message  3019  is received by the key devices at  3024 . The key devices may record a time elapsed from starting the timer to a marker  3025  present in the received lock response message  3024 . The marker  3025  may be a secure marker by virtue of the marker being temporally related to the time of receipt of the secure training sequence in the received lock response message at  3024 , which may be checked as valid by the key device based on generation of a corresponding secure training sequence by the key device. 
     The key devices then provide for the transmission of the further key response message  3023  to the lock group. The further key response message  3023  may be provided for transmission a predefined time after the lock response message  3023  by the key devices of the key group that received the lock response message  3024 . The further key response message  3023  comprising a response to said lock response message  3019  and comprising a common part  3026  comprising the same data transmitted by the other key devices at the same time. The common part may include a further continuation of the secure training sequence for authentication of the further key response message  3023  to the lock devices. The further key response message  3023  further includes an identifier part  3027 , the identifier part including a unique identifier among the key devices, the identifier part provided for transmission in a discrete predetermined time slot assigned to each of said key devices relative to the common part  3026  and different to corresponding time slots assigned to the other key devices of the key group. 
     The key devices may each stop their respective timers on sending of the further key response message  3023  based on a marker  3030  in the further response message. The marker  3030  may be a secure marker by virtue of the marker being temporally related to the time of transmitting of the secure training sequence in the common part  3026  of the further key response message  3023 . Accordingly, each key devices has recorded a first time T tag_identifer [1] between transmitting the key response message and receiving the lock response message  3024  and a second time T tag_identifier [2] between receipt of the lock response message  3024  and the sending of the further key response message  3023 . The timings are made relative to the secure markers in the respective messages. In this embodiment the secure marker comprises the point of the message (which comprises a frame) immediately after the start of frame delimiter field, labelled SFD in  FIG. 30 , although in other embodiments a different temporal secure marker may be used. 
     The further key response message  3023  is received at the lock devices at  3028 . Based on the received further key response message from at least a subset of the key devices of the key group, each lock device may stop its timer that is associated with each key device. The stopping of the timer, in this example, is based on a marker  3031  present in the further key response message from the associated particular key device. The marker  3031  may be a secure marker by virtue of the marker being temporally related to the time of receipt of the secure training sequence in the received further key response message  3028 , which may be checked as valid by the lock device based on generation of a corresponding secure training sequence by the lock device. 
     It will be appreciated that the recording of reception times based on the markers  3025 ,  3031  is based on the cross-correlation of the secure training sequence in the received message  3024 ,  3028  and a secure training sequence determined by the key/lock device and the reception of the key/lock device&#39;s identifier. The time of arrival for a specific lock/key device may be based on the earliest multipath component that is present both in the secure training sequence part of the message and the identifier part of the message. The earliest multipath component may be determined from channel estimate information as will be understood from those skilled in the art. From this time of arrival, the corresponding marker  3025 ,  3031  for a key/lock device can be determined. 
     Accordingly, each lock devices, for each key device with which it has exchanged messages, has recorded a first time T anchor_identifer [1] between receipt of the key response message  3016  and sending the lock response message  3019  and a second time T anchor_identifier [2] between transmitting of the lock response message  3019  and the receipt of the further key response message  3028 . The timings are made relative to a secure marker in the respective messages. In this embodiment the secure marker comprises the point of the frame immediately after the start of frame delimiter field, although in other embodiments a different temporal secure marker may be used. 
     Each key device (tag 1 , tag 4 ) may then send its timings to the lock group in the designated reporting time slot  3021 ,  3022 . 
     The distance between the lock devices and each of the key devices which could receive its messages is based on the round trip time of the messages minus the processing time at the lock device (provided by its timings) and the processing time at the respective key device (provided by its timings). Such a distance calculation will be familiar to those skilled in the art. 
     For double-sided ranging, the intention is to find the distance via the Time of Flight:
 
 d =RTToF· c/ 2=ToF· c.  
 
     Where RTToF is the return time of flight and ToF is the time of flight between the transmitter device and receiver device. 
     It will be appreciated that double-sided ranging offers the feature of reduction of the impact of reference clock imperfections, when compared to single-sided ranging. Double-sided ranging is disclosed in the publication “A new Double Two-Way Ranging algorithm for ranging system”, IEEE CNIDC 2010, by Myungkyun Kwak and Jongwha Chong. 
     For  FIG. 30 , similar equations as recited above for  FIG. 29  hold, where T T [{1,2}] and T A [{1,2}] (time differences between subsequent messages as measured by the tag and anchor, respectively) are to be replaced according to the numbers of the anchor and tag between which the distance is being evaluated. 
     The example method described allows two methods of distance bounding: 
     1) Finding the shortest distance between any one of the anchors and any one of the tags 
     2) A distance measurement for every anchor-tag pair that are in communication range. 
     For method 1), each key or lock device may start its timer based of the position of a secure marker related to the earliest multipath component seen in the key response message/lock response message. It will be appreciated that the earliest multipath component may be determined based on channel estimate information. 
     For method 2), each key or lock device must find the earliest multipath component that corresponds to each lock or key device respectively. This may be done as follows: the received response message, labelled R1 or R2, may be used for carrying out a channel estimation and will result in an estimated set of multipath components (delay, amplitude and phase). This set of multipath components may be used to configure the receiver (e.g. with a RAKE receiver or a channel matched filter) for reception of the identifiers for each device that sent a message. The set of multipath components consists of both channel reflections and direct paths between the receiving key/lock device and all transmitting key/lock devices that are in range. The configuration of the receiving device in this way blocks any attacker that wants to insert its message with a multipath component set that is non-overlapping with the (secret) superset of multipath components. In a most advantageous (for the attacker) attack, the attacker may have a multipath component set that has some overlap with the earliest multipath components in the superset and can therefore not fake a shorter distance than the distance of a genuine key/lock device. The shortest distance between a responding device and the receiving device may be determined by looking to the earliest multipath component out of the superset that is active during the reception of the ID indicator. 
     Subnet Separation 
     A group of first and second devices may form together a subnet. The subnet may use a specific Pulse Repetition Frequency (PRF). In order to be separated from other subnets, each subnet can use a slightly different Pulse Repetition Frequency such that during acquisition in which correlation and averaging is needed to lift the wanted signal above the noise threshold only signals belonging to the desired subnet will be recognized or acknowledged. A difference in PRF between transmitter devices and receiver devices results in less effective accumulation of energy and therefore serves as a rejection mechanism during acquisition of transmissions belonging to a different subnet. 
     In order to separate subnets without need for additional provisions in the header field, the nominal chip rate of 499.2 MHz can be changed. In this way, transceivers with different chip rate settings will be less likely to synchronize to each other and thereby avoid message collisions on level of the PHY layer [12]. 
     In order to support this feature up to the desired level of subnet decoupling, we define a grid of nominal chip rates being r chip *499.2 MHz, where r chip =1+200e−6*(100−N subnet ), and where N subnet ∈{0, 1, . . . , 200}. Overall, therefore, 201 different subnets are defined.