On the Use of the Gap Approximation for the Gaussian Broadcast Channel

In the paper it is shown that, similar to the Gaussian multiple access channel (MAC) that was considered in previous work, the gap approximation can also be used for the Gaussian broadcast channel (BC) to analyze transmission of discrete constellations using superposition. The values of the gap for the Gaussian BC are different than for the Gaussian MAC and depend on the powers of the noises at the receivers. Pulse Amplitude Modulation (PAM) is employed as an example, and it is demonstrated how the gap for the single-user AWGN channel should be modified in the case of the Gaussian BC. Moreover, even when discrete constellations are employed, similar to the capacity-achieving case, it is possible to simplify the implementation of the receivers using Successive Interference Cancellation (SIC) without penalty in performance.