Praise for Fundamentals of WiMAX

370 Chapter 11 • Link-Level Performance of WiMAXthe channel across the various transmit and receive antennas. Since the angular-scattering modelof the wireless channel is not explicitly captured by the ITU channels, we assume that the spatialcorrelation is an exponential function of distance. Thus, for a linear array of antenna elementswith equal spacing, R t and R r can be expressed as a function of ρ t and ρ r , the correlationbetween two adjacent antennas at the transmit and receive ends, respectively:1 ρ t ρ t2 ρ3 tρR t 1 ρ t ρ2 tt =ρ t2 ρ t 1 ρ tρ t3 ρ t2 ρ t 11 ρ r ρ r2 ρ3 rρR r 1 ρ r ρ2r =r. (11.3)ρ r2 ρ r 1 ρ rρ r3 ρ r2 ρ r 1The coloring matrices Q r and Q t can be obtained by Choleski factorization of the correlationmatrices R t and R r , respectively. Table 11.1 shows the various parameters and assumptionsused for the link-level simulation results.11.2 AWGN Channel Performance of WiMAXThe Shannon capacity [18] of a communication system is a theoretical bound that no real communicationsystem can exceed given the SNR and bandwidth constraints. Thus, how close a realworldcommunication system comes to this bound is often used as a measure of its efficiency.Since in an AWGN channel, the receiver does not need to mitigate the effects of the channel,performance is limited only by the modulation and channel coding used. Thus, the performancein an AWGN channel relative to Shannon capacity can be used as a benchmark tounderstand the inherent limitations of a communication system, such as WiMAX. AWGN channelperformance can also be used to determine the SNR threshold for adaptive modulation andcoding. The system can use these thresholds to determine the appropriate choice of modulationand coding formats for a given SNR in a fading channel.A fundamental assumption behind Shannon’s channel capacity is that the transmitter has anarbitrarily large set of continuously varying modulation alphabets and FEC codewords that canbe used to transmit the information. However, a real communication system must operate withinlimited combinations of available modulation alphabets and suboptimal codes. For example, inthe case of WiMAX, the only available modulation alphabets are QPSK, 16 QAM, and 64QAM, as described in Section 8.4. Although it can adapt the modulation according to the currentSNR, the transmitter must choose from one of these three modulation alphabets. In this section,we provide a derivation of a modified capacity of a system constrained to the finite choice ofmodulation alphabets, which we believe is a more appropriate theoretical bound to be comparedagainst the capacity of WiMAX.Figure 11.2 shows a communication system consisting of an information source, a channel,and a detector. The information signal x entering the channel is a sequence of amplified symbolsbelonging to a given modulation alphabet. These symbols are amplified such that the total energyper symbol is E s . An AWGN noise z is added to the signal by the channel before presenting it to