Trade-o s between Diversity Combining and Equalization for Wireless LANs. J. C-L Ng, K. Ben Letaief and R. D. Murch. The Hong Kong University of Science & ...
Trade-o s between Diversity Combining and Equalization for Wireless LANs J. C-L Ng, K. Ben Letaief and R. D. Murch The Hong Kong University of Science & Technology Clear Water Bay, Kowloon, Hong Kong Abstract | In wireless LAN applications with high transmission rates of up to 10-20 Mbit/s the problem of multipath inter-symbol interference (ISI) due to frequency selective fading occurs. Adaptive equalization and diversity combining are two possible techniques for combating multipath ISI. The complexity of digital signal processing on the received signals is one of the main issues of these techniques. In this paper, we will investigate the performance and computational complexity trade-o s between diversity combining and equalization in a quasi-stationary frequency-selective fading with AWGN by means of computer simulations. We consider both MMSE combining and selection diversity combining with up to four diversity antenna branches. The results will be useful to determine the number of diversity branches and feedforward and feedback equalization tap weights in the wireless LAN design.
I. INTRODUCTION Wireless LAN applications require high bit rates of up to 10-20 Mbit/s if they are to compete with wire-line LAN systems such as Ethernet. Higher bit rates may even be required if multimedia services are to be supported. Associated with these high transmission rates however is the problem of multipath ISI due to frequency selective fading. To combat ISI the technique of adaptive equalization is often suggested as a possible method [1], [2], [3], [4]. In the case of the European Wireless LAN standard, HIPERLAN, adaptive equalization will be adopted [5], [6]. Alternatively, diversity combining (or antenna arrays) has been suggested as another countermeasure against multipath ISI [7], [8], [9]. With a carrier frequency of 5 GHz (for HIPERLAN), the antenna separation required of around half-wavelength is 3 cm. Hence, it is possible to have several antenna with acceptable receiver size. The combination of diversity reception and equalization however may provide even greater reductions in ISI and this has been investigated by Balaban and Salz [10]. Their results show signi cant performance improvement from diversity reception with optimum combining and in nitetap decision feedback equalization. However, in practical situations, determing the least number of taps is required to provide this increased performance is important. In this paper, the trade-o s between diversity combining and equalization with respect to the computational complexity and bit error rate performance is studied. We con ne ourselves to MMSE combining and selection diversity (before equalization) in order to make the trade-o tractable. For MMSE combining scheme, a single algorithm with the MMSE criterion is used for both diversity
combining and equalization. For selection diversity, we use power measurement to select the diversity branch before equalization. We simulate the combiner using QPSK modulation with 1 to 4 antennas and various number of feedforward and feedback equalization weights in an indoor radio environment with multipath ISI and AWGN. The organization of this paper is as follows. In section II, we describe the channel model assumption used in our simulations. Section III provides system descriptions. Section IV presents the computer simulation setup, results and discussions. Finally, conclusions are presented in Section V. II. CHANNEL MODEL Radio channels can be represented mathematically by their channel impulse response. We model the impulse response, for a particular diversity channel, using a n-ray model de ned as nX ?1 (1) hk (t) = i;k (t ? iTs =np ) i=0
where n is the number of paths, i;k is the complex gain for the ith path of the kth diversity channel, Ts represents symbol period and np the number of paths per symbol period. The i;k are zero mean, complex Gaussian random variables, with their power following the exponential decay pro le described by 1 t0 (2) E[h2k (t)] = 0 exp(?t= ) for for t < 0: This is a continuous delay pro le with rms delay spread . For the sampled-pro le used in our simulation, we truncated the pro le at 8 to 10 times the delay spread normalized by symbol period, and np in (1) ranges from 8 to 15, with the larger values used for small delay spread. It is assumed that paths with di erent delays are uncorrelated (i.e., uncorrelated scattering). In addition, we also assume that the paths are uncorrelated for each diversity branch [11]. This will be realistic if antenna spacing is greater than 0:4. We can refer to [12] for the e ect of correlation on the antennas. We assume a quasi-stationary channel in which over certain time interval (e.g., a packet) the channel is time invariant.
