Abstract:
This invention modulates data onto a radio channel in such a way that the deleterious effects of the channel are reduced. This is accomplished in three steps: first, the information signal is modulated using a phase-differential modulation scheme. Second, the modulated signal is spread in both time and frequency by passing it through a dispersive filter, transmitting it through the channel, and removing the spreading using a dispersive filter in the receiver with the opposite characteristics of the filter in the transmitter. The third step, after demodulation, is to pass the signal through a low-pass filter to gather up the signal energy which has been dispersed by the channel. All three of these steps can be implemented with simple functional blocks, making this system very inexpensive to implement. Also included are two methods for enhancing the data throughput of the basic system, making it more bandwidth efficient.

Description:
BACKGROUND OF THE INVENTION 
   The reliable transmission of high data rate information through the short hop radio channel (i.e. a wireless channel having receiver-transmitter distance of less than 1 km) remains a complex and elusive engineering problem. The physical nature of the indoor radio channel causes random distortive effects that can render a communications system inoperable. The prior art includes many elaborate schemes that mitigate these effects, however they are generally very complex and unsuitable for applications requiring mobility and/or portability. 
   Nature has already solved this problem, however, in the form of bats. Bats use echolocation for nighttime navigation and face many of the same distortion effects that radio systems do. Through the process of evolution they have developed powerful probing signals called chirps, which overcome many of these effects. 
   The distortive effects referred to previously arise largely from the multipath nature of the radio channel, that is, a signal may travel from transmitter to receiver via many different paths. This is in contrast to a wired channel (a telephone line, for instance) in which a signal can only travel along a single path. Multipath occurs because the physical space between the receiver and transmitter is occupied by objects which reflect the radio signal. The reflections create echoes which appear at the receiver as copies of the original transmitted signal. These echoes have independent (i.e. random) amplitudes and delay times with respect to each other. At the receiver they add together to create an unpredictable total signal; this signal may also change with time as objects in the physical environment move about. 
   When multipath echoes add together as they do in the receiver of a wireless communications system, two main distortive effects can result. First, the addition of the delayed echoes at the receiver stretches out or disperses the original transmitted signal. This dispersion makes the transmitted symbols longer, and if adjacent symbols are not spaced far enough apart in time they can collide and Intersymbol Interference (ISI) can occur. Second, the periodic nature of the transmitted RF carrier along with the random delays of each echo can cause them to add destructively. Under the right conditions, this destructive interference (called fading) between echoes can cause reductions in the received power by a factor of 1000 or more. 
   The main engineering problem arising from these two effects has to do with their relationship to the transmitted signal&#39;s bandwidth. If the transmitted signal has a narrow bandwidth, (i.e. does not cover a large range of transmitted frequencies) the receiver will experience flat fading and the entire signal can sit within a fade for a short period of time. Under these conditions the communication system will not function correctly. This condition can be mitigated by widening the occupied bandwidth of the signal (i.e. so it covers a large range of frequencies). The simplest way to increase the transmitted signal&#39;s bandwidth is to increase the transmitted symbol rate. Unfortunately, increasing the symbol rate also reduces the time between symbols increasing the probability that dispersion in the channel will cause adjacent symbols to collide and produce ISI. This presents the dilemma of wireless data transmission: in order to reduce the possibility of flat fading the symbol rate must be increased to the point where ISI can occur. 
   The art of indoor wireless communications includes techniques that can utilize large bandwidths with respect to their symbol rate; these are commonly referred to as spread spectrum systems. These techniques overcome the paradox between intersymbol interference and flat fading. The two most popular spread spectrum methods, Direct Sequence and Frequency Hopping, both increase the signal&#39;s bandwidth by dividing the symbol time into smaller pieces and performing specific operations on each piece. This operation increases the occupied bandwidth of the system by whatever factor the symbol time was divided, thus eliminating flat fading effects. The cost of using spread spectrum is increased system complexity required for encoding, synchronization and decoding of the aforementioned pieces, which must occur at a much higher speed than the symbol rate. 
