Impact of Underlaid Multi-antenna D2D on Cellular Downlink in Massive MIMO Systems

In this paper, we consider a massive multiple-input multiple-output (MIMO) downlink system underlaid with a network of multi-antenna D2D user equipments (UEs). Each D2D transmitter (Tx) uses all its antennas to beamform information towards its desired D2D receiver, which uses only a single antenna for reception. While beamforming at the D2D Tx reduces D2D interference to the neighbouring cellular UEs (CUEs), the cellular-to-D2D interference is also negligible due to highly directional beamforming at the massive MIMO base station. For the above proposed system, we analyze the average per-user spectral efficiency (SE) of CUEs (R^c,d) as a function of the D2D area spectral efficiency (ASE). Our analysis reveals that for a fixed D2D ASE (R0^(d)) and fixed number of D2D antennas (N), with increasing density of D2D Txs (λ), R^c,d increases (for sufficiently large λ) and approaches a fundamental limit R∞^c,d as λ→∞. Also, R∞^c,d depends on R0^(d) and N, only through the ratio [(R0^(d))/(N-1)], i.e, for a given fundamental limit R∞^c,d, the D2D ASE can be approximately doubled with every doubling in N.