MLSE Diversity Receiver for Partial Response CPM

Transcription

1 MLSE Diversity Receiver for Partial Resonse CPM Li Zhou, Philia A. Martin, Desmond P. Taylor, Clive Horn Deartment of Electrical and Comuter Engineering University of Canterbury, Christchurch, New Zealand Wireless Research Centre, University of Canterbury, Christchurch, New Zealand Abstract In this aer we consider the alication of ersurvivor rocessing and diversity techniques to a artial resonse continuous hase modulation (PR-CPM) maximum likelihood sequence estimation (MLSE) receiver design. In articular, we consider ractical imlementation in a ublic safety narrowband radio environment. Frequency ulse truncation and tilted hase are used to reduce the number of states in the PR-CPM trellis with little loss in real world erformance. Selection, equal gain and maximum ratio combining techniques are also considered to assess the ractical benefit in system deloyment. I. INTRODUCTION Continuous hase modulation (CPM) maintains a constant enveloe and hase continuity throughout transmission. These roerties are ideal for wireless communications due to the good sectral efficiency couled with excellent ower efficiency []. Here, we consider artial resonse continuous hase modulation (PR-CPM) using a hase shaing filter with long correlation length. This lowers sectral side lobes, which reduces adjacent channel interference (ACI) and imroves bandwidth efficiency []. This makes it attractive for narrow bandwidth oerations, which tyify the technology used for long range voice communications in the ublic safety environment. Unfortunately, PR-CPM has several drawbacks. Firstly, the comlex nature of CPM with long correlation length means that conventional maximum likelihood sequence estimation (MLSE) receivers are costly to imlement [5]. Practically this cost resents itself as memory, rocessing comlexity and therefore ower consumtion. Any imlementation of the receiver is sensitive to all these arameters. Secondly, the fading associated with moving vehicles comromises the reliability of conventional channel estimation techniques. In this aer, we describe a design aroach which allows a simlified imlementation of a PR-CPM MLSE receiver. In articular, receiver comlexity is significantly reduced by utilizing trellis state reduction, via the tilted hase aroach [], [8] and frequency ulse truncation []. Public safety oerations commonly occur at seed and oeration in the 800MHz band leads to fade rates requiring more careful attention to this element of the receiver design. To imrove receiver reliability in a fading environment, a er-survivor rocessing (PSP) based aroach [0], [4] to channel estimation is used. In addition, multile receiver antennas and diversity combining are used to further combat the degradation due to the fast fading channel. The novelty lies in the integrated combination of PSP and diversity techniques in a ractical, reduced-state PR-CPM MLSE based receiver design. The aer is organized as follows. The transmitter, channels and PR-CPM are described in Section II. The receiver design is outlined in Section III. Simulation results are resented in Section IV and conclusions are drawn in Section V. II. SYSTEM MODEL We consider an uncoded PR-CPM system. The single-h CPM signal at time t is defined as [9], [2] 2E s(t) = T cos [2πf ct + θ(t; I)+θ n ],t 0, () where the hase state is defined as θ n = hπ n L k= I k (2) and the correlative hase comonent is defined as θ(t; I) =2πh n k=n L+ I k q(t kt), nt t (n +)T () which is secified by the correlative state (I n,,i n L+ ) consisting of comonent M-ary data symbols from the set ±, ±,, ±(M ). T is the symbol time, E is symbol energy and f c is the carrier frequency. The hase resonse affecting the hase transition over L symbol eriods is given by { t 0, t < 0, q(t) = g(τ)dτ = 2, t > LT (4) where g(t) is the frequency ulse, which is a smooth ulse shae on the interval (0,LT), normalized such that g(t)dt =/2. L is the duration of g(t) in symbol eriods and h = m/ is the modulation index, where m and are relatively rime ositive integers. We consider a CPM system with L =4(ensuring a long correlation length to reduce ACI), h = / (to conserve bandwidth at the cost of energy), M =4(to ensure a good M is usually a ower of /0/$ IEEE 50

