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In one of our previous papers, we designed an ultra-low power non-coherent MFSK system using 2-pole bandpass filters to replace matched filters for detection and showed the performance loss between our proposed system and the optimal MFSK system using matched filters for detection was no greater than 1.2 dB in all alphabet size, phase continuity and channel conditions we analyzed. In this paper, we improve our previous design by considering the power-bandwidth tradeoff, and we show that we can save a large percentage of system bandwidth by sacrificing a small amount of power, when the demodulator and coding parameters are optimized. For example, we can save 50&#x0025; of system bandwidth at the cost of 1 dB loss in performance compared to our previous system design. We further extend the results to include Gaussian filtering, we quantify the performance loss as a function of both the system bandwidth saved and the time-bandwidth product of the Gaussian filter, and we compare the performance of the <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-ary GFSK system with the corresponding MFSK system.

Power-Bandwidth Tradeoff for Ultra-Low Power MFSK and G-MFSK Systems