Demodulation unit and method for demodulating a DPSK signal

A demodulation unit for recovering a transmitted symbol from a received signal that has been modulated using an MDPSK modulation scheme is described. The demodulation unit is configured to, for a current time instant, derive a current sample of a phase signal indicative of a phase of the received signal. Furthermore, the demodulation unit is configured to determine a set of discrimination signals for the current sample of the phase signal, based on the current sample of the phase signal and based on one or more previous samples of the phase signal for one or more previous time instants. In addition, the demodulation unit is configured to determine the transmitted symbol for the current time instant based on the set of discrimination signals.

TECHNICAL FIELD

The present document relates to recovering data from a modulated signal that has been transmitted over a noisy transmission network. In particular, the present document relates to the reliable and robust demodulation of a DPSK (Differential Phase Shift Keying) modulated signal that has been transmitted over a noisy transmission network.

BACKGROUND

Data, notably symbols comprising two or more bits, may be modulated onto a carrier signal using a modulation scheme such as DPSK, in order to generate a modulated signal for transmission over a transmission network. At the receiver the data may be recovered from the (distorted) modulated signal using a demodulation scheme.

SUMMARY

The present document addresses the technical problem of providing a reliable and robust demodulation scheme for a MDPSK modulated signal. The technical problem is solved by the independent claims. Preferred examples are described in the dependent claims.

According to an aspect, a demodulation unit for recovering a transmitted symbol from a received signal that has been modulated using an M-ary Differential Phase Shift Keying, MDPSK, modulation scheme is described. The demodulation unit is configured to derive a current sample of a phase signal indicative of the phase of the received signal. Furthermore, the demodulation unit is configured to determine a set of discrimination signals for the current sample of the phase signal, based on the current sample of the phase signal and based on one or more previous samples of the phase signal for one or more previous time instants. In addition, the demodulation unit is configured to determine the transmitted symbol for the current time instant based on the set of discrimination signals.

According to another aspect, a method for recovering a transmitted symbol from a received signal that has been modulated using an M-ary Differential Phase Shift Keying, MDPSK, modulation scheme is described. The method comprises deriving a current sample of a phase signal indicative of the phase of the received signal. In addition, the method comprises determining a set of discrimination signals for the current sample of the phase signal, based on the current sample of the phase signal and based on one or more previous samples of the phase signal for one or more previous time instants. Furthermore, the method comprises determining the transmitted symbol for the current time instant based on the set of discrimination signals.

According to a further aspect, a software program is described. The software program may be adapted for execution on a processor and for performing the method steps outlined in the present document when carried out on the processor.

According to another aspect, a storage medium is described. The storage medium may comprise a software program adapted for execution on a processor and for performing the method steps outlined in the present document when carried out on the processor.

According to a further aspect, a computer program product is described. The computer program may comprise executable instructions for performing the method steps outlined in the present document when executed on a computer.

It should be noted that the methods and systems including its preferred embodiments as outlined in the present document may be used stand-alone or in combination with the other methods and systems disclosed in this document. In addition, the features outlined in the context of a system are also applicable to a corresponding method. Furthermore, all aspects of the methods and systems outlined in the present document may be arbitrarily combined. In particular, the features of the claims may be combined with one another in an arbitrary manner.

DETAILED DESCRIPTION

As outlined above, the present document is directed at providing a reliable and robust demodulation scheme for a DPSK modulated signal. M-ary Differential Phase Shift Keying (MDPSK or DMPSK) may be referred to be differentially encoded and differentially coherently demodulated MPSK (M-ary Phase Shift Keying). The differential coherent demodulation is a noncoherent demodulation scheme, which means that phase coherent reference signals are not needed for demodulation. This feature makes the demodulation process of MDPSK typically simpler than the demodulation of MPSK. On the other hand, this may degrade the performance.

FIG. 1Ashows an example transmission system100which comprises a modulation unit110and a demodulation unit120. The modulation unit110is configured to encode input data111(notably a sequence of bits) into a sequence112of symbols. The sequence112of symbols is modulated onto a carrier signal which is transmitted over a transmission network101.

