Communication rates for fading channels with imperfect channel-state information

Zusammenfassung

The present thesis studies information rates for reliable transmission of information over fading channels in the realistic situation where the receiver has only imperfect channel-state knowledge. Of particular interest are analytical expressions of achievable transmission rates under imperfect and no CSI, that is, lower bounds on the mutual information and on the Shannon capacity. A well-known mutual information lower bound for Gaussian codebooks is obtained when conflating the additive (thermal) noise with the multiplicative noise due to the imperfections of the CSIR into a single effective noise term, and then assuming that this term is independent Gaussian. This so-called worst-case-noise approach allows to derive a strikingly simple and well-known lower bound on the mutual information of the channel. A first part of this thesis proposes a simple way to improve this worst-case-noise bound by means of a rate-splitting approach: by expressing the Gaussian input as a sum of several independent Gaussian inputs, and by assuming that the receiver performs successive decoding of the corresponding information streams, we show how to derive a larger mutual information lower bound. On channels with a single transmit antenna, the optimal allocation of transmit power across the different inputs is found to be approached as the number of inputs (so-called layers) tends to infinity, and the power assigned to each layer tends to zero. This infinite-layering limit gives rise to a mutual information bound expressible as an integral. On channels with multiple transmit antennas, an analogous result is derived. However, since multiple transmit antennas open up more possibilities for spatial multiplexing, the rate-splitting approach gives rise to a whole family of infinite-layering bounds. This family of bounds is closely studied for independent and identically zero-mean Gaussian distributed fading coefficients (so-called i.i.d. Rayleigh fading). Most notably, it is shown that for asymptotically perfect CSIR, any bound from the family is asymptotically tight at high signal-to-noise ratios (SNR). Specifically, this means that the difference between the mutual information and its lower bound tends to zero as the SNR tends to infinity, provided that the CSIR tends to be exact as the SNR tends to infinity. A second part of this thesis proposes a framework for the optimization of a class of utility functions in black-Rayleigh fading multiple-antenna channels with transmit-side antenna correlation, and no CSI at the receiver. A fraction of each fading block is reserved for transmitting a sequence of training symbols, while the remaining time instants are used for transmission of data. The receiver estimates the channel matrix based on the noisy training observation and then decodes the data signal using this channel estimate. For utilities that are symmetric functions of the eigenvalues of the matrix-valued effective SNR (such as, e.g., the worst-case-noise bound), the problems consisting in optimizing the pilot sequence and the linear precoder are cast into convex (or quasi-convex) problems for concave (or quasi-concave) utility functions. We also study an important subproblem of the joint optimization, which consists in computing jointly Pareto-optimal pilot sequences and precoders. By wrapping these optimization procedures into a cyclic iteration, we obtain an algorithm which converges to a local joint optimum for any utility.