On the Exact Distribution of Mutual Information of Two-User MIMO MAC Based on Quotient Distribution of Wishart Matrices

Abstract

The pre-print version of this work can be found in https://arxiv.org/pdf/1601.03439v1.pdf. AbstractWe propose an exact calculation of the probability density function (PDF) and cumulative distribution function (CDF) of mutual information (MI) for a two-user multiple-input multiple-output (MIMO) multiple access channel (MAC) network over block Rayleigh fading channels. This scenario can be found in the uplink channel of MIMO non-orthogonal multiple access (NOMA) system, a promising multiple access technique for 5G networks. So far, the PDF and CDF have been numerically evaluated since MI depends on the quotient of two Wishart matrices, and no closed form for this quotient was available. We derive exact results for the PDF and CDF of extreme (the smallest/the largest) eigenvalues. Based on the results of quotient ensemble, the exact calculation for PDF and CDF of mutual information is presented via Laplace transform approach and by direct integration of joint PDF of quotient ensemble's eigenvalues. Furthermore, our derivations also provide the parameters to apply the Gaussian approximation method, which is comparatively easier to implement. We show that approximation matches the exact results remarkably well for outage probability, i.e., CDF, above 10%. However, the approximation could also be used for 1% outage probability with a relatively small error. We apply the derived expressions to investigate the effects of adding antennas in the receiver and its ability to decode the weak user signal. By supposing no channel knowledge at transmitters and successive decoding at receiver, the capacity of the weak user increases and its outage probability decreases with the increment of extra antennas at the receiver end.

Optical MIMO communication with unequal power allocation to channels

“…Consequently, the Gaussian approximation for mutual information distribution has been used in earlier works as well and, in fact, has been found to work well even for not-so-large number of channels; see for example Refs. [53][54][55][56] in the context of MIMO wireless communication. On the other hand, our choice of Weibull distribution stems from the observation that the PDF of the mutual information for an arbitrary covariance matrix Q often exhibits negative skewness, as will be seen in the next section.…”

A Novel Codeword Selection Scheme for MIMO-MAC Lower-Bound Maximization

“…Then it finds the location index Limited feedback [ 25 , 26 ]. Because the channel matrix dimension is larger than the precoding matrix, the feedback precoding algorithm is better, and the limited feedback of IA achieves greater performance improvement with less feedback and has been widely studied [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ].…”

“…The limited feedback of IA shares the same codebook between the transmitter and receiver, and the receiver quantizes the channel matrix or precoding according to the obtained CSI and sends feedback for the location index of the quantization codeword [ 3 , 4 ]. Because the quantized channel matrix has a larger dimension than the quantized precoding matrix, the quantized precoding scheme has been widely studied [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. This paper proposes a MIMO Multiple Access Channel (MIMO-MAC) limited feedback IA algorithm that maximizes the rate lower-bound of the system user.…”

Spectral statistics for the difference of two Wishart matrices

“…Aside from a mathematical interest, these composite ensembles naturally apply to a variety of problems in physics, engineering and related areas. For instance, sums and products of random matrices have been used in the context of multiple channel communication [5,6,[27][28][29][30][31], quantum entanglement problem [47], neutral network analyses [49,50], and random supergravity theories [51][52][53]. Product of random matrices have also found applications in problems related to stochastic differential equations and Lyapunov exponents [48,[54][55][56][57][58], fixed point analysis for multi-layered complex systems [38], and Markov chains with random transition probabilities [39].…”