The transmitted, modulated carrier signal may be sampled to recover a sequence122of symbol samples. The demodulation unit120may be configured to recover the output data121(which should be equal to the input data111) based on the sequence122of symbol samples.

The MDPSK modulation scheme may be used in various different applications, notably due to its power spectral efficiency. In the Wireless LAN specification IEEE 802.11b, DBPSK and DQPSK may be used, depending on the required data rate. ZigBee makes use of DBPSK at 868/915 MHz. Bluetooth makes use of

π4
DQPSK and 8DPSK in it version 2+ EDR (Enhanced Data Rate). For relatively small values of M, the following alias terms may be used: B=binary (M=2) and Q=quarternary (M=4). For relatively high values of M, the numeric value may be used in the naming of the modulation scheme.

In the following, the modulation schemes that are used in Bluetooth are considered as examples. It should be noted, however, that the methodology may be used for any other MDPSK modulation scheme. The

π4
DQPSK modulation scheme and the 8DPSK modulation scheme are described herein as examples. Furthermore, the demodulation scheme, which is described herein, is described using the above-mentioned example modulation schemes.

Qlog2⁡(M).
Each symbol Bncorresponds to a prescribed phase change Δφn, as defined by the mapping table or constellation diagram of the MDPSK modulation scheme. The mapping between the binary input bq, q=1, 2, . . . . Q, the data symbol Bnand the phase difference Δφnis illustrated in Table 1 for

π4
DQPSK and in Table 2 for 8DPSK. The relation between Bnand bqin Tables 1 and 2 may be obtained using Gray coding.

A sequence of symbols Bnmay be represented by a sequence of complex values sn, situated on the unit circle and in which s0=1+0i or some other arbitrary value of magnitude1. Additionally, to improve the performance a Gray coding is usually applied. The signal snmay be defined as
sn=sn-1ejΔφn,n∈+,s0=1  (1)
wherein the phase difference values Δφnmay be obtained using the underlying mapping table of the modulation scheme.

As may be seen fromFIG. 1B, the

π4
DQPSK modulation scheme alternatively selects the modulated signal points from two QPSK constellations that have a phase of

π4.
In particular,FIG. 1Bshows the constellation diagram150of the

π4
DQPSK modulation scheme, wherein the constellation diagram150indicates which set of target constellation points152may directly follow a source constellation point151. Hence.FIG. 1Bshows the possible transitions153between a source constellation point151and the possible target constellation point152(according to the possible phase difference values Δφn). As can be seen fromFIG. 1B, the signal constellation of

π4
DQPSK does not snow transitions153from one symbol151to another symbol152, which go through the origin of the constellation diagram150, indicating that the envelope of this modulation scheme exhibits less variations than the envelope of DQPSK without the

π4
DQPSK modulation scheme may be differentially demodulated. For

π4
DQPSK with Gray coding, the BEP (Bit Error Probability) Pbmay be approximated using

Pb≈Q⁡(1.176·EbN0)(2)
where Q(·) is the Gaussian distribution Q-function and where

EbN0
is the bit energy-to-noise density ratio.

Unlike the

π4
DQPSK, the 8DQPSK modulation uses all modulated signal points in the constellation150as shown inFIG. 1C. Hence, a transition153from one symbol151to another symbol152may go through the origin. The 8DPSK modulation scheme may be differentially demodulated. The BEP for 8DPSK with Gray coding Pbis given by

Pb=2log2⁡(M)⁢Q⁡(2·log2⁡(M)·EbN0⁢sin⁡(π2⁢M))(3)
where M=8. It should be noted that equation (3) may be approximately

In the present document, a demodulation scheme is described which exploits the fact that successive symbols are typically not (entirely) independent from one another, due to the fact that the phase differences Δφnof successive symbols follow a specific trajectory imposed by the modulation scheme. As a result of this, the probability distribution of the possible target symbols152following a source symbol151is typically non-uniform. In particular, a demodulation scheme is described which is directed at mapping a trajectory of successive symbols to the closed possible trajectory of symbols, in order to compensate for a symbol error. By doing this, benefit can be taken from the entire trajectory of symbols.

