The Effect of Tandem Band and Amplitude Limiting on the E&lt;inf&gt;b&lt;/inf&gt;/N&lt;inf&gt;o&lt;/inf&gt;Performance of Minimum (Frequency) Shift Keying (MSK) (1974)

Minimum (frequency) shift keying (MSK) is a digital modulation technique which can be viewed either as frequency-shift keying (FSK) with peak frequency deviation precisely equal to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\pm(1/4)R_{L}</tex> where R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> is the link bit rate or as an offset-keyed quaternary phase-shift-keyed modulation. In the absence of bandwidth or amplitude limiting between the modulator and the demodulator, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{b}/N_{0}</tex> performance of MSK is identical to that of coherently detected binary phase-shift keying (PSK). This paper briefly reviews and defines MSK. It then presents a system model in which a tandem assembly of a transmit band-limiting filter, a hard limiter, and a receive band-limiting filter are interposed between an ideal modulator and demodulator. This model is aimed at simulating actual links (such as spacecraft-to-ground links) in which channel bandwidth <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(B_{c})</tex> constraints are important, postmodulation filtering at RF is objectionable, and transmission through efficient transmitters which operate as amplitude limiters is a requirement. An analysis then derives the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{b}/N_{0}</tex> degradation due to both bandwidth and amplitude limiting. Band limiting alone causes intersymbol interference on the data carried by each of the quadrature phasors but no interphasor crosstalk under the set of assumptions used. With amplitude limiting also present, an interphasor crosstalk mechanism exists. The average symbol distortion, symbol energy reduction, and noise reduction are derived for several periodic waveforms. For composite systems with 3-dB bandwidth <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(B_{L})</tex> -to-R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> ratios of at least 0.6, the theoretical <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{b}/N_{0}</tex> degradation is less than 1 dB. Parametric experimental data are then reported on the postmodulation spectrum of a transmitter with band limiting plus subsequent hard amplitude limiting. Data are also presented on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{b}/N_{0}</tex> degradation measured using tandem assemblies of a bandlimiting filter, an amplitude limiter, and a second band-limiting filter. The amplitude limiter substantially increases the level of the spectral side lobes beyond the main lobe. It was found that for all significant values of transmit bandpass filtering plus subsequent amplitude limiting, 99 percent of the transmitted energy is contained within B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> = 1.1 R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> . Further, little <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{b}/N_{0}</tex> degradation (tenths of a decibel) was measured if B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> was greater than 0.65 R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> . A rapid degradation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{b}/N_{0}</tex> occurred when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B_{L} = 0.55 R_{L}</tex> . These data apply for the band-band-amplitude-band limited system model. The amplitude limiter placed between the transmit and receive filters caused interphasor crosstalk and distortion of the data symbol shapes as predicted; however, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{b}/N_{0}</tex> degradation caused by the amplitude-limiting effects by themselves (which are a function of B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf> ) never exceeded 0.3 to 0.5 dB for the cases studied.