Transmitter diversity code design for achieving full diversity on Rayleigh fading channels

Traditional code design for fading channels assumes that interleaving is able to make the fading on all received symbols independent. However, the ideal interleaving depth depends on vehicle speed via the Doppler rate. If the vehicle stops, infinite interleaving depth would be required. Transmitter diversity may be used to achieve independent fading without interleaving, even in the presence of zero Doppler. Even so, not all of the fading samples are uncorrelated, and this must be taken into account in code design or the desired diversity might not be achieved. In this work convolutional trellis codes are presented which utilize the full diversity capability of the system. A multichannel signaling model is presented which can accommodate transmitter diversity in addition to time diversity, receiver antenna diversity, and frequency diversity. The exact pairwise error event probability for frequency non-selective Rayleigh fading channels is derived for this model. At high signal-to-noise ratio a tight upper bound is derived. Examination of the error bound shows that the most important design metrics for transmitter diversity on Rayleigh fading channels are the minimum (1) effective Hamming distance ([special characters omitted]) and (2) effective product distance ([special characters omitted]). It is shown that for independent fading with one level of transmitter diversity these metrics are equivalent to the traditional Hamming and product distances. Useful properties of the design metrics are proven. It is shown how to compute [special characters omitted] and [special characters omitted] recursively. This allows efficient algorithms such as the Viterbi algorithm to be employed for code analysis. It is proven that under certain restrictions, codes which are geometrically uniform with respect to [special characters omitted] can only achieve one level of diversity. Other techniques to obtain space-time codes with a uniform distance spectrum are investigated. Design rules are presented which guarantee full diversity codes for any desired diversity level and throughput. Numerous codes are presented