On the Exact Distribution of Mutual Information of Two-User MIMO MAC Based on Quotient Distribution of Wishart Matrices
Pivaro et al. EURASIP Journal on Wireless Communications and
Networking
On the Exact Distribution of Mutual Information of Two-User MIMO MAC Based on Quotient Distribution of Wishart Matrices
Gabriel Pivaro 0
Santosh Kumar 1
Gustavo Fraidenraich 0
0 Department of Communications, State University of Campinas (Unicamp) , Campinas, SP , Brazil
1 Department of Physics, Shiv Nadar University , Gautam Buddha Nagar, Uttar Pradesh , India
We 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.
Multiple access channel; Multiple-input multiple-output; Non-orthogonal multiple access; Mutual information; Outage probability; Rayleigh fading; Wishart matrices; Quotient ensemble; Extreme eigenvalues; Gap probabilities
1 Introduction
It is now well acknowledged that the use of multiple-input
multiple-output (MIMO) scheme is crucial to increase
the capacity and reliability of wireless systems. MIMO
setup provides several benefits such as higher received
power via beamforming, higher channel capacity via
spatial multiplexing without increasing bandwidth or
transmission power, and improved transmission robustness via
diversity coding [1]. Current cellular systems such as 4G
Long-Term Evolution (LTE) are using MIMO, and the next
generation system such as 5G considers the deployment
terminal with dozens of antennas, the so-called massive
MIMO. A new scheme called non-orthogonal multiple
access (NOMA) has been considered as a potential
solution to improve the system capacity of future wireless
systems due to its superior spectral efficiency [2, 3]. The
basic principle of NOMA is to serve multiple users by
power domain multiplexing at transmitter and
successive interference cancellation (SIC) at receiver, which can
achieve the capacity region of the downlink addictive
white Gaussian noise channel and significantly
outperform the orthogonal multiple access (OMA) schemes [3].
In this paper, we derive exact expressions to obtain
the distribution and the outage probability of the mutual
© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
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information for a two-user MIMO multiple-access
channel (MAC). To the best of our knowledge, no exact
expressions were derived before, under the following
assumptions: channel state information at receiver (CSIR),
block Rayleigh fading channel, and successive decoding
[4]. The main difficulty to derive exact expressions for
this scenario is that the mutual information is a random
variable that depends on the quotient of two Wishart
matrices [5]. The recent exact analysis of quotient
ensemble involving Wishart matrices led to the availability of the
corresponding joint probability density function (JPDF)
of the eigenvalues [6]. This opened the possibility to
describe, in an exact manner, the behavior of the mutual
information in a scenario such as MIMO NOMA uplink.
Therefore, we derive the exact expressions related to the
mutual information that allows, for example, the
analysis of the impact of adding more antennas at the base
station on the performance of network. In add (...truncated)