   SUMMARY OF THE INVENTION 
   In this invention, we propose the use of chirp signals (similar to those used by bats) to spread the bandwidth of the original data signal. There is a major difference between this technique and the conventional spread spectrum techniques used in indoor wireless communications, however, in that chirps spread the transmitted signal in both time and frequency rather than frequency alone. This means that the spread signal may have a longer duration than the original data symbol, despite the fact that the symbol rate remains the same. The overlap between adjacent symbols which results from this spreading is not a problem—chirps have a property called “time shift orthogonality” which allows two similar chirp signals to overlap in time provided they possess a small mutual time shift. The lengthening of the spread signals reduces the speed at which any signal processing has to operate as a result of the spread spectrum process. This results in a much simpler hardware realization despite its large occupied bandwidth. 
   This technique (called Chirp Spread Spectrum) has been used in RADAR systems and outdoor wireless communications. The first communications applications of such systems were suggested by Gott and Newsome[3] in 1971 for use in low data rate high-frequency radio communications systems over long distances. However, to date these systems have had low symbol rates and are optimized for channels which have very different characteristics from the indoor wireless channel. In the indoor channel, high data throughput for such applications as Local Area Networks (LANs) is desired, which results in very different requirements from known applications. 
   It is an objective of this invention to provide a novel method of overcoming the debilatative effects of multipath propagation in the indoor radio channel. Another objective of this invention is to include an embodiment that can be realized with simple analog hardware—analog systems have an advantage because they can be implemented in ways that are compact and power efficient at the high frequencies. In an aspect of the invention, there is provided also three hardware elements which are required to meet the above listed objectives. A feature of this invention is that when all three elements are implemented as described herein, no digital signal processing or additional diversity (i.e. antenna or coding) is required for reliable operation in the indoor multipath channel. 
   As well as the above listed features, this invention provides in a further aspect for two methods which can further increase the data throughput of the system described above with a small amount of additional hardware. The first method achieves this by increasing the ensemble of chirp spreading signals which are used and detecting each at the receiver. The second method utilizes an equalizer and a second phase demodulator to reduce the effects of ISI and allow a higher symbol transmission rate. The invention without the methods for increasing the data throughput will henceforth be referred to as the “basic system”. 
   In one embodiment, the invention operates as follows. A chirp signal is generated in which information is carried in the phase of the chirp signal. In a preferred embodiment, the information to be transmitted is first modulated using a known differential phase modulation scheme such as DPSK, DQPSK, D8PSK, etc. The process of modulation converts the data symbols to an RF carrier with some specific phase. It should be noted here that in the basic system the modulated symbol time must be longer than the delay spread of the channel to avoid intersymbol interference. This restricts the symbol time in the average indoor wireless channel to 100–500 ns, resulting in a symbol rate of from 2 to 10 MHz. 
   The phase modulated RF signal is then spread in both time and frequency using a dispersive filter. This filter can be any analog filter with appropriate delay characteristics but the preferred embodiment is a monolithic Surface Acoustic Wave (SAW) type filter due to its compactness. Along with the SAW filter a circuit for reduction of electromagnetic feedthrough (EMF) is included to increase the overall signal-to-noise ratio for the system. The output of the dispersive filter is the aforementioned chirp signal which may have time duration many times longer than the original data symbol. This chirp signal is then upconverted to the transmit frequency and sent over the channel. 
   Upon reception, the modulated chirp signal is downconverted from the transmit frequency to a frequency compatible with the receiver dispersive filter. In an aspect of the invention, after passing through a SAW filter whose dispersion characteristics are matched to the transmitter SAW, the original transmitted symbol will be spread into narrow pulses corresponding to each of the multipath “echoes” of the channel. These echoes will each have a unique phase and as such cannot be easily combined at this point. However, after differential phase demodulation they will have similar phase and may be added together, thus recombining the transmitted energy spread by the channel. 
   The addition of the multipath echoes in the receiver provides a simple yet effective form of diversity for the system. The structure used to add the echoes is known as a RAKE structure. The time diversity provided by the RAKE allows the system to function despite the changing nature of the channel. 
   In addition to the above, two methods may be included whereby the basic system can be enhanced to increase the data throughput. The first method utilizes an ensemble of chirp signals (in contrast to the single linear chirp used in the basic system) each of which is assigned a symbol value. Each of these chirp signals preferably has the same occupied bandwidth and processing gain. When a particular symbol value is to be transmitted, the chirp signal assigned that particular symbol value is used for spreading the differentially phase modulated information signal. The receiver will have the capacity to detect every one of the ensemble of chirp signals used in transmission; thus the chirp signal used by the transmitter will be detected and the symbol value assigned to it recovered. In this way extra data can be conveyed between the transmitter and receiver without affecting the characteristics of the original differentially phase modulated signal. 
