Distributed MIMO Systems with ZF Detectors in Rayleigh-Inverse Gaussian Composite Fading Channels

Abstract

Distributed multiple-input multiple-output (D-MIMO) system has become a promising technique for next generation wireless networks, which offer considerably high throughput and link reliability over conventional point-to-point MIMO. This is achieved by packing multiple antennas at one end of the wireless channel into spatially separated multiple radio ports (RPs). Performance analysis of such distributed antenna systems (DASs) having different propagation paths pertaining to individual RPs becomes a challenging task as the communicating channel experiences combined effect of both small and large-scale fading, also known as composite fading. Composite fading is more realistic for systems like DAS and relay systems, and in such systems small-scale fading alone does not provide accurate statistical distribution of fading channels. In this dissertation, we consider D-MIMO wireless channels experiencing Nakagami-Inverse Gaussian (G) and Rayleigh-Inverse Gaussian (RIG) composite distributions and investigate the uplink performance of such systems in terms of ergodic capacity, average symbol error rate (SER) and outage probability (OP). We begin with the discussion on state-of-the-art composite distributions in modelling single-input single-output (SISO) and MIMO channels. Then the widely used Rayleigh-Gamma
(a.k.a. K) and Nakagami-Gamma (a.k.a. KG) distributions are reviewed in detail, and the
performance of MIMO systems over such channels are compared with RIG and G distributions, respectively in subsequent part of this dissertation. To this end, a reparametrized KG (KG(R)) model is proposed in the formulation of signal-to-noise ratio (SNR) distribution for SISO communication system. In the analysis of Inverse Gaussian (IG) shadowed composite fading channels, upper and lower bounds of ergodic capacity for optimal detectors are evaluated over G fading D-MIMO channels. However, the analysis of exact ergodic capacity and other performance measures can not be accomplished due to the unavailability of joint channel statistics of non-Gaussian fading channels. In order to perform in-depth characterization of channels operating over G distribution, we consider a point-to-point MIMO system with orthogonal space-time block code (OSTBC) transmit diversity technique. Interestingly, the MIMO OSTBC channel can be transformed into an equivalent scalar channel that significantly simplifies the mathematical exercise for analysis. Detailed analytical investigation is performed for MIMO OSTBC systems considering aforementioned figure of merits.
In subsequent analysis, we consider low complexity linear zero forcing (ZF) detector
which requires closed form density function of pseudo inverse of D-MIMO channel matrix. Therefore, analytically tractable Rayleigh distribution is assumed here as small-scale fading component that leads to RIG composite distribution in modelling D-MIMO channels. The presence of spatial correlation was also taken into consideration which is experienced frequently in multi-antenna scenarios. We first demonstrate the effects of spatial correlation on spatially multiplexed point-to-point MIMO system in reference to beamforming system which is highly immune to such correlation. In the next part of the analysis, a systematic characterization of RIG distribution is provided in modelling D-MIMO channels with ZF detectors in presence of transmit antenna correlation. Closed-form expressions of exact ergodic capacity, their approximations in high and low SNR regime and ergodic capacity bounds are found. The analytical expressions of average SER and OP are also deduced in tractable form. Additionally, we propose to formulate simplified expressions of average SER as well as OP in high SNR regime and assess their approximation accuracy. In further analysis of this dissertation, a D-MIMO system is considered in massive MIMO scenario and the performance of the resulting distributed massive MIMO (DM-MIMO) system is evaluated in detail. We consider two different D-MIMO architectures with the base station (BS) containing large number of antennas. The architecture of DM-MIMO-I system is analogous to the D-MIMO systems described earlier. For instance, in uplink scenario the RPs having multiple antennas of a DM-MIMO-I system are placed at arbitrary locations and simultaneously communicate with the centrally located BS. Here, the instantaneous output SNR of kth subchannel is formulated by applying the law of large numbers. On the other hand, the DM-MIMO-II architecture comprises of multiple BSs or remote access units (RAUs), distributed across the cell and arbitrarily located mobile unit. The performance of such
systems are evaluated for both finite and infinite number of RAU antennas. In the latter case, approximated SNR is expressed as a sum of unequal IG random variables and subsequently the closed-form expressions of asymptotic ergodic capacity and average SER are formulated. The correctness of theoretical analysis presented in this dissertation are corroborated through Monte-Carlo simulations. In light of this, the efficacy of considered systems are investigated in various severity of shadowing environments including light, average and frequent heavy shadowing. Moreover, the implications of fading and shadowing parameters, number of antennas, positions of RPs, locations of RAUs, antenna correlation, etc. on system performance are investigated.