## Effects of Multipath Dispersion on the Performance of Digital Transhorizon Systems

5.7.5.3.1 Introduction to Time Dispersion Due to Multipath. The multipath dispersion over a digital transhorizon link is considerably worse than the corresponding dispersion over a LOS link for a given frequency band. Consequently, the onset of multipath dispersion, rather than signal-to-noise ratio as the limiting factor in communications performance, occurs at a lower transmission rate for transhorizon links than for LOS links.

A significant improvement in the performance can be obtained by intrinsic diversity improvement using adaptive equalization.

Predictions of (1) the increase in error probability due to multipath dispersion for a given set of equipment and path parameters, and (2) the improvements in diversity performance and/or the reduction of intersymbol interference that can be achieved by adaptive equalization, are expressed with respect to a, the rms standard deviation of the delay time, which is obtained by expressing the power impulse response of the transhorizon path as a probability density function.

5.7.5.3.2 Performance Predictions and Measurements. The average bit error probability Pe in a digital transhorizon link subject to multipath dispersion is dependent on the following parameters:

2a/T Normalized multipath dispersion (where T is symbol period)

W (Energy per bit/noise spectral density) per diversity channel

For "weak multipath dispersion'' (2a T), no special protection against intersymbol interference is required as normal multiple diversity reception techniques guarantee the requisite probability level of irreducible errors.

In the case of "medium multipath dispersion'' (2a < T), passive measures against antisymbol interference are used in addition to diversity reception. A combination of various passive methods with matched filtering of the multi-path signal characterizes the active methods used to combat intersymbol interference when the elimination of intersymbol interference is accompanied by the effect of implicit diversity in multipath dispersion.

With "strong multipath dispersion'' (2 a > T) the intersymbol interference can only be combated by using special adaptive methods of reception.

In practice, both short-term and long-term variations are observed in the multipath dispersion. Measurements performed in the United Kingdom indicate that for a median 2 a value of 106 ns, the standard deviations of the long-term variation in 2 a taken from 92-s averages of 10-ms samples was 15 ns. The standard deviation of the short-term variation in 2 a taken from the 10-ms samples was 50 ns. For the 124-km test link transmitting 2048 kbps with 4-CPSK, the median value of 2a/T was 0.1.

5.7.5.3.3 Adaptive Equalization. The use of adaptive equalization reduces intersymbol interferences and thereby increases the transmission capacity of digital transhorizon systems. Adaptive equalization permits the diversity inherent within multipath dispersion to be accommodated in receiver design, thereby resulting in a predictable improvement in error performance for a given value of a .

Ideally, adaptive equalization (linear equalization) in a multipath radio channel presupposes a cascade connection of the filter matched with the incoming signal and the transversal filter. However, in real conditions the input filter is matched with the transmitted signal so that, with the elimina tion of the influence of multisymbol interference, the implicit diversity effect cannot be adequately achieved.

The use of decision feedback is a nonlinear method of signal processing and it can be used to compensate for the intersymbol interference caused by precursor signal elements.

Reception with evaluation of a discrete sequence by means of the Viterbi algorithm is considered to be a method for solving, with a maximum of a posteriori probability, the problem of evaluating the sequence of a time-discrete Markov process with a finite number of states. When account is taken of the matched filtering of the multipath signal, the Viterbi algorithm is considered to be the method that offers optimum signal reception in a multipath communication channel.

Spectral processing of a multipath signal involves extracting a number of signal frequency bands at the receiving end when the signal spectrum is wider than the frequency correlation bandwidth of the communication channel. Combining signal samples in the frequency range with specific weighting coefficients makes it possible not only to eliminate intersymbol interference but also—with matched filtering of the output component signal—to achieve an implicit diversity effect.

Successful transmission of information rates of up to 12.6 Mbps at 4.6 GHz using adaptive modems over transhorizon links has been reported.

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