This chapter treats the single-cell scenario of Section 2.2.1, where a base station uses an array of M antennas to communicate simultaneously with K active terminals. A great deal of Massive MIMO phenomenology surfaces in this scenario: the effects of noise, channel non-orthogonality, and channel estimation errors; the details of multiplexing and de-multiplexing; near/far effects; and the significance of power control.

Throughout the chapter, we consider only zero-forcing and maximum-ratio processing. While there are somewhat better performing alternatives: MMSE on the uplink, and suitably optimized regularized zero-forcing on the downlink [30], there are no closed-form non-asymptotic expressions available for their performance. Moreover, zero-forcing and maximum-ratio themselves tend to be optimal under high- and low-SINR conditions respectively.

Uplink Pilots and Channel Estimation

Learning the channel at the base station is a critical operation. As we have seen, a wideband channel can be decomposed into coherence intervals of duration Tc seconds and bandwidth Bc Hz. Every such interval offers τc = BcTc independent uses of a frequency-flat channel as modeled in Section 2.2.1. Figure 2.3(b) illustrates the three activities that occupy each coherence interval: uplink data transmission, uplink pilot transmission, and downlink data transmission. In every coherence interval, the terminals use τp of the τc available samples to transmit pilots that are known at both ends of the link, and from which the base station estimates the channels.

Orthogonal Pilots

Each coherence intervalmust host K pilot waveforms, and in order for them not to interfere, they have to be mutually orthogonal. Henceforth, we assume that the terminals are assigned mutually orthogonal pilot sequences of length τp, where τc ≥ τp ≥ K. Any set of orthogonal pilots with the same energies yield the same performance. The significance of τp is to quantify how much energy each terminal spends on pilots in each coherence interval. In principle, any τp samples in the uplink part of the coherence interval can be used for pilots. In practice, transmitters are typically peak-power limited, so constant-modulus signals, such as orthogonal sinewaves, make ideal pilots.