In particular, a MDPSK demodulator120using Viterbi algorithm is described, wherein the Viterbi algorithm may be used for exploiting the correlation between successive symbols151,152. Hence, the demodulator considers the memory in the modulation schemes. By using this feature, the same error probability may be achieved for a bit energy-to-noise density ratio that is 1 to 1.5 dB lower than a demodulation scheme that does not exploit the correlation between successive symbols151,152.

FIG. 2shows a block diagram of the demodulator or demodulation unit120. The ADC (Analog-to-Digital Converter) of the receiver may be configured to provide the samples122of the received signal as a fixed amplitude cosine (I), i.e. in-phase component, and sine (Q), i.e. quadrature component, of a baseband carrier with frequency modulation. After filtering the signal to reduce the noise level, the PM (phase modulation) signal φ(n)201may be obtained from the I-Q samples122. It should be noted that some receivers may be configured to deliver the baseband PM signal201directly from the received signal, in which case the I-Q samples are not relevant. By making use of the PM signal201, the demodulation scheme may be adapted in a flexible manner to different MDPSK constellations150. Furthermore, the computational complexity may be reduced.

The demodulation unit120comprises a discrimination signal generator Dm(φ)202which is configured to convert the PM signal201into m signals that contain information about the current data symbol and its m−1 predecessors. The knowledge about this history allows correction of errors in the symbol stream, thereby decreasing the error probability for the same bit energy to noise density ratio. The discrimination signals may be generated from the PM signal201in a flexible and efficient manner using the following formula
dm[n]=φ[n]−φ[n−m·Ns]  (4)
wherein Nsis the oversampling rate. Hence, for a time instant n, m different discrimination signals dm[n]203may be generated, wherein the different discrimination signals dm[n]203also depends on the PM signal201at a time instant n−m·Nsprior to the time instant n.

The discrimination signals203may be fed into an estimation unit204which is configured to estimate the transmitted nthsymbol {circumflex over (B)}[n]205based on the set of discrimination signals203. The estimation unit204may be configured to estimate the most likely symbol {circumflex over (B)}[n]205, taking into account one or more previously estimated symbols {circumflex over (B)}[n−1], {circumflex over (B)}[n−2], . . . . The estimation unit205may make use of the Viterbi algorithm.

π4
DQPSK modulation scheme may be considered as an example. By assuming m=2, Table 3 may be generated, which indicates the to-be-expected (i.e. target) discrimination signals203for different sequences (notably pairs) of symbols151,152. Table 3 may be considered to be the

As can be seen from Table 3, d1[n] is equivalent to Δφnin Table 1. On the other hand, the signal d2[n] is the phase difference between symbol n and symbol n−2.

Using Table 3, a 16 state-Viterbi trellis diagram may be generated. Each state in the trellis exhibits four branches as an output with a cost function c as given in (5)
c[n]=|wrapToPi(d1[n]−{circumflex over (d)}1[n]|+|wrapToPi(d2[n]−{circumflex over (d)}2[n])|  (5)
where {circumflex over (d)}1[n] and {circumflex over (d)}2[n] are the calculated discrimination signals203based on the received phase signal201, including noise. Equation (5) can be generalized as:

c⁡[n]=∑m=1Z⁢wrapToPi⁡(dm⁡[n]-d^m⁡[n])(6)
where the function wrapToPi(α) wraps the angle α in radians in the interval [−π, π], and where m=1, . . . , Z, with Z>1.

It is clear from Table 3 that the received sequence of symbols can be represented in a state diagram. This state diagram has the property that from any specific state only four state transitions (in general M transitions for an MDPSK modulation scheme) to four other states (in general M states) out of the available 16 states (in general Mm) are possible. Hence, if an error occurs at the receiver from a specific state to one of the 12 unexpected states, this error can be recovered by the Viterbi algorithm.