2 joint energy-bandwidth tradeoff) and a frequency ulse defined as [5] G (sinc(λ(t LT/2)/T )) g(t) = (cos 2 (π(t LT/2)/T/L) ) for t [0,LT] 0 elsewhere. (5) where G = is a normalization factor and λ =0.75 is a modulation arameter, such that q(t) =/2 for t LT. Here, we consider both additive white Gaussian noise (AWGN) and Rayleigh fading channels. The received signal at time nt for an AWGN channel is given by r(nt )=s(nt )+e(nt ) (6) and for the Rayleigh fading channel by r(nt )=h(nt )s(nt )+e(nt ), (7) where h(nt ) is the channel gain and e(nt ) is AWGN. III. PSP-BASED MLSE RECEIVER DESIGN We now consider the PSP-based MLSE receiver. The standard demodulator used for CPM is MLSE using the Viterbi algorithm (VA) []. We consider PR-CPM with a resonse length of L =4symbol eriods. Then, each CPM encoded symbol can be reresented by a state S = (θ n,i n,i n 2,I n ), where I k {±, ±} and θ n { 0, π, 2π,π, 4π, } 5π. Since there are 64 combinations of I n, I n 2 and I n and 6 values of θ n, the resulting trellis has 84 states, which leads to a comlex receiver. We use trellis state reduction techniques to reduce this comlexity. In addition, we incororate PSP into the MLSE receiver in order to include the channel estimation rocess. Finally, we add diversity combining to the receiver allowing for multile receive antennas. A. Trellis Reduction Reduced-state schemes are used to simlify the imlemented trellis structure by exloiting in art the redundancy in the trellis. The frequency ulse truncation technique of [] is used to truncate the frequency ulse of (5) used in defining the hase resonse q(t). As the amlitudes of the tails of g(t) are small, the resulting hase resonse can be truncated, thereby simultaneously reducing both the number of trellis states and the required number of matched filters, with little erformance degradation. As this truncation actually reduces the correlativestate vector, it is a form of correlative state reduction [8]. In addition, we use the tilted hase aroach of [], [8] to achieve further comlexity reduction. It is based on the decomosition model of []. This transforms the eriodically time-varying trellis usually encountered in CPM into a time-invariant form that tyically has only half as many hase states as the original trellis. It affects only the number of hase states and not the number of correlative states. This combination of techniques allows reduction of the numbers of both hase states and correlative states. reduction is achieved via a three ste aroach. The tilted hase aroach is first used to reduce the number of states to 92. This is followed by frequency ulse truncation which further reduces the number of states to 48 by reducing the number of correlative states. Finally, a further four-fold reduction is achieved by alying a selective frequency ulse excision rocess to obtain the final 2 state receiver. ) Tilted Phase: For all CPM schemes, at any given symbol time, the value of θ n can take only ossible values, even though the total number of ossible θ n values may be either if m is even, or 2 if m is odd [4]. When m is odd (as considered here), the set of 2 ossible θ n values is slit into two subsets, with one subset used at even symbol times and the other at odd symbol times [4]. In articular, at odd symbol times, the hase state takes the values { θ n 0, 2πm, 4πm,, ( )2πm } while at even symbol times, it takes the values { πm θ n, πm, 5πm,, (2 )πm (8) }. (9) A roof of this is found in [4]. This results in a cyclically time variant trellis structure with a eriod of 2 symbol eriods [4]. This time variant trellis can be transformed to an equivalent time invariant trellis called the tilted trellis []. The tilted trellis is arrived at by alying the hase offset υ n = υ n πh(m ) (0) to correct the hase state values, where υ n =0at t =0. Here we consider m =, =and M =4, resulting in υ n = π and υ n = 0 for even and odd symbol eriods, resectively. With this aroach, the effective number of states required to decode PR-CPM is halved in each symbol interval without erformance loss. 2) Frequency Pulse Truncation: Fig. shows how frequency ulse truncation is alied to the PR-CPM signal. Fig. a, shows the effect of the hase resonse q(t) on the transmitted signal for the PR-CPM (L =4) encoding, starting from t =0(current transmission) and tracing back through the revious