THE CAPACITY OF AVERAGE AND PEAK-POWER-LIMITED QUADRATURE GAUSSIAN CHANNELS

The capacity C(rho(a), rho(p)) of the discrete-time quadrature additiv e Gaussian channel (QAGC) with inputs subjected to (normalized) averag e and peak power constraints, rho(a) and rho(p) respectively, is consi dered. By generalizing Smith's results for the scalar average and peak -power-constrained Gaussian channel, it is shown that the capacity ach ieving distribution is discrete in amplitude (envelope), having a fini te number of mass-points, with a uniformly distributed independent pha se and it is geometrically described by concentric circles. It is show n that with peak power being solely the effective constraint, a consta nt envelope with uniformly distributed phase input is capacity achievi ng for rho(p) less than or equal to 7.8 (dB) (4.8 (dB) per dimension), The capacity under a peak-power constraint is evaluated for a wide ra nge of rho(p), by incorporating the theoretical observations into a no nlinear dynamic programming procedure. Closed-form expressions for the asymptotic (low and large rho(a) and rho(p)) capacity and the corresp onding capacity achieving distribution and for lower and upper bounds on the capacity C(rho(a),rho(p)) are developed. The capacity C(rho(a), rho(p)) provides an improved ultimate upper bound on the reliable inf ormation rates transmitted over the QAGC with any communication system s subjected to both average and peak-power limitations, when compared to the classical Shannon formula for the capacity of the QAGC which do es not account for the peak-power constraint. This is in particular im portant for systems that operate with restrictive (close to 1) average -to-peak power ratio rho(a)/rho(p) and at moderate power values.