   The second method utilizes an equalizer in the receiver to reduce the Intersymbol Interference (ISI) between successive symbols thus permitting symbols to be transmitted closer together in time. A slow demodulator (i.e. long symbol time) is used to train the equalizer and a fast demodulator (i.e. short symbol time) is used to transmit the information symbols. This method utilizes the inherent high channel resolution provided by the compressed chirp signals to train the equalizer. Once trained, the equalizer will reduce ISI between successive symbols permitting faster data rates. 
   The objects listed at the beginning of this summary and the system functioning will become more apparent upon consideration of the following detailed description, when read in conjunction with the attached drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     There will now be described preferred embodiments of the invention, with reference to the drawings, by way of example and without intending to limit the generality of the claims, in which like reference characters denote like elements and in which: 
       FIG. 1  is a schematic of the transmitter portion of the invention. Included are signals which would be seen at the various stages of the device. 
       FIG. 2  is a block diagram of the receiver portion of the invention. Included are signals which would be seen at the various stages of the device. 
       FIG. 3  is a schematic diagram of the I-Q modulator and RF switch used in the transmitter. 
       FIG. 4  is a schematic diagram of the dispersive filter block used in both the receiver and transmitter. 
       FIG. 5  is a schematic diagram of the analog differential phase demodulator used in the receiver. 
       FIG. 6  is a schematic diagram of the transmitter portion of the device with the data throughput enhancement feature. 
       FIG. 7  is a schematic diagram of the receiver portion of the device with the first data throughput enhancement feature (nonlinear chirps). 
       FIG. 8  shows one embodiment of the group delay characteristics for the transmitter and receiver dispersive filters for both linear and nonlinear chirp configurations. It also has examples of waveforms produced by those filters. 
       FIG. 9  shows a schematic diagram of the receiver portion of the device with the second data throughput enhancement feature (equalizer). 
       FIG. 10  shows the transmitted symbol sequence which is required by the second data throughput enhancement feature. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The basic apparatus which performs the operations described above consists of a transmitter ( FIG. 1 ) and a receiver ( FIG. 2 ). The transmitter&#39;s function is to modulate the data onto chirp signals and transmit these signals over the channel. The receiver&#39;s function is to recover the transmitted signal and reconstruct the original transmitted data.  FIG. 6  and  FIG. 7  show the transmitter and receiver schematics for the first enhanced version of the device, and  FIG. 9  shows the receiver schematic for the second enhanced version of the device. 
   The schematic diagram of the basic transmitter is shown in  FIG. 1 . Also included in  FIG. 1  are approximate plots of the signals at each stage of the device. Data from a data source  10  (which may be a computer or other digital information producing device) is fed into a differential phase modulator  12  which differentially encodes it onto a carrier. The encoding scheme should be a differential phase modulation scheme such as DPSK, DQPSK or one of higher order (see [4] for details). This carrier is then converted from a continuous wave to one which is pulsed in nature through RF pulse  14 . Data source  10 , differential phase modulator  12  and RF pulse  14  together comprise a chirp signal generator. The conversion process increases the bandwidth of the modulated wave. The switched pulse will have a period equal to the symbol time of the information signal and to provide sufficient bandwidth (wide enough to probe the SAW filter completely) the on-time of the switched pulse should be from 10–20 nS. The duty cycle of the pulsed signal is typically short, for example, about 8%. The carrier frequency of the modulated wave must be compatible with the centre frequency of the dispersive filter  16 . The pulsed modulated signal is then passed through dispersive filter  16  which spreads the pulse out in time. The output of the dispersive filter  16  is the aforementioned chirp signal. The output of the dispersive filter  16  is then upconverted from the carrier frequency used in dispersive filter  16  to the desired transmit frequency and amplified through RF upconverter  18 , after which antenna  20  transmits it over the wireless channel. RF upconverter  18  and antenna  20  together comprise an RF section. 
