Outage analysis and optimization of a stacked orthogonal space-time architecture and near-outage codes

We propose the stacked orthogonal space-time architecture for the quasi-static, multi-input multi-output (MIMO) Rayleigh fading channel where the K transmit antennas are divided into K/2 groups. Each group employs the Alamouti design as the inner code with the indeterminates being uncoded symbols or symbols from some outer code. Successive group interference suppression strategies based on the decorrelating and minimum mean-squared error (MMSE) filters are used to decode the component codes in some fixed or channel dependent order. These strategies exploit the specific structure of the inner codes to yield high diversity orders while preserving the decoupling property thereby enabling the use of single-input, single-output (SISO) outer codes. Due to the special structure of the effective channel matrix induced by the inner codes, the problems of finding exact frame error probability (FEP) or outage probability of the interference suppression schemes even for a fixed order of decoding are challenging. Nevertheless, these analysis problems are solved for the decorrelating case and the resulting FEP and the outage probabilities are optimized over the rate-power allocations across antenna groups. Alternatively, the outage probability is minimized over channel dependent ordering rules via a greedy algorithm for any given rate and power tuples. We also demonstrate the intimate connection between outage probability and the achievable FEP for long framelengths. When no outer codes are employed, the FEP of the optimized stacked orthogonal block code is shown, at a moderate spectral efficiency, to improve upon the FEP of uncoded VBLAST system when the latter is detected using even the maximum likelihood rule. This improvement is obtained with a much lower detection complexity. In the case of the optimized stacked space-time systems with (SISO) outer coding, we show that much better diversity orders and frame error probabilities (of about 4 dB in one example) are obtained relative to the codes of [1] and these improvements are also obtained with a lower decoding complexity.