Information-bearing noncoherently modulated pilots for MIMO training

In this correspondence, we deal with noncoherent communications over multiple-input-multiple-output (MIMO) wireless links. For a Rayleigh flat block-fading channel with M transmit- and N receive-antennas and a channel coherence interval of length T, it is well known that for T ≫ M, or, at high signal-to-noise-ratio (SNR) p ≫ 1 and M ≤ min {N, {⌊T/2cg⌋}, unitary space-time modulation (USTM) is capacity-achieving, but incurs exponential demodulation complexity in T. On the other hand, conventional training-based schemes that rely on known pilot symbols for channel estimation simplify the receiver design, but they induce certain SNR loss. To achieve desirable tradeoffs between performance and complexity, we propose a novel training approach where USTM symbols over a short length T_T (< T) are used as pilots which carry information to the receiver, and coherent communication is used for the remainder of the block. This new approach considerably reduces the receiver complexity when T is a small fraction of T, and recovers part of the SNR loss experienced by the conventional training-based schemes. When p → ∞ and T ≥ T_T ≥ 2M = 2N → ∞, but the ratios α = M/T, α₁ = T_T/T are fixed, we obtain analytical expressions of the asymptotic SNR loss for both the conventional and new training-based approaches, serving as a guideline for practical designs.