The same methodology can be applied on 8DPSK and to any MDPSK modulation scheme. In 8DPSK modulation scheme, the Viterbi trellis diagram has 64 states. Each state in the trellis diagram has 8 branches with the same cost function as shown in (5) or (6).

Generally, the MDPSK Viterbi demodulator120comprises Mmstates and Ltbtrace back length. The trace back length Ltb=M for optimal performance. At each state, the survival path may be selected, which is the minimum of c[n] plus the previous path metric, i.e. with the minimal cumulated cost.

The maximum likelihood sequence is the sequence that has the minimum path metric accumulation (i.e. the minimum cumulated cost) over Ltbbits,

It can be shown that using the scheme outlined in the present document, the bit error rate (BER) may be reduced (compared to a conventional demodulator).

As indicated above, oversampling may be applied for determining the PM signals201and the discrimination signals203. The estimation unit204, notably the Viterbi algorithm, may be executed in the down-sampled domain, thereby reducing the computational complexity and power consumption.

Hence, a demodulation unit120for recovering a transmitted symbol205from a received signal122that has been modulated using an M-ary Differential Phase Shift Keying, DPSK, modulation scheme is described. The MDPSK modulation scheme may be a

π4
DQPSK modulation scheme or a 8DPSK modulation scheme.

The demodulation unit120may be configured to, for a current time instant, derive a current sample of a phase signal201indicative of a phase of the received signal122. For this purpose, the demodulation unit may be configured to determine an in-phase sample of the received signal and to determine a quadrature sample of the receive sample. The current sample of the phase signal may then be determined based on the in-phase sample and based on the quadrature sample.

Furthermore, the demodulation unit120may be configured to determine a set of discrimination signals202for the current sample of the phase signal201, based on the current sample of the phase signal201and based on one or more previous samples of the phase signal201for one or more previous time instants. The set of discrimination signals202may comprise two or more discrimination signals202.

In addition, the demodulation unit120may be configured to determine the transmitted symbol205for the current time instant based on the set of discrimination signals202. In particular, the transmitted symbol205for the current time instant may be determined based on the set of discrimination signals202using a maximum likelihood detection scheme, notably using the Viterbi algorithm.

The demodulation unit120makes use of multiple samples of the phase signal201at multiple different time instants, thereby exploiting correlations between the transmitted symbols at multiple different time instants. By doing this, the robustness and the reliability of demodulation may be improved.

The demodulation unit is typically configured to derive a current sample of the phase signal201, to determine a set of discrimination signals202, and to determine the transmitted symbol202for a sequence of current time instants, thereby iteratively recovering a sequence of transmitted symbols205for a corresponding sequence of current time instants n.

The demodulation unit may be configured to determine a first discrimination signal202{circumflex over (d)}1[n] based on the current sample of the phase signal for the current time instant n and based on a previous sample of the phase signal201for a first previous time instant, notably n−1. In addition, a second discrimination signal202{circumflex over (d)}2[n] may be determined based on the current sample of the phase signal201for the current time instant n and based on a previous sample of the phase signal201for a second previous time instant, notably n−2. The transmitted symbol205for the current time instant n may then be determined in a reliable and robust manner based on the first discrimination signal202and based on the second discrimination signal202.

In particular, the set of discrimination signals {circumflex over (d)}m[n]202, with m=1, . . . , Z, and with Z>1, for the current time instant n may be determined as
{circumflex over (d)}m[n]=φ[n]−φ[n−m·Ns]
wherein φ[n] is the current sample of the phase signal201for the current time instant n; wherein φ[n−m·Ns] is the previous sample of the phase signal201for the previous time instant n−m·Ns; and wherein Nsis an oversampling factor with Ns≥1. It should be noted, that if oversampling (Ns>1) is used, then sub-time instants k may be used. Oversampling may be used to further increase the reliability and robustness of demodulation.