symbols. From t =0to t = 4T,thevalueof q(t) increases from 0 to 0.5. This time san corresonds to the correlative state of the transmitted signal, as described by (), which is defined by the three symbols I n, I n 2 and I n immediately receding the current symbol, I n.thisis reresented in Fig. a as the white region in the grah. For t 4T,thevalueofq(t) remains constant at 0.5, and the sum of all the symbols transmitted at and before this time frame defines the hase state θ n of the transmitted signal. This is shown in Fig. a as the shaded region. The recise imlementation of frequency ulse truncation relies on the articular shae of q(t). In articular, it can be seen from Fig. a that at t = T, q(t) 0.5. Therefore, the effect of the last symbol I n can be merged into θ n.this reduces the ulse time varying resonse length L by, which reduces the number of trellis states from 92 to 48. Note that this makes no difference to the allowable values of the hase state θ n. 502

3 (a) (b) T - L = 4 Correlative t = 0 t = -T t= -2T t= -T t= -4T - T - L = 4 L' = 2 Correlative t = 0 t = -T t= -2T t= -T t= -4T - Frequency ulse truncation n - n t = -5T Phase The effect of the last symbol has merged into hase state. - - t = -5T Phase t = - t = - Fig.. The change in the correlative state and hase state uon alication of frequency ulse truncation. Note that this is equivalent to erforming a hase truncation as the hase ulse is simly the integral of the frequency ulse. It can also be seen that at t = T, q(t) is small. Therefore, we excise the effect of the symbol at t = T on the correlative state. The resulting hase resonse length or correlative state definition is further reduced by, givingl =2, which means that the number of trellis states at each symbol time is reduced to 2. The new states corresonding to the reduced trellis are reresented by S =(θ n,i n 2 ), based on which the VA then decodes the signal. Fig. 2 shows the reduced 2 state PR-CPM trellis. It also demonstrates the PR-CPM alternating hase states feature discussed earlier. This aroach is called correlative state reduction, as the last element of the correlative state vector has been merged into the hase state vector [7] and the first element of the correlative state vector has been ignored. The final aearance of the hase resonse and the corresonding correlative and hase state are shown in Fig. b as the dashed trajectory. B. Channel Estimation using Per-Survivor Processing We now consider the Rayleigh fading channel and use PSP [0] to estimate the channel in the MLSE receiver. In a PSP receiver different channel resonses are simultaneously estimated along the surviving aths associated with each state in the trellis of the VA. Each ath maintains and udates its own channel estimate based on the corresonding hyothesized transmitted data sequence [0], [6], and that estimate is used to calculate branch metrics only for that ath. The existence of individual gains for surviving aths means that each gain estimate is confined to the articular survivor ath, along with S S2 S S4 n, I n- = (0, ) (0, -) (0, ) (0, -) S5 (, ) S6 (, -) S7 (, ) S8 (, -) S9 (, ) S0 (, -) S (, ) S2 (, -) Fig. 2. Odd symbol times n, I n- = S (, ) S2 (, -) S (, ) S4 (, -) S5 (, ) S6 (, -) S7 (, ) S8 (, -) 5 S9 (, ) S0 ( 5, -) 5 S (, ) 5 S2 (, -) Even symbol times Trellis examle of the reduced state PR-CPM receiver. its error. Unlike conventional MLSE, if the gain for a articular surviving ath is corruted with noise or distortion, then the rest of the surviving aths may not be affected. As decision making is based on the best surviving ath, this error tends not to roagate through the decoding sequence. Further, as the gain is estimated based on the revious surviving aths, in general, the more reliable the surviving ath is, the more reliable is the associated channel estimation. Hence PSP is suitable for time-varying channels and achieves significant reduction in the effects of error roagation. The drawback of such PSP-based MLSE receivers is their comutational comlexity as channel estimation is required for each survivor ath rather than requiring only one global channel estimate. It can be shown that the correlation function between the received signal r(t) and the tentative decoded signal s(t), corr(r, s), is a noisy estimate of the channel gain. Hence we can obtain a more accurate estimate of the channel gain by reducing the noise comonent of the correlation function. This can be done by averaging, ossibly in a weighted manner, N successive estimates to obtain a better gain estimate, where the choice of N is based on the Doler sread. In this aer, a least mean squared error estimate of the channel gain is used. We assume a Jakes Doler sectrum and estimate the channel gain as the weighted sum h(nt )=w 0 corr(r, s)+w h((n )T )+w 2 h((n 2)T ) + + w N h((n N +)T ), () where w T =[w 0,w,w 2,,w N ] is defined by the Yule- Walker equation [9] w = R y. (2) 50

