FURTHER RESULTS ON THE BIT ERROR PROBABILITIES OF MDPSK OVER THE NONSELECTIVE RAYLEIGH FADING CHANNEL WITH DIVERSITY RECEPTION

This paper presents a fundamental approach for deriving the bit error probability of BDPSK and QDPSK over the nonselective Rayleigh fading c hannel for a receiver with an arbitrary IF filter, and for a fading pr ocess with an arbitrary Doppler spectrum with arbitrary Doppler bandwi dth. The results generalize those published earlier which were restric ted to matched filter reception and to a fading process with a small D oppler bandwidth compared to the symbol rate. This allows the error pr obability to be studied in the presence of varying degrees of ISI due to bandlimitation of the received signal by the IF filter, and in the presence of fading fluctuations of various rates. The analytical appro ach here is simple, and yet powerful in that it can handle the case of diversity reception. This is a great advantage over the alternative a pproach of using the distribution of the differential phase of the rec eived signal over a symbol interval. The bit error probability results apply to both conventional BDPSK and QDPSK, as well as pi/2-2DPSK and pi/4-4DPSK, and allow the irreducible bit error probability as well a s the SNR at which this irreducible value sets in to be studied as a f unction of Doppler bandwidth and IF filter bandwidth. The computed res ults presented here are applicable to the design of digital cellular m obile communication systems.