GB2524944A

GB2524944A - Low complexity GMSK receiver for fast varying channels and narrow bandwidth channels

Info

Publication number: GB2524944A
Application number: GB1403211.4A
Authority: GB
Inventors: Brian Gaffney
Original assignee: Neul Ltd
Current assignee: Huawei Technologies Research and Development UK Ltd
Priority date: 2014-02-24
Filing date: 2014-02-24
Publication date: 2015-10-14
Also published as: CN104869088A; GB201403211D0

Abstract

In a modulated (eg. Gaussian Minimum Shift Keying GMSK) signal decoder subject to Intersymbol Interference (ISI), the signal is filtered to form a sample representing a symbol, comprising a weighted sum of the symbol and its immediate predecessor and successor, then multiplied by a complex sinusoid having, at integer multiples of (eg. four times) the symbol interval, alternately: (i) a zero real component and a non-zero imaginary component and (ii) a non-zero real component and zero imaginary component, to generate a complex value. A constellation may then be generated and the differences to an expected constellation tracked in order to decode the final symbol.

Description

LOW COMPLEXITY GMSK RECEIVER FOR FAST VARYING CHANNELS AND

NARROW BANDWIDTH CHANNELS

This invention relates to a method and apparatus for decoding a signal suffering from intersymbol interference.

Gaussian Minimum Shift Keying (GMSK) is a continuous phase modulation scheme in which the phase of the carrier signal is varied by the information to be transmitted.

GMSK uses a pre-modulation Gaussian filter having a narrow bandwidth and sharp cut-off. The Gaussian filter suppress the high frequency components and makes the output power spectrum more compact. In addition, because GMSK uses only phase modulation, it is a constant-envelope modulation scheme. Consequently GMSK is a modulation scheme which enables efficient low power transmitter design and therefore is attractive for battery powered communications devices that must achieve very long battery life.

Demodulating signals generated by a continuous phase modulation scheme is complicated by the fact that the initial phase of each symbol is determined by the cumulative phase of previously transmitted symbols. A receiver cannot, therefore, make a decision on one symbol without taking the whole sequence of transmitted symbols into account. GMSK is also particularly prone to Intersymbol Interference (ISI) which complicates receiver design. Equalization is normally required, and is typically performed by a maximum likelihood equaliser such as a Viterbi decoder. These equalisers are not well suited to changing channel conditions or phase noise introduced by the transmitter and receiver, however, and small Doppler shifts or phase changes due to phase noise can result in significant performance degradation. This is particularly a problem when the GMSK symbol rate is low, so that the signal can fit in a narrow bandwidth channel, because a given Doppler shift or phase noise performance will result in a larger phase change over each symbol period.

Therefore, there is a need for an improved method for decoding signals that are subject to intersymbol interference.

According to one embodiment, there is provided a method for decoding a symbol in a received signal that suffers from intersymbol interference, the received signal comprising a plurality of symbols spaced by a symbol interval, the method comprising filtering the received signal to form a sample, representing the symbol, which comprises a weighted sum of the symbol and the symbols that immediately precede and succeed it in the received signal, multiplying the sample by a complex sinusoid having, at integer multiples of the symbol interval, alternately: (i) a zero real component and a non-zero imaginary component and (ii) a non-zero real component and a zero imaginary component, to generate a complex value and decoding the symbol in dependence on said complex value.

The received signal may be such that the sample comprises the weighted sum of a symbol, which is either predominatly real or predominantly imaginary, and the symbols that immediately precede and succeed it in the received signal are predominantly the other of real or imaginary.

The method may comprise, if the weighted component of the symbol is predominately real, and the complex sinusoid has a zero real component and a non-zero imaginary component at the integer multiple of the symbol interval that corresponds to the sample, decoding the symbol in dependence on the imaginary part of said complex value.

The method may comprise, if the weighted component of the symbol is predominately real, and the complex sinusoid has a non-zero real component and zero imaginary component at the integer multiple of the symbol interval that corresponds to the sample, decoding the symbol in dependence on the real part of said complex value.