4 The (i, j) th comonent of the covariance matrix, R y,isgiven by R yi,j =2γ s J 0 ( 2πfd(max) T (i j) ) + δ((i j), 0), () where f d(max) is the maximum Doler frequency, γ s is the signal to noise ratio (SNR) of the channel and J 0 is the zero order Bessel function. The cross correlation vector (of length L) has i th comonent given by i = 2γ s J 0 ( 2πfd(max) T (i +) ), i =,,L. (4) This takes into account the seed of fading, and weights the successive estimates accordingly. The weighted sums rovide channel gain estimates for each surviving ath, which are incororated into the branch metrics given by B(nT )=Re {r(nt )h (nt )s (nt )}, (5) where denotes comlex conjugate and Re{} denotes the real art. By setting the weights w =, we obtain a simle average, which can be used, but leads to inferior erformance. C. Diversity Combining We now look at the imact of receiver diversity through the use of multile, N r, receive antennas. Three standard aroaches to diversity combining are considered, namely selection combining (SC), equal gain combining (EGC) and maximum ratio combining (MRC). For selection combining, the strongest received signal from one of the antennas is chosen as the received signal. PSP is erformed using the selected received signal. EGC and MRC erform PSP on each received signal stream rior to actual diversity combining. EGC uses a hase coherent unweighted linear sum of the received signals. The required hase estimates are directly rovided by the PSP rocess. MRC uses a hase coherent weighted linear sum of the received signals [2]. The weights are the ratio of the channel gain magnitude to the noise energy [2]. Hence, MRC requires both the estimated channel hase and magnitude from PSP. As both EGC and MRC erform PSP on each received signal, they have higher comlexity than SC. PSP of the received signal streams can be done in arallel to avoid increased latency. Due to PSP roviding full channel state estimates, EGC and MRC have similar comlexity. IV. SIMULATION RESULTS We use simulation to evaluate erformance. N win =0was chosen as the decision deth in the VA as it resulted in very similar erformance to large deths such as N win =0.SNR is measured as bit energy, E b, divided by noise ower sectral density, N 0. Fig. shows the bit error rate () erformance of the reduced state MLSE receiver in an AWGN channel. It can be seen that there is a slight degradation in error erformance as the number of trellis states is reduced from 92 to 48. This is exected as an aroximation is made in the frequency ulse truncation rocess, and thus, a small extra error is introduced states 48 states 92 states 84 states E b /N 0 (db) Fig.. MLSE receiver erformance using 2, 48, 92 and 84 states on an AWGN channel. into the decoding rocess. Similarly, the state reduction from 48 to 2 states also leads to a further small error erformance degradation. As there is only a very small degradation in erformance it is clear that the significant effects of the correlative state are retained. The curve for the PSP-based MLSE receiver in a fading environment is resented in Fig. 4 for averaging length N =5in () and Doler frequencies of 5Hz, 40Hz and 80Hz. Note that a longer integration length would result in better channel estimation and slightly imroved. As exected, PSP using a weighted sum significantly outerforms PSP with standard averaging and no PSP at Doler frequencies above 5Hz. Performance could be further imroved by adatively changing the weight coefficients based on minimizing the error in a mean square sense. This is the aroach used in [6] for linear modulations. The erformance with diversity combining is shown in Fig. 5 for a Doler frequency of 80Hz. As exected, MRC rovides