A Performance Study of Massive MIMO Heterogeneous Networks with Ricean/Rayleigh Fading

electronics Article A Performance Study of Massive MIMO Heterogeneous Networks with Ricean/Rayleigh Fading James Kweku Nkrumah Nyarko * ID and Christian Ango Mbom School of Electronics and Information Engineering, Northwestern Polytechnical University, Xi’an 710072, China; * Correspondence: Received: 2 May 2018; Accepted: 18 May 2018; Published: 23 May 2018



 Abstract: Massive multiple-input and multiple-out (massive MIMO) systems and heterogeneous networks (HetNet) are envisioned to meet the new performance objectives of evolving networks. Now, the main challenge of massive MIMO with HetNet in two-tier networks is how to alleviate interference generated by the randomly deployed femtocells to the macro cells. In this paper, we investigate massive MIMO with HetNet, where the intended macro base station (MBS) transmission follows Ricean fading and interfering femto BS transmissions follow Rayleigh fading. Then, by exploiting matrix and stochastic geometric tools, we derive tight approximations for the intended signal power and aggregated interfering power signal. And derive the signal-to-interference (SIR) with the convolution of the two power signals. Then, we obtain the performance objectives: coverage and outage probabilities, and area spectral efficiency. Further, to reduce the cell edge effects and improve the SIR, we study the role of massive MIMO beamforming coordination with the high-powered MBSs. Thus, we develop maxi-min optimization to control the MBS transmit power. Numerical results show that the coverage and outage performance converge for different user locations, pathloss and Ricean factor. The monotonic increase in Ricean factor improves the SIR of a user located within coverage region. Optimal values of macro BS antenna and transmit power guarantee rate-fairness between the coordinating MBSs, and avoid strong Ricean channel correlation. Also, the performance gain is dependent on the user location, but independent of the cell size. Keywords: massive MIMO; Ricean fading; beamforming; stochastic process; Heterogeneous network; interference coordination; spectral efficiency 1. Introduction The next generation wireless networks are to support the growing demands for high data rate especially over the coverage area; these require efficient network modeling and design. Traditionally, cellular networks assume hexagonal, circular and square shape topologies, with the base station (BS) at the center of the cell. Recent network design in urban and suburban areas require random clustering [1]; this has necessitated the redesigning of the traditional cellular networks. A wireless network is heterogeneous, such that the small cells are offloading the macrocell, thereby improving the cell-center, cell-edge and indoor performance. The HetNets are envisioned to provide the solution with fast, flexible, cost efficient, fine tuned design and network expansion for the traditional cellular network architecture [2]. The base stations (BSs) in HetNets are characterized by the transmit power: different low-power BSs (Pico, Femto Access Points, micro) in addition with traditional high-power MBS to meliorate the coverage. The tiers consisting of BSs are ordered with the transmit power such that the served tier provides the highest signal power [3,4]. Thus, the tier’s BSs transmit power, fading, path loss and resource allocation. Consequently, the neighboring tier’s BSs Electronics 2018, 7, 79; doi:10.3390/electronics7060079 www.mdpi.com/journal/electronics Electronics 2018, 7, 79 2 of 21 generate severe interference which is a limiting factor for the signal-to-interference (SIR) in achieving the network throughput [5,6]. This requires new approach to reduce the interference. 1.1. Related Works Massive MIMO with HetNet takes into account the placement of BSs, user terminals and propagation model (In practical perspective, occurrence of random fading due to scattering and LoS signals depend on the environmental factors such as distance, geographical structure and clutter). Recently, Random matrix theory and stochastic geometry are used to study the SIR distribution and the performance gain of massive MIMO HetNet systems [7,8]. But the coexistence of the multiple and different BSs generate interference signals. User-centric analysis of the interference with massive MIMO HetNet is comprehensively discussed in [5,6,9,10], where the SINR is modeled over the locations of the users, BSs and characterized by multi-path fading. Incorporating multi-path fading into the point process model [11], the path loss with the fading can be geometrically characterized, then the coverage performance is conditioned on the user locations [12]. The trade-off between the link reliability and area spectral efficiency (ASE) in multiuser MIMO HetNet is discussed in [10], this primarily requires efficient analysis of the channel fading. Then, performance of massive MIMO HetNet can be analyzed in the uncorrelated Rayleigh channel and uncorrelated Ricean MIMO channel. In [13,14], massive MIMO HetNet have been studied for uplink and downlink deployment, respectively, under Rayleigh channel fading. Also, the average rate performance over generalized fading channels are analyzed in [15,16], where desired and interfering signals are separately derived with different fading models such as Rayleigh and Nakagami fading. And in [3,13], the channels are modeled with Rayleigh fading, these works analyzed both the desired and interfering signals of the downlink SINR with Rayleigh fading model. But the assumption that all the channel fading are dominated with non line of sight (NLoS) transmissions is practically unrealistic. Therefore, the authors in [17,18] studied the general performance gain with the path loss of the LoS and NLoS signal. Then, massive MIMO channel can propagate jointly with both NLoS and LoS channel, where the phases and power are combined, thus, the mean power determines the Ricean channel gain. An analytical approach for evaluating the coverage probability of HetNet with the desired propagation signals modeled with Ricean fading and interfering propagation signals modeled with Rayleigh fading, has recently been introduced in [19]. This is due to the fact that the signal strength deteriorates at the cell edge as propagation enters the shadowed region, where dominate LoS is difficult to exist. As such, the interfering signals at the location of a typical user are dominated with scattering signals [1]. Consequently, owing to the complexity in analyzing Ricean distribution, especially the difficulty in approximating the Bessel function, the majority of present contributions in literature [9,10,14–16,20,21] have focused on Rayleigh distribution for the coverage and outage probabilities. In [19], the authors analyzed coverage probability with Ricean and Rayleigh distributions for desired and interfering signals, respectively, while the authors in [22,23] investigated the perfo (...truncated)