The method may comprise, if the weighted component of the symbol is predominately imaginary, and the complex sinusoid has a zero real component and a non-zero imaginary component at the integer multiple of the symbol interval that corresponds to the sample, decoding the symbol in dependence on the real part of said complex value.

The method may comprise, if the weighted component of the symbol is predominately imaginary, and the complex sinusoid has a non-zero real component and zero imaginary component at the integer multiple of the symbol interval that corresponds to the sample, decoding the symbol in dependence on the imaginary pad of said complex value.

The method may comprise decoding the symbol in dependence on one of the real and the imaginary component of the complex value and estimating the intersymbol interference in dependence on the other of the real and the imaginary component of the complex value.

One period of the complex sinusoid may be equal to an integer multiple of four times the symbol interval.

The modulation method may be GMSK.

The time bandwidth product of the GMSK modulation may be greater than or equal to 0.3.

The method may comprise generating, in dependence on the complex sinusoid, a constellation of expected symbols, monitoring a deviation between the plurality of symbols and the constellation of expected symbols and tracking changes to a channel over which the signal is received in dependence on the monitored deviation.

The method may comprise generating an expected symbol representing the complex value that would have been generated had the received symbol been the same as the decoded symbol.

The method may comprise generating the expected symbol by summing the decoded symbol with decoded symbols generated from the symbols that immediately preceded and succeeded the received symbol in the received signal.

The method may comprise dividing the expected symbol by the received symbol, subtracting the output of said division from a channel estimate, providing the subtracted signal to an adaptive filter as representative of an error in a channel estimate that the adaptive filter uses to process the received signal and updating the channel estimate in dependence on the subtracted signal.

According to a second embodiment, there is provided a decoder for a receiver configured to receive a signal that suffers from intersymbol interference, the received signal comprising a plurality of symbols spaced at regular intervals, the decoder comprising a filter configured to filter the received signal to form a sample, representing the symbol, which comprises a weighted sum of the symbol and the symbols that immediately precede and succeed it in the received signal, a multiplier configured to multiply the sample by a complex sinusoid having, at integer multiples of the symbol interval, alternately: (i) a zero real component and a non-zero imaginary component and (ii) a non-zero real component and zero imaginary component, to generate a complex value and a decision unit configured to decode the symbol in dependence on said complex value.

The present invention will now be described by way of example with reference to the accompanying drawings. In the drawings: Figure 1 shows a method for decoding a symbol in a received signal; Figure 2a shows an example of a complete constellation including data symbols and intersymbol interference; Figure 2b shows an example of a complete constellation including data symbols and intersymbol interference in the presence of noise; Figure 3 shows an example of a method for tracking channel changes; and Figure 4 shows an example of a receiver structure.

An example of a method for decoding a symbol in a received signal that suffers from intersymbol interference is shown in Figure 1. The method comprises receiving a signal that represents a plurality of symbols, with a given interval between each (step 101). The symbol interval may be denoted 7. In this context the word "symbol' is used to mean any unit of data, so each "symbol" may represent any number of one or more bits. The received signal is filtered to produce a sequence of samples (step 102). Each sample in the sequence preferably represents the sum of one of the symbols together with at least the symbols that immediately precede and succeed it in the received signal. The sample may be formed from a weighted sum of the symbols. Combining neighbouring symbols to form each symbol reflects the intersymbol interference: each symbol is affected by those on either side of it.

The sequence of samples is then multiplied by a complex sinusoid (step 103).

Preferably the complex sinusoid has, at integer multiples of the symbol interval, either a zero real component and a non-zero imaginary component, or a non-zero real component and a zero imaginary component. The result of this multiplication is a sequence of complex values corresponding to the samples. The method then decodes each symbol in dependence on the complex value corresponding to it in the sequence (step 104).

