Analytical and practical evaluation of diversity penalties in multi-bit-rate coherent FSK systems

Fully analytical expressions are presented for calculating the bit-error-rate (BER) and sensitivity penalties in frequency-shift-keying (FSK) receivers with noncoherent square-law IF detection. With these results one can directly compute the sensitivity and diversity penalties as a function of the IF filter bandwidth. Postdetection filtering is included in the analysis. The BER of such receivers can be expressed in terms of a sum of generalized Laguerre polynomials, which can easily be evaluated. This yields relations between the IF bandwidth expansion factor and the sensitivity that can be applied directly for practical system analysis. This is illustrated using the results from a coherent multi-bit-rate, multichannel FSK receiver, which was used at bit rates of 140 and 560 Mb/s. The discrepancy between theory and practice is less than 0.15 dB for diversity penalties and 0.4 dB for the bit rate penalty.<>