On capacity of noncoherent MIMO with asymmetric link strengths

Abstract

We study the generalized degrees of freedom (gDoF) of the block-fading noncoherent MIMO channel with asymmetric distributions of link strengths, and a coherence time of T symbol durations. We first derive the optimal signaling structure for communication over this channel, which is distinct from that for the i.i.d MIMO setting. We prove that for T = 1, the gDoF is zero for MIMO channels with arbitrary link strength distributions, extending the result for MIMO with i.i.d links. We then show that selecting the statistically best antenna is gDoF-optimal for both Multiple Input Single Output (MISO) and Single Input Multiple Output (SIMO) channels. We also derive the gDoF for the 2 × 2 MIMO channel with different exponents in the direct and cross links. In this setting, we show that it is always necessary to use both antennas to achieve the optimal gDoF, in contrast to the results for 2 × 2 MIMO with identical link distributions.

Generalized Degrees of Freedom of Noncoherent Diamond Networks

“…The above works considered a DoF framework for the noncoherent model, in the sense that for high-SNR, the link strengths are not significantly different, i.e., the links scale with the same SNR-exponent. The gDoF framework for noncoherent MIMO was considered in [12], [13] and it was shown that several insights from the DoF framework may not carry on to the gDoF framework. It was shown that a standard training-based scheme is not gDoF optimal and that all antennas may have to be used for achieving the gDoF, even when the coherence time is low, in contrast to the results for the MIMO with i.i.d.…”

“…From [17], we obtain that a Han-Kobayashi scheme [6] for IC can achieve the following rate region for all p (U 1 ) p (U 2 ) p (X 1 |U 1 ) p (X 2 |U 2 ): 12 for gDoF, since both of these cases obtain α = 0. Hence, we can have λ p = 1/INR.…”

“…The DoF was shown to be M * (1 − M * /T ) in that case. The case of the noncoherent MIMO channel with asymmetric statistics on the link strengths was recently studied in [15], [16]. In this work, the authors showed that the gDoF for single-input-multiple-output (SIMO) and multiple-input-single-output (MISO) channels can be achieved by using only the strongest link.…”

Generalized Degrees Freedom of Noncoherent MIMO Channels With Asymmetric Link Strengths

“…The capacity of fading multiple input multiple output (MIMO) channels when neither the receiver nor the transmitter knows the fading coefficients was first studied by Marzetta and Hochwald [2]. They considered a block fading channel model where the fading gains are Shorter version of this work appeared in [1] with an outline of proofs. This version has complete proofs.…”

“…This method of scaling the channel strengths with different SNR exponents to obtain the gDoF region is also done in other works like [9], [10]. 1 For ease of analysis, we absorb the transmit SNR into the channel strengths, hence the capacity characterization does not include the transmit SNR explicitly. The noise at receivers are of unit variance.…”