Innovations based maximum likelihood sequence estimation for Rayleigh fading channels

This thesis deals with the use of the innovations approach for developing a general maximum likelihood sequence estimation (MLSE) receiver for digital signals transmitted over Rayleigh fading channels. First, it is shown that the innovations process and the normalized linear prediction errors are mathematically equivalent regardless of whether the given gaussian random process is stationary or not. Then the conceptually powerful and elegant innovations approach is applied to Rayleigh fading channels to derive the receiver structure which can be implemented by a bank of time-invariant FIR linear filters followed by squaring operations and a Viterbi processor. The proposed receiver, with a computational complexity independent of the transmitted signal sequence length, is applicable to most practically modulated signals and to fast or slow frequency-selective or nonselective Rayleigh fading channels. A unified interpretation of MLSE of signals transmitted over both gaussian noise channels in the presence of ISI and Rayleigh fading channels is presented based on the innovations process. The innovations-based MLSE receiver has a reasonable geometrical interpretation. It is shown that, in some special cases, the MLSE of data is in fact one of choosing the signal sequence which minimizes the linear prediction errors. Error performance of the receiver is studied theoretically by using the innovations approach and discrete-time Karhunen-Loeve transform. An analytical expression for the sequence pairwise error probability, which is determined by the eigenvalues of a matrix generated from the autocorrelation function or the received signal, and an upper bound on the bit error rate are derived. The efficiency of diversity reception is investigated. Computer simulations are performed and the results are presented to validate analysis.