We now extend the single-cell performance analysis of Chapter 3 to the multi-cell setting as modeled in Section 2.2.2. The activities in the various cells occur synchronously, but otherwise there is no cell-to-cell cooperation, with the exception of pilot assignment and possibly power control. Each base station serves its own terminals. Data transmission activities are identical to their single-cell counterparts. The channel estimation, however, has to account for reuse of pilots in other cells.

The culmination of this chapter is Table 4.1 that summarizes effective SINRs analogous to Table 3.1 in the single-cell case. Compared with the single-cell SINRs, the multi-cell SINRs contain additional effective noise terms that correspond to inter-cell interference of two types: non-coherent interference that is independent of the number of base station antennas, and coherent interference that scales with the number of base station antennas.

Throughout this chapter, we denote the home cell by the index l. Although the terminals within each cell have mutually orthogonal pilots, some reuse of pilots from cell to cell is permitted. The assumption is that for any two distinct cells, the pilot sequences are either perfectly orthogonal from cell to cell, or are perfectly replicated. Cells that use the same pilots as the home cell cause pilot contamination. We call these cells contaminating cells and denote the set of their indices by Pl, where by definition Pl also includes the home cell l. For all l ʹ ∈ Pl, the kth terminal in the lʹth cell is assigned the same kth pilot sequence.

We use the capacity bounding techniques of Chapter 3, but in our treatments of the uplink we immediately adopt the “use and forget” technique, thereby skipping the forms of capacity bounds that require taking expectations of logarithms.

Uplink Pilots and Channel Estimation

During the training phase, the terminals in each cell transmit pilot sequences, as in (3.2). Upon reception of the pilots, the base station performs a de-spreading operation. Because of pilot reuse, the resulting signal is a linear combination of channel matrices from all cells that share the same pilot sequences.