Quasi-concavity for Gaussian multicast relay channels

Upper and lower bounds on the capacity of Gaussian multicast relay channels are shown to be quasi-concave in the receiver signal-to-noise ratios and the transmit correlation coefficient. The bounds considered are the cut-set bound, decode-forward (DF) rates, and quantize-forward rates. The DF rates are shown to be quasi-concave in the relay position and this property is used to optimize the relay position for example networks.