   The schematic diagram of the basic receiver is shown in  FIG. 2 . The transmitted signal is picked up by the receive antenna  22 , amplified and downconverted by the RF downconverter  24  from the transmit frequency to a carrier frequency compatible with the dispersive filter  26 . The output of the RF downconverter  24  is passed through receiver dispersive filter  26  which is similar in configuration to transmitter dispersive filter  16 . The difference between dispersive filters  16  and  26  is that they have reciprocal group delay characteristics. The signal seen at the output of dispersive filter  26  is the resolved overlapping chirp signals corresponding to the multipath characteristics of the channel centered at the RF carrier frequency of the dispersive filter. The output of dispersive filter  26  is then demodulated using differential phase demodulator  28  to produce an Inphase (I) and a Quadrature (Q) component each consisting of cophased channel impulse responses with the phase information signal modulated on them. This baseband channel impulse response is then integrated through low-pass filters  30  and the resultant symbols are extracted and recovered using data extractor  32 . Elements  28 ,  30  and  32  together comprise a data recovery section. 
     FIG. 3  shows a detailed schematic diagram of the phase modulator block  12  and the RF pulse circuitry  14 . The data source  10  will produce differentially encoded Inphase (I) and Quadrature (Q) data components according to a differential quadrature phase modulation scheme [4]. The baseband differential phase modulator  12  converts the encoded data from the data source  10  into a differentially phase encoded RF carrier. An I-Q modulator consisting of double-balanced mixers  38  and  40  and 90° phase shifter  36  upconverts the baseband I-Q signal produced by the data source  10  to a carrier frequency compatible with the dispersive filter  16 . A local oscillator  34  controls this centre frequency. After adding the I and Q components with summer  42 , the signal at the appropriate carrier frequency is passed through a single pole single throw (SPST) RF switch  44 . 
   The switching action for the RF switch  44  is controlled by a monostable multivibrator  46 . The time constant of monostable  46  can be set to control the width of the RF pulse produced by RF switch  44 . Typically, a switching time of from 10–20 ns is desired, thus a high speed logic family such as Emitter Coupled Logic (ECL) is the preferred embodiment for monostable  46 . The clock line for monostable  46  (which triggers the start of the RF pulse) is supplied by the data source  10  and must be synchronized with the start of each data symbol. The output of RF switch  44  is fed into dispersive filter  15 . 
     FIG. 4  shows a detailed schematic diagram of the dispersive filter block used in both transmitter dispersive filter  16  and receiver dispersive filter  26 . Dispersive filter block  16  and  26  is fed with a carrier signal from the RF pulse  14  in the transmitter and RF downconverter  24  in the receiver. This signal is a modulated data signal at the appropriate carrier frequency for dispersive filter  16  and  26 . A cancellation circuit is utilized to remove unwanted signals which result from electromagnetic feedthrough (EMF) between the input to the output of the SAW filter. The carrier input signal is split into two separate paths, one of which goes through dispersive SAW filter  48  and the other through amplifier  46 . Amplifier  46  is chosen such that its gain exactly matches the gain of dispersive SAW filter  48  with a phase shift of 180° relative to dispersive SAW filter  48 . The output of amplifier  46  and dispersive SAW filter  48  are then summed with summer  50  and the filtered signal output is fed to the RF upconverter  18  in the transmitter or phase demodulator  28  in the receiver. 
   This cancellation technique described above is well known in the art and is employed in this invention to eliminate unwanted spurious signals from feeding through dispersive SAW filter  48 . Because the input signal to transmitter dispersive filter block  16  is pulsed, RF coupling between the input and output ports of the filter can cause the signal produced by the RF pulse  14  to jump across the terminals of dispersive SAW filter  48 . In the receiver dispersive filter  26 , the cancellation technique is used to further reduce unwanted signals; this increases the system&#39;s signal to noise ratio and reduces the errors during demodulation. 
     FIG. 5  shows a schematic diagram of the receiver demodulator circuit. The signal from receiver dispersive filter  26  is split into two streams each of which feed into a double balanced mixer  56  and  60 . This same signal is passed through delay  54  whose delay time is equal to the symbol time of incoming data. Thus the symbol time of the system must be known by the receiver a priori. The embodiment of delay  54  can be a delay line, a SAW filter or simply a cable with the appropriate propagation time. The signal from delay  54  is fed into double balanced mixer  56  and through 90° phase shifter  58 . The output of the 90° phase shifter  58  feeds into the second double balanced mixer  60 . As a result of the mutual phase shift between the two double balanced mixers  56  and  60  caused by 90° phase shifter  58 , the output of double balanced mixer  56  will be the Inphase (I) component of the signal, and the output of double balanced mixer  60  will be the Quadrature (Q) component of the signal. Both of the I and Q components are fed through low-pass filters  30 , which integrate the symbol energy and reproduces the transmitted data symbol. After low-pass filter  30  a data extractor  32  then extracts the data symbol by looking for the peak of the signal coming out of low-pass filter  30  and sampling the symbol at the appropriate point. 
