Hybrid Beamforming Designs for Massive MIMO Millimeter-Wave Heterogeneous Systems

Network densification through the deployment of small cells along the coverage area of a macro-cell, employing massive multiple input multiple output (MIMO) and millimeter-wave (mmWave) technologies, is a key approach to enhancing the network capacity and coverage of future systems. For ultra-dense mmWave heterogeneous scenarios with a massive number of users, one should address both inter- and intra-tier interferences contrary to the low-density scenarios, where the network is mainly noise limited. Therefore, this paper proposes low complex hybrid analog-digital receive and transmit beamforming techniques for ultra-dense uplink massive MIMO mmWave heterogeneous systems to efficiently mitigate these interferences. At the small cells, the hybrid analog-digital receive beamforming/equalizer is computed in a distributed fashion, where the analog processing is performed at the small cell base stations or access points and the digital part at a central unit for joint processing. To optimize the analog part of the hybrid equalizer and the precoders used at the user terminals, we consider as a metric the distance relative to the fully digital counterpart induced by the Frobenius norm. In the optimization problem, apart from the analog constraints usually considered in the homogeneous systems, we further impose the constraints inherent to the distributed nature of the access points. To cancel the inter-tier interference, the digital parts of the precoders employed at the small cell user terminals are designed so that this interference resides in a low-dimensional subspace at the macro base station. The results show that the performance of the proposed hybrid analog-digital precoder/equalizer scheme is close to the fully digital counterpart and is able to efficiently remove both inter- and intra-tier interferences.