This chapter summarizes some open questions that demand further research, and briefly discusses selected topics that we have been unable to cover in the book but on which substantial investigations have taken place, or are taking place at the time of this writing.
Alternative Approaches to Performance Analysis
Our capacity analyses use techniques first developed in  for the uplink, and  for the downlink. This approach has several advantages: the resulting capacity bounds are rigorous and do not involve approximations, and the resulting expressions are in closed form and easy to interpret intuitively.
Alternative approaches to the capacity analysis of Massive MIMO exist. Most notably, the sequence of papers [50–52] used asymptotic random-matrix theoretic results in order to obtain “deterministic equivalent” capacity expressions. An advantage of that approach is that MMSE and regularized zero-forcing processing can be analyzed, whereas the theory developed in this book is only applicable to zero-forcing and maximum-ratio processing. While our capacity analyses assume independent small-scale fading, [50–52] accounted for spatial correlation; however, they were unable to obtain exact closed-form performance expressions.
Massive MIMO, in contrast to Point-to-Point MIMO, works extremely well with only single-antenna terminals. Nothing in our discussion, however, precludes the use ofmultipleantenna terminals. A multiple-antenna terminal, for example, could enjoy throughput in proportion to the number of antennas that it possesses without requiring exponentially growing SINRs. The simplest mode of operation would treat the multiple-antenna terminal as a multiplicity of single-antenna terminals. Alternatively, a terminal could use multiple antennas for out-of-system interference suppression, facilitated by adding a “quiet interval” in each coherence interval, during which none of the base stations or terminals transmits. The terminals (and incidentally the base station) could each identify the subspace in which the interference is contained, and then operate in the orthogonal interference-free subspace.
Pilot Contamination and Pilot Assignment
We saw in Chapter 6 that pilot contamination can be a significant impairment in a multi-cell system and that it may be mitigated by adopting a pilot reuse factor greater than one. However, the greater overhead of high reuse factors limits the number of mobile terminals that can simultaneously be served.