Capacity of MIMO Dispersive Fading Channels and the Achievable Error Performance of OFDM Signals in Frequency Dispersive Fading Channels

Licentiate thesis, 2008

Communication over a single-input single-output (SISO) and a multiple-input multiple-output (MIMO) dispersive fading channel were studied in the context of the ergodic Shannon channel capacity and the achievable error performance. A major contribution to the study is the equivalent SISO and MIMO vector channel models, derived from the corresponding waveform channel models, using a complete orthonormal and finite set of eigenfunctions to represent the waveform channel's output. The discretization of the continuous-time waveform channel model using the eigenfunctions of the autocorrelation function of the fading channel's output leads to a simple and tractable vector channel model equivalent to the waveform model, since the observables represent the sufficient statistics (SS). The equivalent vector channel model obtained comprises of parallel equivalent fading channels. The ergodic capacity results obtained using the equivalent vector channel models for the SISO and MIMO WSSUS fading dispersive channels respectively indicate that the fading channel capacity closely approaches that of the AWGN only channel, provided that the channel is known at the receiver. In the second part of the study, the achievable error performances of two different types of OFDM receivers were compared for OFDM signaling over an AWGN only channel and over a time-selective flat-fading channel with AWGN. Both types of receivers (one optimal, one suboptimal) employ maximum-likelihood (ML) symbol sequence detection. However, the SS observables (input to the ML detector) are provided only by the receiver that discretizes the receive signal with respect to the complete orthonormal set that spans the receive signal space. The suboptimal receiver employs direct sampling of the received signal, and this method in this case is information-lossy. The numerical results for the achievable error performance, where the error performance is quantified via the average OFDM symbol error probability, were obtained using the A* heuristic tree-search algorithm, for the channel known at the receiver. Two important observations stem from the numerical results obtained. First, for the case of time-selective flat-fading SISO and MIMO channels, the error performances of both types of OFDM receivers benefit from the implicit temporal diversity offered by the fading channel. This strongly motivates us to adopt signaling schemes that take advantage of the implicit diversity offered by the channel. This is achieved by taking the OFDM symbol duration to be longer than the coherence time of the channel, so that each OFDM signal tone undergoes several independent channel fades. Secondly, given a signal-to-noise ratio (SNR), the optimal OFDM receiver outperforms the direct signal sampling receiver. OFDM receivers that perform direct signal sampling are necessarily information-lossy, and do not derive the full benefit of the implicit fading channel diversity. Computing the exact error performance in fast fading becomes a computationally complex task for a high number of signal tones in the OFDM signal. A tight analytical upper bound on the exact ML symbol error rate performance for multitone signaling via time-selective fading channels is proposed. This upper bound is named the 2-dimensional expurgated union bound. It provides a significant improvement over the classical union bound and the expurgated (1-dimensional) union bound. It also provides insight into the effects of time-selective fading on both the interchannel interference (ICI) and the optimally detected SNR. In addition, we proposed two tight simulated bounds on the exact ML error performance in time-selective fading: a simulated upper bound that uses a modified trellis search detector, and a simulated lower bound, that uses limited knowledge of the ICI caused by Doppler spreading.