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 cellularto-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 (R (d) 0 ) 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 R (d) 0 and N , only through the ratio R (d) 0 N−1 , i.e, for a given fundamental limit R c,d ∞ , the D2D ASE can be approximately doubled with every doubling in N . Index Terms-Downlink, spectral efficiency, massive MIMO, multi-antenna, underlaid, D2D interference.

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Abstract-In this paper, we consider the 2 × 2 multi-user multiple-input-single-output (MU-MISO) broadcast visible light communication (VLC) channel with two light emitting diodes (LEDs) at the transmitter and a single photo diode (PD) at each of the two users. We propose an achievable rate region of the Zero-Forcing (ZF) precoder in this 2 × 2 MU-MISO VLC channel under a per-LED peak and average power constraint, where the average optical power emitted from each LED is fixed for constant lighting, but is controllable (referred to as dimming control in IEEE 802.15.7 standard on VLC). We analytically characterize the proposed rate region boundary and show that it is Pareto-optimal. Further analysis reveals that the largest rate region is achieved when the fixed per-LED average optical power is half of the allowed per-LED peak optical power. We also propose a novel transceiver architecture where the channel encoder and dimming control are separated which greatly simplifies the complexity of the transceiver. A case study of an indoor VLC channel with the proposed transceiver reveals that the achievable information rates are sensitive to the placement of the LEDs and the PDs. An interesting observation is that for a given placement of LEDs in a 5 m × 5 m × 3 m room, even with a substantial displacement of the users from their optimum placement, reduction in the achievable rates is not significant. This observation could therefore be used to define "coverage zones" within a room where the reduction in the information rates to the two users is within an acceptable tolerance limit.