III.SYSTEM DESCRIPTION This section de nes the modulation, receiver and combining/equalization structure under study. In Figure 1 the schematic for how the diversity antenna branches are modeled is shown. We assume a coherent receiver, and therefore the equivalent baseband model is given. QPSK modulation is utilized since it allows us to investigate the combiner/equalizer with complex weights. Thus the data symbol stream di takes values of 1 j. The combined e ects of lters in various stages is lumped into the signal function g(t). We choose a raised cosine roll-o function for g(t). The transmitted signal u(t) is then the convolution between di (impulse train) and g(t). y1(t)
h1(t) u(t)=Σ d i g(t-iTs ) i
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Fig. 1. A baseband diversity channel model
We consider MMSE combining rst. For timing recovery, we follow the practical method of squaring timing loop [13], [9]. The timing instant td (timing epoch) is given by " na # X 1 (3) td = 2 phase Fk k=1
where phase[:] denotes the modulo-2 phase in radians, na is the number of antennas and Fk is the rst harmonic of the mean value of jyk (t)j2 averaged over the input data for the kth diversity branch. Fk is given by nX ?1 nX ?1 sin (l=np ? m=np ) l;k m;k Fk = (l=np ? m=np ) l=0 m=0 ?j(l=np +m=np ) e 1 ? 2 (l=n ? m=n )2 (4) p p where is the roll-o factor, l;k , np and n are given by (1). Figure 2 shows the general structure for the diversity combiner and equalizer to be studied. There are na diversity branches, n1 feedforward weights and n2 feedback weights. Thus, the total number of complex weights is na n1 + n2 for MMSE combining. For selection diversity, we consider power measurement selection before equalization as it is the simplest and most common technique. With this arrangement it is also possible to use only one down-converter. For this selection diversity scheme only one diversity branch in Figure 1 with the largest average signal power is selected. Despite
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of simplicity, selection diversity based on power measurement does not take into account ISI. We will also study the best selection scheme in which the channel with smallest Pe is chosen to see the best performance that can be obtained from selection diversity. For best selection, we obtain the Pe with equalization for each diversity branches independently, and then select the smallest Pe . The performance of other selection schemes, such as selection using coding [14], should lie between these two. Recursive least-squares (RLS) and Least-mean-square (LMS) are two common algorithms used in adaptive equalization [15]. RLS has better tracking capabilities and faster convergence. While LMS is simpler and more suitable for high speed transmission in practice if a longer training sequence is a ordable. For simplicity, we only use the LMS algorithm in our simulation. Our results can also be applied to the case of RLS because the steady state performance of LMS and RLS are similar in a stationary channel. IV. SIMULATION RESULTS A. Simulation Setup
We use computer simulation to study the trade-o s between diversity combining and equalization in a quasistationary frequency-selective fading channel. Firstly, we generate the random channel impulse response (1) and (2). We then use the LMS algorithm to obtain the biterror-rate Pe for each channel impulse response. Because we want to eliminate the e ect of convergence, 1000 training symbols are used to ensure convergence. Furthermore, perfect reference signals are provided after the training period so as to eliminate the error propagation e ect. In practice, less then 500 symbols (with suitable step size for LMS algorithm) is already sucient for convergence. For QPSK signaling, we assume a roll-o factor of 0.35. For each average error probability (Pe ), more than 500 transmissions with independent channels are simulated. A data packet consists of 5000 data symbols for each transmission. In the simulation, the rms delay spread normalized by symbol period, d, ranges from 0.6 to 2.0. In a typical indoor environment, the rms delay spread is usually less than 50 ns. For 20 Mbit/s QPSK signal, 50 ns is equivalent to d of 0.5. We study large values of d because we want to study the capability of the system for combating
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ISI. The results provided in Figures 3-10 demonstrate the performance trade-o s between the number of antennas, feedforward and feedback tap weights. In the Figures the notation (na ; n1; n2) is used to specify a combiner/equalizer structure, using MMSE diversity combining, with na antennas, n1 feedforward and n2 feedback weights. For selection diversity combining, sp(na ; n1; n2) and sb(na ; n1; n2) are used to represent selection diversity based on power measurement and best selection diversity, respectively. Delay spread is speci ed by the rms delay spread normalized by symbol period d (i.e., d = =Ts.) SNR is given in terms of Eb=No .
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Fig. 4. Average e for MMSE combiner/equalizer with 17 and = 1 0.
