Further Results on the Capacity and Error Probability Analysis of Noncoherent MIMO Systems in the Low SNR Regime

Abstract

Abstract-The noncoherent single-user multiple-input-multiple-output (MIMO) channel in the low signal-to-noise ratio (SNR) regime is investigated from two viewpoints: capacity and probability of error analysis. The novelty in both viewpoints is that we allow an arbitrary correlation structure for the Gaussian observation noise. First, we look at the capacity of the spatially correlated Rayleigh fading channel. We investigate the impact of channel and noise correlation on the mutual information for the ON-OFF and Gaussian signaling schemes. Our findings establish that, in the low SNR regime, mutual information is maximized when the transmit antennas are fully correlated (the same holds for the receive array). Then, the deterministic channel setup is considered and a pairwise error probability (PEP) analysis for the generalized likelihood ratio test (GLRT) receiver is performed. This leads to a codebook design criterion on which we base the construction of new space-time constellations. Their performance is assessed by computer simulations and, as a byproduct, we show that our codebooks are also of interest for Bayesian receivers, which decode constellations with nonuniform priors.Index Terms-Channel capacity, colored noise, correlated Rayleigh fading, Gaussian modulation, generalized likelihood ratio test (GLRT) receiver, low signal-to-noise ratio (SNR), maximum a posteriori (MAP) estimation, multiple-input-multiple-output (MIMO) systems, noncoherent communications.

Low SNR analysis of the non-coherent MIMO channel under arbitrary channel and noise correlation structures

“…Further, we view the channel correlation matrix K as a system parameter which we can introduce and track. The generalization to arbitrary channel covariance matrices K comprises many scenarios of interest as special cases: the popular separable (Kronecker) spatial correlation model [2,3], a recently proposed spatial correlation model that takes into account coupling between transmit and receive sides [10], uncorrelated rayleigh fading channel model [8], etc. For a fair comparison of different correlation cases, we assume that tr(K) = M N ; A2 (Transmit power constraint) We impose the power constraint E[tr(…”

“…), we assume tr(Υ) = N T . In A3, as in [2], we let the data model depart from the customary assumption of spatio-temporal white Gaussian observation noise. In real scenarios the E term often has a very rich correlation structure, e.g, see [3] and pp.…”

“…In [1,2], the authors have extended the results from [8] to the case of the correlated Rayleigh fading channel model that obeys the Kronecker structure, with arbitrary noise covariance matrix. Here, we argue that this is also the case for the correlated Rayleigh fading channel model with an arbitrary channel covariance matrix (as in [1,2], the noise term is allowed to have an arbitrary covariance matrix). Moreover, we maximize the mutual information with respect to (w.r.t.)…”

“…This is due to the fact that a variety of digital communication systems (more specifically in wireless, sensor and satellite networks) operate in the power-limited region. See [2,3] for a more thorough discussion of this topic.…”

“…It is argued that the advantage of having multiple antennas is best realized when the fading is fully correlated, i.e., a performance gain of M N and a peakiness gain of M 2 N T can be achieved where M , N and T represent the number of transmit, receive antennas, and the length of the coherence interval, respectively. In [2], the approach in [8] has been extended as both noise and channel correlation have been taken in account.…”