Asymptotic performance of M-ary orthogonal signals in worst case partial-band interference and Rayleigh fading

It is shown that for worst-case partial-band jamming, the error probability performance (for fixed E/sub b//N/sub I/) becomes worse with increasing M for (M>16). The asymptotic probability-of-error is not zero for any E/sub b//N/sub I/(>ln 2), but decreases inverse linearly with respect to it. In the fading case, the error-probability performance (for fixed E/sub b//N/sub 0/) improves with M for noncoherent detection, but worsens with M for coherent detection. For large E/sub b//N/sub 0/ the performance of the Rayleigh fading channel asymptotically approaches the same limit as the worst case partial-band jammed channel. However, for values of M at least up to 4096, the partial-band jammed channel does better. While it is unlikely that an M-ary orthogonal signal set with M>1024 will be used in a practical situation, these results suggest an important theoretical problem; namely, what signal set achieves reliable communication. >