This paper proposes a new hypothesis test to check the randomness and nonrandomness of the contaminated high dimensional signal. Specifically, for a signal plus noise model, we propose a statistic to distinguish whether the corresponding signal is random or not. In order to analyze the performance of the proposed method, we also prove two important results for signal plus noise models: 1) No eigenvalues outside the support of the limiting spectral distribution of the noncentered and centered sample covariance matrix; and 2) Exact separation of eigenvalues of the noncentered and centered sample covariance matrix. Simulation studies demonstrate that our proposed method works well under a variety of settings.

In this paper, we consider the fluctuation of mutual information statistics of a multiple input multiple output channel communication systems without assuming that the entries of the channel matrix have zero pseudovariance. To this end, we also establish a central limit theorem of the linear spectral statistics for sample covariance matrices under general moment conditions by removing the restrictions imposed on the second moment and fourth moment on the matrix entries in Bai and Silverstein (2004).

Using large-dimensional random matrix theory (RMT), we conduct mutual information analysis of a multiple-input multiple-output (MIMO) multiple access channel (MAC). Our channel model reflects the characteristics in small-cell networks where antenna correlations, line-of-sight components, and general type of fading distributions have to be included. The mutual information expression can be expressed as functionals of the Stieltjes transform through the so-called Shannon transform. Ideally, if the Stieltjes transform is known in the context of the large-dimensional RMT, then the problem is solved. However, it is difficult to derive the Stieltjes transform of the considered channel models directly, especially when the transmit correlation matrices are generally nonnegative definite and the channel entries are non-Gaussian. To overcome this, we use the generalized Lindeberg principle to show that the Stieltjes transforms of this class of random matrices with Gaussian or non-Gaussian independent entries coincide in the large-dimensional regime. This result permits to derive the deterministic equivalents (e.g., the Stieltjes transform and the ergodic mutual information) for non-Gaussian MIMO channels from the known results developed for Gaussian MIMO channels. As an application, we determine the capacity-achieving input covariance matrices for the MIMO-MACs and prove that the capacity-achieving input covariance matrices are asymptotically independent of the fading distribution.

In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the test statistics of the EBD algorithms. Two EBD algorithms using sample covariance matrices are considered: maximum eigenvalue detection (MED) and condition number detection (CND). The earlier studies usually assume that the number of antennas (K) and the number of samples (N) are both large, thus random matrix theory (RMT) can be used to derive the asymptotic distributions of the maximum and minimum eigenvalues of the sample covariance matrices. While assuming the number of antennas being large simplifies the derivations, in practice, the number of antennas equipped at a single secondary user is usually small, say 2 or 3, and once designed, this antenna number is fixed. Thus in this paper, our objective is to derive the asymptotic distributions of the eigenvalues and condition numbers of the sample covariance matrices for any fixed K but large N, from which the probability of detection and probability of false alarm can be obtained. The proposed methodology can also be used to analyze the performance of other EBD algorithms. Finally, computer simulations are presented to validate the accuracy of the derived results.

Random matrix theory is used to derive the limit and asymptotic distribution of signal-to-interference-plus-noise ratio (SIR) for a class of suboptimal minimum mean-square-error (MMSE) receivers applied to large random systems with unequal-power users. We prove that the limiting SIR converges to a deterministic value when$K$and$N$go to infinity with$\lim K/N =y$being a positive constant, where$K$is the number of users and$N$is the number of degrees of freedom. We also prove that the SIR of each particular user is asymptotically Gaussian for large$N$and derive the closed-form expressions of the variance for the SIR variable under real-spreading and complex-spreading channel environments. It is revealed that for a given$(K,N)$pair, under certain mild conditions, the variance of the SIR for complex-spreading channels is half of that for the corresponding real-spreading channels. Since the suboptimal MMSE receiver becomes optimal for the case when the users are equally powered, our results show that the conjecture made by Tse and Zeitouni for the complex-spreading case is not affirmative. We also derive the asymptotic distribution for SIR in decibels which provides better description when$N$is small. Numerical results and computer simulations are provided to evaluate the accuracy of various limiting and asymptotic results obtained in this paper.

This correspondence studies the asymptotic performance of output signal-to-interference-plus-noise ratio (SINR) for reduced-rank linear receivers with principal component filter. We prove that for code division multiple access (CDMA) systems with random spreading codes, when the number of users and the spreading gain go to infinity with their ratio being fixed, the output SINR converges to a fixed constant with probability 1, which is consistent with the conjecture made in Honig and Xiao, "Performance of reduced-rank linear suppression," IEEE Trans. Inf. Theory, vol. 47, no. 4, pp. 1928-1946, May 2001

This paper studies the asymptotic performance of signal detection for large random multiple-input multiple-output (MIMO) systems. Two iterative receivers are considered: unconditional MMSE receiver with soft interference cancellation (U-MMSE-SIC) and block-iterative generalized decision feedback equalizer (BI-GDFE). We prove that for the limiting case, the output SINRs at each iteration for both receivers converge in probability to their respective deterministic limits. We also show that for U-MMSE-SIC, the limiting SINR is determined by the statistics of the soft estimates; while for BI-GDFE, the limit is determined by the statistical reliability of the hard decisions. Numerical results have shown that the U-MMSE-SIC receiver has faster convergence than the BI-GDFE receiver with the price of higher computational complexity in each iteration due to the use of soft interference cancellation.