Transmission Characteristics of an M-ary Coherent PSK Signal Via a Cascade of N Bandpass Hard Limiters

This paper provides a general analysis of the transmission characteristics of a coherent PSK signal, where an
M
-ary coherent signal is transmitted via a repeater system composed of a cascade of
N
bandpass hard limiters. The probability density function of a composite phase of the signal and noise over the system is newly derived to obtain an error probability. In addition, the comparison with the repeater system composed of a cascade of
N
linear amplifiers is made to clarify the features of the transmission characteristics. It is found that the probability density function of the composite phase over the system is symmetric about each input carrier-to-noise power ratio (CNR), and it reduces to some well-known results. It is also shown that for a reasonably large input CNR in each stage, the presence of the bandpass hard limiter (BPHL) provides some improvement, but that for small input CNR it causes degradation in performance.