digital phased array
space signal processing
space-time signal processing
I. M. Bannikov, M. M. Valeev, O. V. Saltykov
In the article the model of digital signal processing of antenna elements of a phased array based on the processing of complex envelopes is submitted. In the model we use multiplication of signals by phase factors dependent on radio signal frequency and also complex envelope delays. It is shown, that phase factors during processing of complex envelopes are necessary in any case, even for broadband signals, and delays should be applied only in case of wideband signals and signal delays should use only for aligning of time divergences between antenna elements signals (for narrow-band signals these divergences can be neglected). Multiplication by phase factors of complex envelopes is equivalent to signals phasing on a radio frequency (beamforming). Delays liquidate additional distortions of complex envelopes.
On the basis of this model some types of distortions of a complex envelope in the output are investigated. Three types of such distortions are considered:
1) distortions of the output complex envelope and directional diagram during phasing of antenna elements signals with the help of one-phase changers and without delays;
2) distortions of a directional diagram at quantized delays of radio signals of antenna elements;
3) distortions of an output signal connected to residual random spread of delays of complex envelopes of antenna element signals.
For the first kind of distortions the criterion in the form of addititional interference arising from time separation of complex envelopes of antenna elements for their evaluating is introduced. As a measure of distortions, we consider energy of residual signal between the exact coherent sum of envelopes and their copies shifted on some times. The signal-to-noise merit with average energy of a useful signal and entered noises is also considered. Then the form for dependence of the signal-to-noise merit on signal bandwidth is deduced. This form is concretized for a signal model with constant power spectral density in a considered band that is typical for signals of modern high-speed digital HF communication systems with high spectral efficiency. Examples of use of the deduced dependence for a linear equispaced array and for a ring array are given. To the same kind of distortions we refer distortions of the directional diagram depending on a band signal. It is shown, that in HF channel it is possible to process signals only by phase changers in rather wide band (up to hundreds of kilohertzes), that does not result in essential deterioration of a noise immunity of a radio line and directional diagram deformation.
The second type of distortions arises in case of antenna element signal phasing with the help of delay lines with taps when you have only a final set of delays which can be applied in this process. It is shown, that the given method of phasing is practically inexpedient when using digital antenna signal processing, at least for a HF channel.
The third type of distortions is similar to the first one except for residual delays in channels are caused by the casual distribution law. It can be residual delays after algorithm of phasing which cannot liquidate all destabilizing factors completely. As a rule, the distribution law of similar delays will be normal. Influence of similar delays on the signal-to-noise merit in various signal bands is considered. The residual disorder of delays of antenna element complex envelopes results in deterioration of a noise immunity of a radio line. To make this deterioration unobtrusive we use permissible residual delay spread for each type of a signal. This delay is measured in HF band in values from submicrosecond up to units of milliseconds.