This method results in a low complexity receiver structure that is particularly suitable for channels that experience flat fading. The method is very robust to changing channels and is robust to phase noise introduced by the transmitter and receiver. The method also allows standard signal processing algorithms that were developed for linear modulation schemes (such as BPSK, QPSK, etc.) to be easily adapted for GMSK or other continuous phase modulation schemes.

The method and receiver apparatus will now be described with specific reference to an implementation in which the received signal has been modulated using GMSK. This is not intended to be limiting, however, as the methods and apparatus described herein may be equally applicable to other modulation methods, particularly continuous phase modulation methods.

First, GMSK modulation will be described.

The data to be transmitted is suitably formed as a non-return-to-zero (NRZ) sequence a,ç, E {-1, +i}. This is the modulation data, and it can be differentially encoded.

The modulation data is suitably embodied as a square pulse: (1) 0 otherwise The modulation data is then filtered by a Gaussian filter to obtain the frequency pulse cp(t). The Gaussian pulse is given by: g(t) = /2182 exp () (2) Where: 2irfl j3 is the bandwidth-time product. It is suitably 0.3.

The signal is then modulated according to: s(t) = CX (-127th J ap(t -kT)) (3) where h is the modulation index of 0.5 and T is the symbol interval.

Using Laurent decomposition, this signal can be decomposed into a sum of pulse amplitude modulated signals. This allows the non-linear modulation of GMSK to be expressed in a recognisable linear fashion. The decomposition of GMSK can be written as: s(t) = _coIocq(k)hq(t -kT) (4) Where cq(t) and hq(t) are the signal and shaping filter respectively for the qth pulse amplitude modulated signal.

For the time bandwidth product 0.3, the signal for q=0 contains the majority of the energy. The transmitted signal can therefore be approximated as: s(t) EL.CJ, c0(k)h0(t -kT) (5) with = EcU jk_la a (6) It is also possible to differentially encode the data for transmission (i.e. ak = dkak_l, where dk E f-i, +1} is the information sequence). This implies that dk = akak_l. The sequence of equations below assumes that differential encoding has been applied.

Differential encoding is not necessary, however, and the method and apparatus described herein may equally be implemented without differential encoding.

The received filter is typically filtered by a filter matched to h0(t) to provide the following input to the demodulator: -Vw k-1,.j t (j p -L,jc=-cci LLkILML -tIs Equation 7 represents an approximation the ideal received signal. It can be seen from equation 7 that if this approximation of the ideal signal were sampled at the symbol interval, those symbols would alternate between being real and imaginary. In a real system, not only is the approximation likely to not be entirely accurate but the signal will have been subject to noise and other degradations during transmission. Therefore, sampling the signal is not likely to give wholly real or wholly imaginary samples but samples that are predominantly real or imaginary instead.

Unlike some other modulation schemes, such as BPSK, the matched filter response hM(t) is not Nyquist. Therefore, there is intersymbol interference, which means some form of equalisation is needed to obtain the maximum likelihood estimate of the input data dk. An example of a suitable equaliser is a Viterbi equaliser.

A specific example of the decoding method will now be described.

The received signal r(t) represents a plurality of data symbols cik spaced at regular intervals T. The method suitably starts by filtering the signal using a matched filter.

The matched filter hM(t) can be approximated by a discrete three tap filter. The taps are preferably at the symbol spacing T.For the example in which the time bandwidth product is 0.3, the taps may be weighted as 1⁄2, 1, 1⁄2. For higher time bandwidth products, an accurate three tap approximation can be made and, provided the weightings are symmetric the constellation formulation described above can be applied. There will be a difference in the resulting ISI magnitude, however, because the ISI taps are preferably less than 1/2 for higher time bandwidth products. The approximation can also be applied to lower time bandwidth products. A loss of performance may be observed, however due to the three tap approximation being less accurate for lower time bandwidth products (i.e. ISI components are greater outside of the three taps).

