Performance Upper Bound of Adaptive Qam in Slow Rayleigh Fading Environments

The performance of adaptive modulation schemes that employ either n o transmission, BPSK, QPSK, 16 Square Q A M a n d 64 Square Q A M is characterised for transmissions over Rayleigh channels. T h e optimum value for the switching levels between the Axed modulation schemes is found. Th i s is achieved by ,optimising the B E R a n d throughput for wireless computer d a t a and speech systems. Using the optimised switching thresholds, the system performance is also evaluated over Rician channels. 1. I N T R O D U C T I O N Following Shannon's fundamental work and Lee's seminal contribution on the channel capacity of fading channels [I] in this treatise we propose a scheme allowing us to approach the predicted channel capacity potential of fading wireless channels. The rapid fluctuations in received power result from multi-path propagation in a mobile radio environment. In the past systems operated at increased average transmit powers in order to account for these fluctuations and hence to obtain the desired Bit Error Rate (BER). However, in a mobile radio environment increasing the average transmit power has undesirable consequences in terms of coand adjacent-channel interference and power consumption. A more attractive alternative to mitigate this fast fading is to employ a more robust modulation scheme, when a low ins tantakus SNR is expected at the receiver. Moreover, when the instantaneous SNR increases again, a less rugged scheme exhibiting a higher throughput should be employed. This was initiated by Steele and Webb and presented in a keynote paper [2], which discussed adaptive differential modulation and considered the effect of SNR and co-channel interference. Morinaga [3] considers the employment of such adaptive modulation in terms of its future within mobile multimedia apparatus. In order for a transmitting radio to select the appropriate modulation scheme there must be some information available to it upon the instantaneous quality of the channel. This can be achieved by using Time Division Duplex (TDD), which provides a convenient framework for exploiting the correlation between the upand down-link complex envelope of the channel, given that the normalised Doppler frequency is sufficiently low. Therefore, adaptive modulation, within a TDD scenario relies upon the correlation ISPACS'96 SINGAPORE 26-28 NOV. 1996 Figure 1: Received power fluctuation over the duration of one TDD slot, when compared with the deviation over the whole channel results in a single slot exhibiting nearGaussian channel characteristics. The correlation between corresponding slots in adjacent TDD frames may be exploited. between received and transmitted frames to estimate s, the instantaneous power that will be received for a given set of symbols. Figure 1 shows this principle, and demonstrates that it is reasonable to assume that the channel does not fluctuate rapidly over the duration of a received slot. The estimation of s is compared against a set of n switching levels, I,, and the appropriate modulation scheme is selected accordingly. Following Kamio et a1 [4] Binary Phase Shift Keying (BPSK), Quaternary Phase Shift Keying (QPSK) and multilevel Quadrature Amplitude Modulation (QAM) can be invoked on the basis of the following thresholding operations: No Transmission if l l < s BPSK if 11 5 s < 12 MS = { QpsK if l z 5 s < l3 (1) Square 16 Point QAM if 13 5 s < 14 Square 64 Point QAM if s 5 14 where the threshold values of 1, will be discussed later. The thresholds 11, lz, l3 and L 4 predetermine the performance of an adaptive modulation scheme under given channel conditions. The lower the threshold values, tho h;mh..'Lthroughput,, that is, on average more bits will be transmitted using a higher number of Bits Per Symbol (BPS). Conversely, the higher the values of 11, 12, 13 arid 14, the lBwer the BER of the overall adaptive modulation scheme for given channel conditions. Clearly, BER can be traded with BPS performance and vice versa. The optimum trade-off will depend upon the type of information being transmitted and the source and channel coders used. The trade-off is dependent upon the type of information that is to be transmitted, in order to satisfy the different network characteristics required by video, voice and computer data. Generally, interactive video and voice information cannot sustain as much latency across the link as computer data information. However, computer data information is less robust to channel errors. The BER performance of the adaptive modulation identifies how robust the information transmitted over the link needs to be. The latency introduced depends upon whether the information is buffered at the transmitter, when the instantaneous channel SNR is low. As the instantaneous channel SNR increases, the buffer may be emptied but latency has been incurred. The latency is therefore dependent upon the average BPS performance of the system. The source coder and adaptive modulation scheme should be selected for optimum compatibility. Correct selection of the source coder [5] can allow improved quality of transmission in poor channel conditions by reducing the bit rate and consequently the data experiences a lower BER. Moreover, in good channel conditions, the overall source representation quality can be improved by increasing the bit rate, although the associated BER will typically also be increased. 2. PERFORMANCE OPTKMISATKON The upper-bound performance of the underlying adaptive modem scheme was characterised in Reference [6]. The BER performance of coherent modulation schemes with 1, 2, 4 and 6 Bits Per Symbol (BPS) assuming perfect clock and carrier recovery, in a Gaussian channel are known [7]. The corresponding expressions are given below: where Q(r ) = & Jzm e ~ ~ / ' dx, y is the slgnal-to-noise ratio (SNR), while Pb(y), Pq(y), P ~ c ( y ) and Psr(y), are the mean BERs of BPSK, QPSK, square 16 point square QAM, and square 64 point QAM, respectively. The PDF of the fluctuations in instantaneous received power, s, over a Rayleigh channel are given by: where S is the average signal power. Assuming a sufficiently low normalised Doppler frequency in order to maintain a near-constant fading envelope and hence Gaussian conditions for the duration of a modulation symbol and employing Pilot Symbol Assisted Modulation (PSAM) [8], upper bound BER performances can be obtained for the above four modulation schemes over a Rayleigh channel. For any of the modulation schemes, if X,(y) is the Gaussian BER performance, as given in Equations (Z), (3), (4) or (5), then X , (SIN) given below will be the upper bound for the BER performance in a Rayleigh channel: Therefore, the narrow-band upper bound BER performance of an adaptive modulation scheme similar to that described in [4] may be computed from: (8) where 11, 12, Is, 14 and B are the thresholds between transmission off, BPSK, QPSK, square 16 point and square 64 point QAM, while B is the mean number of BPS, given by: Adaptive modulation schemes may select the appropriate modulation level for the transmitted frame on the basis of either the number of errors encountered in the received frame or the received signal strength L.71. The former is only possible in a system that includes some error detection. Hae , the received signal strength relative to the switching values of 11, 12, ls and /4 is used to select the appropriate modulation level for each frame. The difference between this upper bound performance and a certain desired performance can be used as a cost function for given modulation switching levels of Z1, Z2, Z3 and 14. Minimisation of this cost function may be achieved iteratively by varying the switching levels, [9] 11, 12, 13 and la using Powell's optimisation algorithm [lo]. The BER and BPS performances were evaluated for average channel SNRs in the range of 0 dB to 50 dB in IdB intervals. The optimisation cost function was defined as: Total Cost = BER Cost(i) + BPS Cost(i) (10) IEEE ICCSnSPACS '96 1655