A unified analysis of multipath degradation in multilevel modulation radio systems

Abstract

In microwave digital radio transmission, waveform distortion due to frequency selective fading becomes a dominant factor of degradation. To evaluate the degradation of different systems in a unified way, the waveform factor is defined first. With the aid of concept “waveform factor,” the eye aperture is easily obtained. We also evaluate the waveform factors for various modulation schemes. Next, on the basis of the relation between propagation parameters and waveform factor in two‐ray fading, the estimation formula of the outage probability for various digital radio systems in line‐of‐sight propagation is derived. The proposed factor is determined uniquely by system parameters, such as modulation scheme, system impulse response, and symbol rate. With the aid of this factor, digital radio system performance during multipath fading is easily evaluated.

A statistical characterization of point-to-point microwave links using biased Rayleigh distributions

“…In fact, radio propagation studies often treat dominant interfering rays as the cause of signal distortions that are an inevitable consequence of the multipath propagation phenomenon. However, to conform with common usage [6], [8], [12]- [14], the term "two-ray model" is used where the distribution for the magnitude of the second ray or reflected ray refers to that of the resultant random process caused by the superposition of interfering rays at the microwave receiving antenna.…”

“…Or from experiments, the gamma-density distribution for was used in [14]. Also, during duct-type fading the density distribution for was predicted in [12] to be of the form . The earlier work [16] has shown that delay differences for the two-ray model can be expected to be typically a few nanoseconds.…”

“…Since both and are parts of the phase of the second ray in our two-ray model, a knowledge of the aggregate distribution for the second ray's phase would put a constraint on the distribution for , had the delay parameter been predicted to assume a statistical distribution. As for the notch-position parameter authors seem, however, to agree that from physical intuition, it is reasonable to assume a uniform density distribution for the notch-position parameter in most cases [1], [8], [12], [14]. A distribution for the notch-depth parameter is now required that reflects the true mechanism of the two-ray model.…”

“…But before countermeasures to combat distortion due to frequency-selective fading can be devised, applied, and optimized, a convenient yet accurate characterization of the transmission channel is desirable. As has been pointed out in [1], [12], and elsewhere [13], a purely deterministic description of the transmission performance over randomly time-varying channels (such as microwave relay channels) would be unreasonable. With this in mind, the results obtained from measuring equipment are usually processed to give cumulative distributions of the received signal that can be used to characterize transmission performance [1].…”

“…From the works in the field of time-variant channel modeling, simulation, and channel sounding, starting perhaps with Bello [3], Kailath [10] (in the sixties or even earlier), Cox [11], and Jakes [15] in the seventies to recent works [17], and from the works in the field of characterization of radio transmission performance (Rummler [6], [7], Lavergnat and Sylvain [13], Greenstein and Czekaj [9], Jakes [16], Murase [12], and others), we relate the two-ray channel model's transfer function to the time-variant and bi-frequency kernels of the channel model. Frequency-selective fading is incorporated in the two-ray channel function, a feature that follows directly from the two-ray model, familiar to the designers of point-topoint microwave relay systems.…”