Code and receiver design for the non-coherent fast fading channel

We consider the problem of design of coding/modulation and demodulation/decoding schemes for single- or multiple-antenna communication systems over a block independent Rayleigh fading channel, when the channel state information (CSI) is not available at the transmitter and the receiver.; For the choice of pilot assisted transmission schemes, we explore two possible receiver designs with increasing degree of sophistication. The first one utilizes a simple and explicit non-iterative channel estimation algorithm at the receiver. We show that this pilot-assisted system is exactly equivalent, in terms of performance analysis and design, to an appropriately "degraded" system having perfect CSI at the receiver. For the second receiver choice we propose a family of well-justified and simple suboptimal iterative detection/estimation algorithms that when considered in conjunction with pilot assisted transmission scheme and turbo-like outer codes, outperform the unitary constellations investigated in the literature in terms of both complexity and performance. Specific instances of the proposed systems (that use optimized irregular LDPC outer codes) are designed, that achieve a good tradeoff between complexity and performance and can be used to bridge the gap between the high complexity/high performance optimal scheme and low complexity/mediocre performance non-iterative estimation/coherent detection scheme.; To gain a better understanding of the fundamental limits of communication over non-coherent fading channels, we show that the capacity achieving input is isotropically distributed, unitary and has an independent amplitude distribution that has bounded support. Based on a well-founded conjecture in the literature that the amplitude distribution is discrete, we show theoretically and through numerical evaluations that starting from a single amplitude scheme, adding some probability mass to the zero amplitude increases the mutual information achieved.; Finally, the code design problem for very fast fading channels is considered and a novel system design that incorporates the zero mass point is proposed. Through constrained capacity analysis and Monte-Carlo simulations, this system is shown to provide some of the gain promised by information theoretic analysis. Simulations of the proposed system report at least 0.55 dB gain over conventional systems with no additional complexity.