the best erformance followed by EGC and SC. The largest gains are obtained by increasing from to 2 receive antennas. V. CONCLUSIONS The aer has described a ractical design for a PSPbased MLSE receiver for PR-CPM which is alicable to ublic safety narrow band deloyment around the world. The modulation described here is characterized by a long imulse resonse. Nevertheless, state reduction has been successfully alied which minimizes the resources required for DSP or FPGA imlementation whilst maintaining excellent receiver erformance in the mobile environment. Diversity has also been examined and the results show the deloyment of diversity can substantially imrove the faded 504

5 erformance assuming the diversity channels are sufficiently de-correlated. The integration of PSP with MRC is the key ractical advance in this work. As PSP rovides channel estimates and hence the diversity coefficients at each state for each received signal comonent, diversity combining using EGC and MRC have similar comlexity, allowing the suerior erformance of MRC for negligible additional comlexity. Moreover, PSP resolves any hase ambiguities [6]. Satial diversity reresents the obvious method of acquiring these gains and modern ublic safety base stations are becoming available with this caacity. ACKNOWLEDGMENT We acknowledge the assistance of Prof. J. K. Cavers who develoed the weighted sum aroach in () and shared it with us in a ersonal communication. Unfortunately, it is not available ublicly. REFERENCES [] J. B. Anderson, T. Aulin, and C.-E. Sundberg, Digital Phase Modulation. New York: Plenum Press, 986. [2] D. G. Brennan, Linear diversity combining techniques, Proc. IEEE, vol. 9,.-56, 200. [] M. Kalkan, CPM erformance with diversity in mobile radio, in Proc. 7th Mediterranean Electrotechnical Conference, vol.,. 2-4, 994. [4] M. J. Miller, Detection of CPFSK signals using er survivor rocessing, in Proc. MILCOM, 998. [5] F. A. Monteiro and A. J. Rodrigues, Phase Error Resilience to I/Q Mismatch of a Simlified CPM Receiver, IEEE Microwave and wireless comonents letters, vol. 5, Se [6] M. J. Omidi, S. Pasuathy and P. G. Gulak, Joint data and Kalman estimation for Rayleigh fading channels, Wireless Pers. Commun., vol. 0,. 9-9, 999. [7] E. S. Perrins, Reduced comlexity detection methods for continuous hase modulation, Ph.D. Thesis, Brigham Young University, Dec [8] E. Perrins and M. Rice, Reduced-comlexity detectors for Multi-h CPM in aeronautical telemetry, IEEE Trans. Aerosace and Electronic Systems, vol. 4, , [9] J. G. Proakis, Digital Communications, 4th Edition, New York: McGraw-Hill, 200. [0] R. Raheli, A. Polydoros and T. Ching-Kae, Per-Survivor Processing: a general aroach to MLSE in uncertain environments, IEEE. Trans. Commun., vol. 4, no. 24, , Feb.-Mar.-Ar [] B. E. Rimoldi, A decomosition aroach to CPM, IEEE Trans. Inform. Theory, Vol. 4, No. 2, , Mar [2] C. E. Sundberg, Continuous hase modulation, IEEE. Commun. Mag., vol. 24,. 25-8, 986. [] A. Svensson, C.-E. Sundberg and T. Aulin, A Class of Reduced- Comlexity Viterbi Detectors for Partial Resonse Continuous Phase Modulation, IEEE. Trans. Commun., vol. 2, No. 0, , Oct [4] W. Tang, A receiver for continuous hase modulation in Walsh signal sace, Ph.D. Thesis, University of Winnieg, Manitoba, Canada, Set [5] TIA, APCO roject 25 system and standards definition, TIA/EIA Telecommunications Systems Bulletin, TSB02-A 995. [6] G. M. Vitetta and D. P. Taylor, Maximum likelihood decoding of uncoded and coded PSK signal sequences transmitted over Rayleigh flat-fading channels, IEEE Trans. Commun., Vol. 4, , Nov Hz No PSP 40Hz No PSP 5Hz No PSP 80Hz PSP average 40Hz PSP average 5Hz PSP average 80Hz PSP weighted 40Hz PSP weighted 5Hz PSP weighted E /N (db) b 0 Fig. 4. erformance of 2-state PSP-MLSE receiver using standard averaging and weighted sum comared to that of the MLSE receiver without PSP in Rayleigh fading channel. Symbol time T = /6000. Doler frequencies 5Hz, 40Hz and 80Hz Hz CH 80Hz CH2 SC 80Hz CH2 EGC 80Hz CH2 MRC 80Hz CH SC 80Hz CH EGC 80Hz CH MRC 80Hz CH4 SC 80Hz CH4 EGC 80Hz CH4 MRC E b /N 0 (db) Fig. 5. erformance comarison for 2-state PSP-MLSE receiver using no diversity (CH), dual (CH2), trile (CH) and quadrule (CH4) diversity systems in Rayleigh fading channel at Doler frequency of 80Hz. Symbol time T =/