Variable-rate variable-power M-FSK scheme for power limited systems

The first two authors have recently proposed a variable-rate and fixed-power (VRFP) non-coherent M-ary frequency shift keying (M-FSK) scheme for power limited systems [1], [2]. In this paper, we propose a variable-rate and variable-power (VRVP) scheme which offers some additional power saving. In this scheme, we impose the power assignment function as a design variable to minimize the objective function which is the average transmitted power while meeting the average spectral efficiency and bit error rate (BER) constraints. The power allocation mechanism is executed based on the channel gain feedback estimates. Our results show that the proposed system provides power saving varying from roughly 2.3 up to 5 dB. Moreover, the power loading function exhibits two interesting features. The first is that its peak is always less than the fixed amount of power used to guarantee the same system performance. The second is the self control type of behavior in which the peak occurs at a moderate value of channel gain while it tends to allocate less power at both high and low values of channel gain. We further investigate the problem with an additional maximum power constraint. In this case, we obtain a modified power loading function which can still fulfill the rate constraint up to a certain limit after which there is a rate maximum-power tradeoff.