Lower Bounds on Mutual Information of QPSK and BPSK in General Memoryless Channels

We derive novel lower bounds on the mutual information in general memoryless channels with quadrature-phase-shift-keying (QPSK) or binary-phase-shift-keying (BPSK) modulation. These novel bounds are very easy to evaluate and result in closed-form expressions. The bounds’ derivation is based on the mean squared error (MSE) of the channel input given the channel output. To emphasize the usefulness of these bounds, we evaluate the bounds for two cases of interest. We consider a general additive white noise channel, and derive simple bounds on the mutual information that depend solely on the noise variance (and not on its distribution). In addition, we derive a closed-form lower bound for QPSK modulation over a Rician fading channel with 1-bit analog to digital converter (ADC) at the receiver. The bound characterizes the achievable performance as function of the SNR and the ADC phase offset and is shown to be tight in the absence of a phase offset and quite close to the actual mutual information at any phase offset (for example, at most deviation at an SNR of 14dB).