TABLE OF CONTENTS The downlink and uplink channels shown in Figure 14.1 appear to be quite similar: the down-link is almost the same as the uplink with the direction of the arrows reversed. However, there are three fundamental differences between the two channel models. First, in the down-link there is an additive noise term associated with each receiver, whereas in the uplink there is only one additive noise term (because there is only one receiver). A second fundamental difference is that the downlink has a single power constraint associated with the transmitter, whereas the uplink has different power constraints associated with each user. Finally, on the downlink both the signal and interference associated with each user travel through the same channel, whereas on the uplink these signals travel through different channels, which gives rise to the near far effect. Despite extensive study of uplink and downlink channels individually, there has been little effort to draw connections between the two models or exploit these connections in analysis and design. In this section we describe a duality relationship between the two channels, and we show how this relationship can be used in capacity analysis and in the design of uplink and downlink transmission strategies.
We say that K-user downlink and uplink, as shown in Figure 14.1 for K = 3, are duals of each other if all of the following three conditions hold.
The channel impulse responses h k (t), k = 1, , K