   Low-pass filter  30  can have many different embodiments—digital filters as well as analog low-pass designs can be used, provided the cutoff frequency of the low-pass filter is equal to one over the symbol time of the data signal. If an analog filter is used for low-pass filter  30 , reductions in hardware complexity can be achieved. The preferred embodiment for low-pass filter  30  is a 2-pole butter worth low-pass configuration. 
     FIG. 6  shows a schematic diagram of an embodiment of the transmitter which has been modified to increase data throughput of the system through the use of nonlinear chirps. Data source  62 , differential modulator  12  and RF pulse  14  are identical to data source  10  differential phase modulator  12  and RF pulse  14  in the basic system, with the exception that additional data lines from data source  62  control multiplexer  64 . The output signal from RF pulse  14  feeds into analog multiplexer  64  which is controlled by data source  62 . The analog multiplexer  64  will switch the output of RF pulse  14  into one of N dispersive filters  66  of a dispersive filter bank, according to a control line produced by data source  62 . Each of the filters in the dispersive filter bank  66  is designed to produce a different nonlinear chirp signal. Thus the analog multiplexer  64  will cause a different chirp signal to be transmitted according to the state of the control line from data source  62 . The signals from each of dispersive filters of the dispersive filter bank  66  is added together with adder  68  and fed into RF upconverter  18  and antenna  20  before being transmitted over the channel. 
     FIG. 7  shows a schematic diagram of the receiver embodiment which has been modified to match the increased throughput transmitter of  FIG. 6 . As with the receiver in the basic system, antenna  22  captures the transmitted signal which is then amplified and downconverted to a useful carrier frequency by RF downconverter  24 . At this point the signal is split into the same number of paths as are dispersive filters in dispersive filter bank  66  in the transmitter. Each path contains a dispersive filter  68 , a phase demodulator  28  low-pass filters  30  and data extractor  32 . The only difference between the various paths is that each dispersive filter  68  will be matched to a single dispersive filter in the transmitter dispersive filter bank  66 . For example, dispersive filter #1 in the receiver  68  will be matched to dispersive filter #1 in the transmitter dispersive filter bank  66 . After data extractor  32  provides the data output from each of the dispersive filters  68 , a data multiplexer  72  determines which filter bank has the highest output signal level. In so doing, the receiver can determine the state of the data line feeding the multiplexer  72  in the transmitter, thereby increasing the number of bits per symbol of the system. After combining this data with the data obtained through phase demodulator  28 , low-pass filter  30  and data extractor  32 , the entire data symbol can be sent to whatever device needs to utilize the information. 
     FIG. 8  shows an embodiment of the time-frequency characteristics of the transmitter dispersive filter  16  and the receiver dispersive filter  26  (the linear case), as well as an embodiment for the enhanced transmitter dispersive filter  68  and the enhanced receiver dispersive filter  68  (the nonlinear case). In the linear case, the transmitter filter delay characteristics  76  and the receiver filter group delay characteristics  80  must have opposite slopes so that their mutual group delay is constant. At the transmitter, linear chirp waveform  74  will be produced which is the desired signal to be transmitted over the channel. At the receiver this signal will be processed through receiver dispersive filter  26  to produce a narrow pulse,  78 . It is this narrow pulse that allows the multipath of the channel to be resolved. 
   In the nonlinear case, a complex function  84  describes the group delay characteristics of both the transmitter dispersive filter  66  and the receiver dispersive filter  68 . Many different embodiments of the transmitter delay  84  and the receiver delay  88  may be used, provided they are chosen such that their mutual delay is constant. As with linear chirp  76 , a transmitter chirp waveform  82  will be produced which is the desired signal to be transmitted over the channel. At the receiver this signal will be processed through receiver dispersive filter  68  to produce a narrow pulse,  86 . 
