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 T c seconds and bandwidth B c Hz. Every such interval offers τ c = B c T c 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 τ p of the τ c 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 τ p, where τ c ≥ τ p ≥ K. Any set of orthogonal pilots with the same energies yield the same performance. The significance of τ p is to quantify how much energy each terminal spends on pilots in each coherence interval. In principle, any τ p 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.