On approaching wideband capacity using multitone FSK

In the wideband limit, certain types of "flash" signaling, such as flash frequency-shift keying (FSK), achieve the capacity of multipath fading channels. It is not clear, however, whether these asymptotic results translate into insights for practical fading channels in the finite-bandwidth, power-limited regime. It is known that, for flash FSK, the size of the input alphabet grows slowly with increasing bandwidth, leading to very high-peak power per tone. Thus, for flash FSK, the codeword probability of error decays very slowly with bandwidth and feasible rates approach the wideband capacity limit extremely slowly. Without contradicting the above results, our results in this paper point to a more optimistic outlook, from the point of view of error exponents and achievable rates, for the applicability of flash techniques in practical scenarios. We consider multitone FSK (MFSK), which has the same asymptotic capacity-achieving property as flash FSK in the wideband limit, but allows a larger input alphabet size with the same bandwidth. First, we show, using an error exponent approach, that multitone FSK allows lower peak power per tone than flash FSK. Next, we present the capacity of single-tone and two-tone FSK schemes with hard-decision detection at finite bandwidths. For typical channel parameters, the capacities are close to the wideband capacity limit.