Simple empirical BER equations for diversity combining with FH NCFSK in noise jamming

There are a large number of diversity combining methods available to enhance the anti-jam capability of M-ary NCFSK modulation. Analytic determination of the error performance has been found for a few of the simpler combining methods for certain jamming types and small values of M and diversity level, L. It was noticed from simulation results that, for wideband AWGN jamming, the plot of log(BER) versus L is approximately a straight line. For a given signal-to-noise-plus-jammer ratio, SNJR, the lines for all the diversity methods necessarily converge to the same well known BER value at L=1. For a given diversity combining method, it was discovered that the lines for different values of SNJR approximately converge at some unrealizable value of L<1. For 8-ary NCFSK, values of the BER and the L at which these lines converge are given for a variety of methods. This BER is slightly dependent on SNJR. Therefore, only an average BER is given for all the methods providing a coarse approximation. Also, an SNJR-dependent BER is given for linear envelope combining to give a more accurate approximation. Over the range of output BER>10^-3, the accuracy of the BER for the coarse approximation is well within a factor of two of the actual BER over a wide range of L and SNJR. The accuracy of the more accurate approximation for linear combining is better than ±5%. For binary NCFSK, the convergence point is given for linear combining only. It is shown how this method can be extended to partial-band noise jamming for linear diversity combining. With these values, one can very quickly and easily compute the performance of a wide variety of diversity combining methods