Optimal Spatial Correlations for the Noncoherent MIMO Rayleigh Fading Channel

Abstract

The behavior in terms of information theoretic metrics of the discrete-input, continuous-output noncoherent MIMO Rayleigh fading channel is studied as a function of spatial correlations. In the low SNR regime, the mutual information metric is considered, while at higher SNR regimes the cutoff rate expression is employed. For any fixed input constellation and at sufficiently low SNR, a fully correlated channel matrix is shown to maximize the mutual information. In contrast, at high SNR, a fully uncorrelated channel matrix (with independent identically distributed elements) is shown to be optimal, under a condition on the constellation which ensures full diversity.In the special case of the separable correlation model, it is shown that as a function of the receive correlation eigenvalues, the cutoff rate expression is a Schur-convex function at low SNR and a Schur-concave function at high SNR, and as a function of transmit correlation eigenvalues, the cutoff rate expression is Schur-concave at high SNR for full diversity constellations. Moreover, at sufficiently low SNR, the fully correlated transmit correlation matrix is optimal. Finally, for the general model, it is shown that the optimal correlation matrices at a general SNR can be obtained using a difference of convex programming formulation.

Capacity bounds for peak-constrained multiantenna wideband channels

“…Hence, both receive and transmit correlation are beneficial for sufficiently large bandwidth. This observation agrees with the results for memoryless and block-fading channels reported in [10]- [12]. In the wideband regime, while transmit correlation is beneficial in both the coherent and the noncoherent setting because it allows for power focusing, receive correlation is beneficial rather than detrimental in the noncoherent setting for the following reason: for fixed M T and M R , the rate gain obtained from additional bandwidth is offset in the wideband regime by the corresponding increase in channel uncertainty (see Figs.…”

“…For the separable (Kronecker) spatial correlation model [8], [9], Jafar and Goldsmith [10] proved that transmit correlation increases the capacity of a memoryless fading channel. Moreover, in the low-SNR regime, the rates achievable with on-off keying on memoryless fading channels [11] and with finite-cardinality constellations on block-fading channels [12] increase in the presence of spatial correlation at the transmitter, the receiver, or both.…”

“…For each slot, we express the input and output vectors in the coordinate systems defined by the eigendecomposition of the transmit and receive correlation matrices, respectively. A similar transformation is used in [10], [12] for a frequencyflat block-fading spatially correlated MIMO channel. Let the eigendecomposition of the spatial correlation matrices be…”

On the Achievable Rate of Stationary Fading Channels

“…Regarding further reading on capacity results for the noncoherent capacity we refer back to Section 1.1. In addition, the scenario of spatial antenna correlation in the noncoherent case has been examined in [51], [111] and [129], where the first and the second one discuss this problem in the context of a block fading channel and the third one assumes a temporally uncorrelated channel, i.e., both setups are different to ours.…”

Capacity lower bound and energy efficiency of training‐based MIMO systems over correlated channels

“…Practical MIMO channels exhibit various correlations especially spatial fading correlation [8,9], which should not be ignored in the theoretical analysis. And it has been shown that spatial correlation provided known a priori should be viewed as a potential benefit, rather than a hindrance especially at low SNR, for example, in [10][11][12] for channel estimation, [13] for energy efficiency of coherent communications and [14,15] for mutual information of noncoherent channels.…”