   In linear chirp case  76 , rather than have transmitter dispersive filter  16  with a group delay which has the negative of the slope of the receiver dispersive filter  26 , the receiver RF downconverter  24  can employ sideband inversion with respect to the transmitter (i.e. the local oscillator chosen such that is centre frequency is the RF carrier frequency plus IF frequency while the transmitters local oscillator is the RF frequency minus the IF frequency), this is a technique well known in the art. If sideband inversion is used in the receiver RF downconverter  24 , then identical linear SAW filters can be used in both receiver and transmitter. This embodiment is preferred since it improves phase matching between the receiver and transmitter dispersive filters  16 ,  26 . In the case of nonlinear chirps, sideband inversion cannot generally be used. 
   Since the multipath nature of the channel is resolved by receiver dispersive filter  26 , it is the channel dispersion which determines the minimum time between symbols and the maximum symbol rate. Symbols must be transmitted at a rate no greater than the total delay spread of the channel to avoid intersymbol interference (ISI). Despite the fact that the symbol rate is essentially fixed for a given set of channel characteristics, the data throughput can be increased both by the use of the throughput enhanced embodiment ( FIG. 6  and  FIG. 7 ) and by increasing the constellation size of the differential modulation scheme. For instance, a system using DPSK can be increased to DQPSK, DQPSK can be raised to D8PSK, and so forth. 
     FIG. 9  shows the schematic diagram of the receiver embodiment which has been modified to increase data throughput of the system using an equalizer. As with the basic system embodiment, an antenna  90 , an RF downconverter  92  and a dispersive filter  94  perform the receiver front-end signal capture and processing. Unlike the basic system, this embodiment has two phase demodulators; a slow phase demodulator  98  whose delay T  54  is large with respect to the channel excess delay, and a fast demodulator  96  whose delay is small with respect to the channel excess delay. The only difference between the two phase demodulators  98  and  96  is their delay. The slow phase demodulator  98  is used to obtain the channel multipath profile. The slow phase demodulator  98  provides the reference signal for I and Q equalizers  100  and  102 . The fast phase demodulator provides the input signal for I and Q equalizers  100  and  102 . 
   Equalizers  100  and  102  are designed to suppress or remove intersymbol interference (ISI), many different equalizer topologies are possible. Using equalizers to remove ISI in this way is a technique well known in the art, and thus the details of equalizers  100  and  102  are not discussed herein. For more detailed information [5] can be consulted. 
   After equalization and ISI removal, the I and Q signals are filtered through lowpass filters  106  and  104  respectively. The outputs of low-pass filters  106  and  104  are then fed into a data extractor  108 , wherein the information bits are extracted as with the basic system. 
     FIG. 10  demonstrates the preferred embodiment of the transmit data format which can be used to ensure proper equalizer functionality. In this embodiment, some number of training symbols M are transmitted at the beginning of each data block. The received version of these symbols  110  will consist of a known data sequence, (“1”s, for instance) convolved with the channel impulse response. The time between these symbols  110  will be chosen such that they are farther apart than any anticipated excess delay introduced by the channel (i.e. there is no possibility of ISI during the training symbols). During this so-called “training sequence” equalizers  106  and  104  utilize the outputs of the slow phase demodulator  98  for training the equalizers  106  and  104 . The number of training symbols M transmitted depends on the characteristics of the particular equalizer used for the implementation of  106  and  104 . 
   After training, information symbols  112  are transmitted with an intersymbol time which is much shorter that the channel excess delay. These symbols will typically overlap and suffer ISI until passed through equalizers  100  and  102 . After equalization, ISI caused by channel spreading will be reduced and the bit error rate of the received data will be improved. In this way the time between symbols can be made shorter than without the equalization and the information throughput rate of the system can be increased. 
   REFERENCES 
   
       
       [1] Campbell, C.: ‘Surface Acoustic Wave Devices and Their Signal Processing Applications’, (Academic Press, Boston, 1989). 
       [2] Pinkney, J., Behin, R., Sesay, S., and Nichols, S.: ‘A High-Speed DQPSK Chirp Spread Spectrum System for Indoor Wireless Applications’, Electronics Letters, October 1998, 34, (20), pp. 1910–1911 
       [3] Gott, G. F and Newsome, J. P.: ‘H. F. Data Transmission Using Chirp Signals’,  Proc. IEE , September 1971, 118, (9), pp. 1162–1166. 
       [4] Proakis, J. G.: ‘Digital Communications’, (McGraw-Hill, New York, 1995). 
       [5] Haykin, S.: ‘Adaptive Filter Theory’, (Prentice Hall, New Jersey, 1996). 
     
  
   Immaterial modifications may be made to the invention described here without departing from the essence of the invention.