Bandwidth Efficiency and Probability of Error Performance of MSK and Offset QPSK Systems

Abstract

In this paper a model of Minimum Shift Keying (MSK) is introduced, an analysis of which shows that the theoretical maximum bandwidth efficiency of MSK is 2 bits/s/Hz, the same as for Quadrature Phase Shift Keying (QPSK) and Offset Quadrature Phase Shift Keying (Offset QPSK). The filtering necessary to achieve minimum spectrum width as well as a raised cosine spectrum while maintaining the condition of zero intersymbol interference for Offset QPSK is reviewed, and the equivalent filtering for MSK derived. In addition, partioning of this filtering between transmitter and receiver for optimum probability of error (P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> ) versus receiver input signal to noise ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S/N</tex> ) ratio is given. Computer simulation results are presented for a MSK system and an Offset QPSK system, both filtered for 0%, 50% and 100% excess bandwidth raised cosine spectrum. The results show fully open eyes at the decision threshold input for all cases. They also show that when filtered to give the same spectrum the different system have identical P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> versus <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S/N</tex> performance, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S/N</tex> being defined at the input to the receiver decision threshold, i.e., after all the filtering for the desired raised cosine spectrum. This performance is best for 100% excess bandwidth filtering and worst for 0% excess bandwidth filtering.