Gaussian fading broadcast channels with CSI only at the receivers: An improved constant gap

We examine the capacity region of the K-user Gaussian fading broadcast channel with channel state known at the receivers but unknown at the transmitter. For binary expansion superposition signaling, we derive a new achievable rate based on soft decision decoding of the binary inputs. The approach is based on a simple tight bound on the output entropy of a high-SNR AWGN channel with a continuous uniform input. We show that a binary superposition signaling scheme is for each user within a constant gap of 5.443 b/s/Hz of the broadcast channel capacity for all fading state distributions.