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Figures 3-6 present average Pe for various structure con gurations with MMSE combining as a function of the number of feedback tap weights n2 for d = 0:6; 1:0; 1;5 and 2:0. The n2 = 0 intercept can be considered as the results for a linear equalizer/combiner. Because the feedback lter can eliminate the residual ISI, our structure with feedback taps (n2 > 0) has signi cantly better performance than a linear equalizer/combiner (n2 = 0). This performance can be provided with moderate increases in complexity. However, in general once beyond a certain number of feedback tap weights the average Pe converges and performance is not improved. For example in Figure 3 for n2 > 3 performance only increases slightly. In practical settings using too many feedback weights may lead to increases in error propagation. To provide further improvement it is better to increase n1 as the results demonstrate. Comparing (2; 3; n2) with (3; 2; n2) and (2; 4; n2) with (4; 2; n2) in Figures 4-5, we can see that using more antennas but with the same number of tap weights at small delay spread provides better performance. However, there is no bene t for using more than 2 antennas for larger values of d and same number of total taps (see Figure 6). In
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Fig. 7. Comparison between diversity combining and equalization with b o = 17 . E =N
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other words, if MMSE combining is used for a channel with large ISI dual antenna diversity is the best choice. Comparing (2; 4; n2) with (1; 8; n2) in Figure 6, the significant performance improvement by dual antenna diversity with MMSE combining is shown. Their total number of weights are the same but the cost is an extra antenna and a down-converter. Figure 7 demonstrates the di erence between MMSE diversity combining and adaptive equalization for various d. Diversity combining has very good performance for small values of d but such performance degrades rapidly as d increases. For equalization the performance improves as d increases at the beginning. However, the performance degrades quickly for larger values of d. With equalization using more tap weights, the performance is better for larger values of d because the equalizer can take advantages from the implicit time-diversity. For small values of d, using more weights has little e ects on the performance. Comparing (2; 3; 0) and (3; 2; 0), which have the same number of total weights, (3; 2; 0) has better performance at small values of d and both performances converge as d increases. This is probably because there is more ISI but less uctuation in received power for large values of d.
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C. Selection Diversity Combining Results
Figure 8 presents average Pe for various structure con gurations with selection diversity combining as a function of the number of feedback tap weights n2 for d = 0:6. Figures 9 and 10 present results in the same form but for d = 2:0. In the Figures, the label sb and sp represent selection diversity based on power measurement and best selection diversity, respectively. For selection diversity based on power measurement, only one feedforward lter is required. Thus the total number of weights is n1 + n2. For best selection diversity, choosing the diversity branch with the smallest Pe may not be feasible in practice but the results show the best performance that is possible by
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selection diversity. Comparing sb(2; 6; n2), sp(2; 6; n2) with (2; 3; n2) in Figure 8, where d = 0:6, MMSE combining is better than the best selection diversity. Comparing the same con gurations in Figure 9, where d = 2:0, selection diversity based on power measurement is better than MMSE combining with the same number of tap weights. However, if the total number of feedforward weights are increased to 8 as in Figure 10, MMSE combining is superior. We can see that for small numbers of taps selection diversity provides proportionally larger increases in performance than for larger taps. V. CONCLUSIONS We have presented results demonstrating the performance and complexity trade-o s between antenna diversity and equalizer structure. The results presented in Figures 3-10 will be useful to predict the required number of diversity branches and feedforward and feedback equalization weights in wireless LAN applications. Taking a system in which we require a Pe of 10?3 with d = 0:6 and Eb=No = 17dB as an example, the minimum con guration would be (1; 4; 3) (equalization only), (2; 2; 1), or (3; 1; 2) with MMSE combining while sp(2; 3; 3) or sp(2; 6; 1) for power measurement-based selection diversity (recall that (na ; n1; n2) stands for na antennas, n1 feedforward and n2 feedback weights). For Pe of 10?3 and d = 2:0, the required con guration would be (1; 10; 8) (equalization only), (2; 4; 3), (2; 5; 1), (3; 3; 1) or (4; 2; 3) with MMSE combining while sp(2; 8; 7), sp(3; 6; 6) or sp(3; 8; 5) with power measurement based selection diversity. For MMSE combining, using more antennas (with the cost of more down-converters) provide large performance improvement for small delay spread while less improvement for large delay spread. Our results show that if MMSE combining is used, dual diversity is the best choice for large delay spread. Selection diversity can provide proportionally larger performance improvement when equalization tap weights are insucient. To decide on whether to use MMSE combining or selection diversity, we have to also consider the cost of down-converter and the design of the selection scheme.
References
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