A Sphere Packing Bound for AWGN MIMO Fading Channels under Peak Amplitude Constraints

An upper bound on the capacity of multiple-input multiple-output (MIMO) additive white Gaussian noise fading channels is derived under peak amplitude constraints. The tightness of the bound is investigated at high signal-to-noise ratio (SNR), for any arbitrary convex amplitude constraint region. Moreover, a numerical simulation of the bound for fading MIMO channels is analyzed, at any SNR level, for a practical transmitter configuration employing a single power amplifier for all transmitting antennas.