Capacity analysis for parallel and sequential MIMO equalizers

It is well known that linear MMSE can outperform its zero-forcing counterpart. In combination with a successive interference canceller, MMSE can fully exploit the capacity of MIMO (MultipleInput-Multiple-Output) channels [1, 2]. In practice, however, such an advantage is compromised due to its implementation complexity and the requirement of accurate SNR estimate. Thus other equalizers such as zero-forcing may present an attractive alternative as long as the performance gap is tolerable. This motivates a need to quantify the tradeoff between MMSE and zero-forcing in both parallel and sequential structures. In this paper, the capacity performance of different equalization schemes is investigated, with closed-form formulas provided in terms of two key measures: capacity gaps and ratios. We also conclude that the capacity gain via structural choice (between parallel and sequential) far out-weights that via filter choice (between zero-forcing and MMSE). Indeed, the latter is found to be almost negligible for most practical SNR regions. It is also shown that the sequential zero-forcing equalizers can asymptotically reach the channel capacity when SNR approaches infinity, irrelevant of the detection order. Although this paper is focused on the flat-fading channels, the result is directly extendable to the ISI case by slicing the frequency band into infinitesimal stripes, each of which can be treated as flat. 1. MATHEMATICAL CHANNEL MODEL We consider a general MIMO communication system adopting transmit and receive antenna elements: (1) where , are sample stacks of the complexvalued receiver data and transmission sequences, and is the channel transfer function. The total transmission power is constrained to and is shared by the transmitting antennas with distribution factors : , where . The thermal noises are both spatially and temporally white i.i.d Gaussian random processes with independent real and imaginary parts and variance . Assuming independent inputs, the capacity of the MIMO system in (1) is well known as