The output of the filter based on an ideal received signal (so no added noise or other degradations) can be written as: r(t) = jk_2d5(t -(k -1)T5) + E_wJk_ldkS(t -kT5) + lEJkd8(t -(Ic + 1)T) (8) The filtered signal is thus a weighted sum of a symbol and its immediate neighbours.

This is the signal that is input into the demodulator.

Sampling r(t) at every symbol interval T gives the signal: r[nil!jrn_2d +Jmdm +Imdrn+i (9) And finally multiplying by a complex sinusoid with frequency equal to /4T gives: = j_(rn_1)r[mI *II -7 lI J Urn_i +Urn +J Urn+i -7 li__I = Urn +J Urn_i +J Urn+i = drn drn_i +Ldrn+i (10) The significance of the complex sinusoid is that it has a value that is either solely real or solely imaginary at each symbol interval. Since the samples of the filtered signal, r[m], alternate between being real and imaginary (for the ideal case of no added noise or other signal degradations), multiplying the sampled filtered signal by the complex sinusoid splits the symbol and its intersymbol interference between the real and imaginary parts of the complex product. The complex sinusoid could be any suitable frequency, but preferably its period is an integer multiple of four times the symbol interval.

The real pad of equation 10 represents the data symbol. The imaginary pad represents the intersymbol interference. In practice, both the real and imaginary parts will be subject to noise in an analogous manner to a BPSK signal. The soft estimate of the data can be taken as d(m) = real(?[m]) and this can be used in subsequent stages in the same manner as data estimates in other modulation schemes (such as BPSK). The intersymbol interference can be taken as imag(f[m]) and this can be used to adapt the decoding process to remove intersymbol interference.

It will be understood that in other examples the imaginary pad of equation 10 might represent the data symbol and the real pad might represent the intersymbol interference: it depends on the correspondence between a particular complex sinusoid and a particular sampled, filtered signal as to whether the data symbol is multiplied by an odd power of j or an even power of j (and similarly for the intersymbol interference).

Another important point is that the intersymbol interference can only take certain values. In the example of equation 10, these values are j, 0, -j. Thus the complete signal constellation is known. The ideal constellation, without noise, is shown in Figure 2a. An example of a constellation with noise is shown in Figure 2b. The signal constellation can be used for channel tracking, e.g. by monitoring the deviation of received symbols from the constellation points they are mapped to during the decoding process. In this context, channel tracking includes tracking both Doppler shifts and phase noise or frequency offsets introduced by the transmitter and receiver implementation.

Viterbi equalization requires the calculation of branch metrics and then tracing back to determine the most likely state. For low bandwidth GMSK signals, the channel can change quite quickly relative to the symbol period and the frequency error can also drift. This results in potentially significant channel changes as the branch metric is being calculated. The traceback operation can then occur in error. In addition, decision directed tracking is not accurate because the delay caused by traceback.

With the derived formulation, the real part of the signal contains the information which can be instantly estimated. This allows almost instantaneous updating of the channel estimate. The channel or frequency value can also be estimated by calculating the expected symbol (including the complex component) and comparing it with the received value.

A benefit in using the method and apparatus described herein is its low complexity ability to track channel and frequency changes. An example of one possible tracking scheme is shown in Figure 3, which will be described with reference to the receiver structure shown in Figure The receiver structure comprises a matched filter 401, a multiplier 402 and an equaliser 403 (for example, a single tap MMSE equaliser). The receiver also comprises a decision unit 404 for identifying the real or imaginary part, as appropriate, of the multiplied signal and outputting that as the soft data symbol. The receiver structure also comprises a feedback loop for feeding back information to the equaliser, enabling it to adapt to changing channel conditions and multipath. The feedback loop comprises a reconstruction unit 405, a divider 406 and a tracking loop (407). Operation of these three units is described below with reference to Figure 3.