The demodulation unit120may be configured to determine the transmitted symbol205for the current time instant n in dependence of a truth table which is indicative of a plurality of target sets of discrimination signals dm[n] for a corresponding plurality of sets of possibly transmitted symbols. An example truth table for the

π4
DQPSK modulation scheme is shown in Table 3. The truth table depends on the constellation diagram150and/or on possible transitions153between constellation points151,152of the constellation diagram150of the MDPSK modulation scheme. By taking into account a truth table for the set of discrimination signals202, a particularly precise and reliable demodulation may be achieved.

The demodulation unit120may be configured to determine a plurality of cost values of a cost function for the corresponding plurality of target sets of discrimination signals [n]. The cost function for a particular target set of discrimination signals dm[n] may be indicative of a deviation of the determined set of discrimination signals dm[n]202from the particular target set of discrimination signals dm[n]. The cost function may comprise an accumulation of the magnitude of the deviation, e.g. of the square root of the sum of the deviations. The cost function may make use of a weighing function for the different deviation terms.

In particular, the cost function c[n] for the particular target set of discrimination signals dm[n] may be determined as

The demodulation unit120may be configured to determine the transmitted symbol205for the current time instant n in dependence of the plurality of cost values of the cost function for the corresponding plurality of target sets of discrimination signals dm[n]. By way of example, the transmitted symbol205(i.e. the most probable symbol) may be selected based on the minimum cost. In particular, the demodulation unit120may be configured to determine the transmitted symbol205for the current time instant n in dependence of the minimum of the plurality of cost values of the cost function for the corresponding plurality of target sets of discrimination signals dm[n], notably in dependence of the transition153between constellation points151,152of the constellation diagram150of the MDPSK modulation scheme that corresponds to the minimum of the plurality of cost values of the cost function for the corresponding plurality of target sets of discrimination signals dm[n]. As a result of this, the robustness and the reliability of demodulation may be increased further.

The demodulation unit120may be configured to populate a state trellis for the current time instant n using the plurality of cost values of the cost function for the corresponding plurality of target sets of discrimination signals dm[n]. The state trellis comprises a plurality of different states for the corresponding plurality of target sets of discrimination signals dm[n]. In particular, the state trellis comprises Mmdifferent states. The state trellis may be indicative of cumulated cost values for the plurality of different states of the state trellis for the previous time instant n−1.

The demodulation unit120may be configured to determine the cumulated cost values for the plurality of different states of the state trellis for the current time instant n based on the cumulated cost values for the plurality of different states of the state trellis for the previous time instant n−1 and based on the plurality of cost values of the cost function for the corresponding plurality of target sets of discrimination signals dm[n]. Furthermore, the demodulation unit120may be configured to determine the transmitted symbol205for the current time instant n based on cumulated cost values associated with the plurality of different states of the state trellis for the current time instant n. As a result of this, correlations between successive symbols may be exploited in a particularly reliable manner, thereby increasing the reliability and the robustness of demodulation.

FIG. 3shows a flow chart of an example (notably computer-implemented) method300for recovering a transmitted symbol205from a received signal122that has been modulated using an M-ary Differential Phase Shift Keying, MDPSK, modulation scheme. The method may be repeated in an iterative manner for a sequence of current time instants, in order to recover a corresponding sequence of transmitted symbols205.

The method300comprises, for a current time instant, deriving301a current sample of a phase signal201indicative of the phase of the received signal122. Furthermore, the method300comprises determining302a set of (two or more) discrimination signals202for the current sample of the phase signal201, based on the current sample of the phase signal201and based on one or more previous samples of the phase signal201for one or more previous time instants. In addition, the method300comprises determining303the transmitted symbol205for the current time instant based on the set of discrimination signals202. By making use of samples of the phase signal201at multiple time instants for recovering the transmitted symbol205at the current time instant, recovery of the transmitted symbol205may be performed in a particularly reliable manner.