Frequency-shift keying for ultrawideband - achieving rates of the order of capacity

In wideband systems that decorrelate in time and frequency, capacity can be reached in the limit of infinite bandwidth by using impulsive frequency-shift keying (FSK) with vanishingly small duty cycle. The richness of the codebook is then created through the large bandwidth, thus requiring very large bandwidths in order to approach capacity. We show that FSK with small duty cycle can achieve rates of the order of capacity in ultrawideband systems with limits on bandwidth and peak power. The richness of the codebook is then built in both time and frequency. We consider single tone and two-tone FSK schemes. Our results indicate that, for typical wireless conditions, we can achieve rates within a few dB of the energy-limited, infinite-bandwidth capacity with these simple FSK schemes. At high signal-to-noise ratios (SNRs), the FSK schemes are bandwidth-limited rather than energy-limited. In the high SNR regime, multi-tone FSK is significantly less bandwidth-limited than single-tone FSK.