The tracking scheme consists of three main phases (I to Ill), respresented by the dashed lines in Figure 4. After a symbol has been decoded (step 301), the expected constellation symbol is calculated in phase I using the three decisions which affect this symbol (step 302). This step essentially takes the decoded symbol and estimates what the output of the multiplier would have looked like had the received symbol been the same as the decoded symbol. Assuming the symbol has been correctly decoded, any difference between the expected symbol and the actual received symbol is due to distortion during transmission. Comparing the two values therefore provides an indication of channel conditions. (Note that Figure 4 shows a causal system, so the expected constellation symbol lags the decisions by one. This is for the purposes of example only. It is a straightforward matter to extend the principles described herein to a non-causal system.) The channel response is calculated by dividing the expected symbol into the received signal (step 303; phase II). The difference between this and the current tracked channel is calculated (step 304). This difference is then used as an error signal into the adaptive tracking loop of phase Ill to update the channel estimate to its new value (step 305). That is, the channel tap estimate at time n, an, is used to update the channel estimate at time ni-i by an+i=ani-pen, where p is the tracking parameter which controls tracking speed and en is the error at time n. Finally the new channel value is used in the equalizer (step 306), which can be, for example, a single tap MMSE equaliser (e.g. ht/(1h12+a2), where Q2 is the noise variance) or any other equaliser.

Other channel and frequency tracking schemes which are used for other constellation types (BPSK, QPSK, etc.) can easily be adapted by substituting in the new constellation formulation.

Figure 4 shows a specific receiver structure. This is for illustrative purposes only. Each structure shown in the figure corresponds to a function that might be performed by any suitable functional unit, component or collection of components. Such a functional unit might be implemented in hardware or software or a combination of both. The structures shown in Figure 4 are not intended to define a strict division between different parts of hardware on a chip or between different programs, procedures or functions in software. In some embodiments, some or all of the algorithms described herein may be performed wholly or partly in hardware. In many implementations, at least part of algorithms may be implemented by a processor acting under software control (e.g. the CPU or DSP of a communication device). Any such software is preferably stored on a non-transient computer readable medium, such as a memory (RAM, cache, hard disk etc) or other storage means (USB stick, CD, disk etc).

In most implementations the receiver structure will form part of a larger communication device. Examples include M2M equipment, mobile phones, smart phones, line connected phones, laptops, tablets, etc. A typical communication device includes an antenna, a CPU, memory, signal processing circuitry, such as a DSP and filters, etc. The methods described herein may be applied to a communication network configured for Internet of Things (loT) communication. An example would include a network configured to operate according to the WeightlessTM protocol (although the methods described herein may be readily implemented by networks configured to operate according to a different protocol, such as e.g. LTE, Bluetooth, WiFi, V0IP). Typically the network will consist of a number of communication devices (e.g. base stations) that are each configured to communicate with a large number of geographically spaced terminals. The network may be a cellular network, with each communication device being responsible for over the air communications with terminals located in a respective cell. The methods described may be particularly advantageous for communication systems in which the channel bandwidth used by the GMSK signal is relatively low, for example less than 100 kHz.

In one example, the receiver structure may be configured to operate in accordance with the Weightless1M loT specification. WeightlessTM uses a cellular WAN architecture, with protocols optimised for the requirements of an loT system (low terminal cost, low terminal duty cycles and hence low power consumption, and scalability to very low data rates). It was originally designed to operate in TV Whitespace spectrum from 470 to 790 MHz, but the PHY is generalised to operate in licensed, shared licensed access and license-exempt bands of varying bandwidths.

The applicant hereby discloses in isolation each individual feature described herein and any combination of two or more such features, to the extent that such features or combinations are capable of being carried out based on the present specification as a whole in the light of the common general knowledge of a person skilled in the art, irrespective of whether such features or combinations of features solve any problems disclosed herein, and without limitation to the scope of the claims. The applicant indicates that aspects of the present invention may consist of any such individual feature or combination of features. In view of the foregoing description it will be evident to a person skilled in the art that various modifications may be made within the scope of the invention.

