Error rate performance metrics for digital communications system

In this thesis, novel error rate performance metrics and transmission solutions are investigated for delay limited communication systems and for co-channel interference scenarios. The following four research problems in particular were considered. The first research problem is devoted to analysis of the higher order ergodic moments of error rates for digital communication systems with time- unlimited ergodic transmissions and the statistics of the conditional error rates of digital modulations over fading channels are considered. The probability density function and the higher order moments of the conditional error rates are obtained. Non-monotonic behavior of the moments of the conditional bit error rates versus some channel model parameters is observed for a Ricean distributed channel fading amplitude at the detector input. Properties and possible applications of the second central moments are proposed. The second research problem is the non-ergodic error rate analysis and signaling design for communication systems processing a single finite length received sequence. A framework to analyze the error rate properties of non-ergodic transmissions is established. The Bayesian credible intervals are used to estimate the instantaneous bit error rate. A novel degree of ergodicity measure is introduced using the credible interval estimates to quantify the level of ergodicity of the received sequence with respect to the instantaneous bit error rate and to describe the transition of the data detector from the non-ergodic to ergodic zone of operation. The developed non-ergodic analysis is used to define adaptive forward error correction control and adaptive power control policies that can guarantee, with a given probability, the worst case instantaneous bit error rate performance of the detector in its transition fi'om the non-ergodic to ergodic zone of operation. In the third research problem, novel retransmission schemes are developed for delay-limited retransmissions. The proposed scheme relies on a reliable reverse link for the error-free feedback message delivery. Unlike the conventional automatic repeat request schemes, the proposed scheme does not require the use of cyclic redundancy check bits for error detection. In the proposed scheme, random permutations are exploited to locate the bits for retransmission in the predefined window within the packet. The retransmitted bits are combined using the maximal-ratio combining. The complexity-performance trade-offs of the proposed scheme is investigated by mathematical analysis as well as computer simulations. The bit error rate of the proposed scheme is independent of the packet length while the throughput is dependent on the packet length. Three practical techniques suitable for implementation are proposed. The performance of the proposed retransmission scheme was compared to the block repetition code corresponding to a conventional ARQ retransmission strategy. It was shown that, for the same number of retransmissions, and the same packet length, the proposed scheme always outperforms such repetition coding, and, in some scenarios, the performance improvement is found to be significant. Most of our analysis has been done for the case of AWGN channel, however, the case of a slow Rayleigh block fading channel was also investigated. The proposed scheme appears to provide the throughput and the BER reduction gains only for the medium to large SNR values. Finally, the last research problem investigates the link error rate performance with a single co-channel interference. A novel metric to assess whether the standard Gaussian approximation of a single interferer underestimates or overestimates the link bit error rate is derived. This metric is a function of the interference channel fading statistics. However, it is otherwise independent of the statistics of the desired signal. The key step in derivation of the proposed metric is to construct the standard Gaussian approximation of the interference by a non-linear transformation. A closed form expression of the metric is obtained for a Nakagami distributed interference fading amplitude. Numerical results for the case of Nakagami and lognormal distributed interference fading amplitude confirm the validity of the proposed metric. The higher moments, interval estimators and non-linear transformations were investigated to evaluate the error rate performance for different wireless communication scenarios. The synchronization channel is also used jointly with the communication link to form a transmission diversity and subsequently, to improve the error rate performance.