Claims

CLAIMS1. A method for decoding a symbol in a received signal that suffers from intersymbol interference, the received signal comprising a plurality of symbols spaced by a symbol interval, the method comprising: filtering the received signal to form a sample, representing the symbol, which comprises a weighted sum of the symbol and the symbols that immediately precede and succeed it in the received signal; multiplying the sample by a complex sinusoid having, at integer multiples of the symbol interval, alternately: (i) a zero real component and a non-zero imaginary component and (H) a non-zero real component and a zero imaginary component, to generate a complex value; and decoding the symbol in dependence on said complex value.
2. A method as claimed in claim 1, in which the received signal is such that the sample comprises the weighted sum of a symbol, which is either predominantly real or predominantly imaginary, and the symbols that immediately precede and succeed it in the received signal, which are predominantly the other of real or imaginary, the method comprising: if the weighted component of the symbol is predominantly real, and the complex sinusoid has a zero real component and a non-zero imaginary component at the integer multiple of the symbol interval that corresponds to the sample, decoding the symbol in dependence on the imaginary part of said complex value; if the weighted component of the symbol is predominantly real, and the complex sinusoid has a non-zero real component and zero imaginary component at the integer multiple of the symbol interval that corresponds to the sample, decoding the symbol in dependence on the real part of said complex value; if the weighted component of the symbol is predominantly imaginary, and the complex sinusoid has a zero real component and a non-zero imaginary component at the integer multiple of the symbol interval that corresponds to the sample, decoding the symbol in dependence on the real part of said complex value; and if the weighted component of the symbol is predominantly imaginary, and the complex sinusoid has a non-zero real component and zero imaginary component at the integer multiple of the symbol interval that corresponds to the sample, decoding the symbol in dependence on the imaginary part of said complex value.
3. A method as claimed in claim 1 or 2, comprising decoding the symbol in dependence on one of the real and the imaginary component of the complex value and estimating the intersymbol interference in dependence on the other of the real and the imaginary component of the complex value.
4. A method as claimed in any preceding claim, in which one period of the complex sinusoid is equal to an integer multiple of four times the symbol interval.
5. A method as claimed in any preceeding claim, in which the modulation method is GMSK.
6. A method as claimed in any preceeding claim, in which the time bandwidth product of the GMSK modulation is greater than or equal to 0.3.
7. A method as claimed in any preceding claim, comprising: generating, in dependence on the complex sinusoid, a constellation of expected symbols; monitoring a deviation between the plurality of symbols and the constellation of expected symbols; and tracking changes to a channel over which the signal is received in dependence on the monitored deviation.
8. A method as claimed in any preceding claim, comprising generating an expected symbol representing the complex value that would have been generated had the received symbol been the same as the decoded symbol.
9. A method as claimed in claim 6, comprising generated the expected symbol by summing the decoded symbol with decoded symbols generated from the symbols that immediately preceded and succeeded the received symbol in the received signal.
10. A method as claimed in claim 7, comprising: dividing the expected symbol by the received symbol; subtracting the output of said division from a channel estimate; providing the subtracted signal to an adaptive filter as representative of an error in a channel estimate that the adaptive filter uses to process the received signal; and updating the channel estimate in dependence on the subtracted signal.
11. A decoder for a receiver configured to receive a signal that suffers from intersymbol interference, the received signal comprising a plurality of symbols spaced at regular intervals, the decoder comprising: a filter configured to filter the received signal to form a sample, representing the symbol, which comprises a weighted sum of the symbol and the symbols that immediately precede and succeed it in the received signal; a multiplier configured to multiply the sample by a complex sinusoid having, at integer multiples of the symbol interval, alternately: (i) a zero real component and a non-zero imaginary component and (H) a non-zero real component and zero imaginary component, to generate a complex value; and a decision unit configured to decode the symbol in dependence on said complex value.
12. An apparatus configured to operate a method as claimed in any of claims 1 to 7.
13. A method substantially as herein described with reference to the accompanying drawings.
14. A decoder substantially as herein described with reference to the accompanying drawings.