Multiposition Synthetic Aperture Radar (MPSAR) 

              Alexander V Ksendzuk 

8. Pseudonoise signals in Multiposition SAR.

        8.1. General remarks.

Radiolocation signals (just as signals used in arbitrary radio engineering system) can be divided into deterministic and random. Deterministic processes are defined as functions each value of argument (time) of which is assigned single-valued non-random function (signal). Random signals are defined as time functions particular shape of which is a realization from a great number of possible. The value of such function in some time point is random. Usage of random signals especially in multiposition radiolocation systems and synthetic aperture systems is difficult in consequence of processing peculiarities. For this reason, for the remote sensing tasks it is advisable to use certain random processes realization with given probability density functional (here includes pseudorandom vectors). We define such sequences as pseudorandom sequences.

Figure 8.1. Pseudorandom sequence 1 and appropriate phase-, frequency- and amplitude- modulation  graphs 2-4. Spectra of these pseudonoise signals are shown in the image below.

Signal Groups in Multiposition SAR

      8.2. Radar Image Quality estimation.

For the pseudonoise signals it is necessary to take into account output division into signal, noise and interference components. In this case signal-to-noise ratio in monostatic and bistatic SAR will be

,                                                                       (8.1)

where  - signal component of the matched filter output;

- noise component of the matched filter output;

 - interference.

 Differentiating into signal and interference components are possible by separation pint target response (space ambiguity function of the SAR) into signal (main lobe) and interference (sidelobes) parts, Figure 8.2.

Figure 8.2. Comparison of the SAR point target response, pulse signal 1 and pseudonoise signal 2 with separation into signal and interference parts.

Radar cross-section estimation is determined by ambiguity function side lobes behaviour and complex reflectance of the surface as the function of the spatial coordinates. For most practically important cases, estimation will be unbiased.

For pulse signal signal-to-noise ratio (SNR) is defined as follows , where

,                                                        (8.2)

.                                                          (8.3)

Substituting into this equation simplified surface model we will achieve that signal to-noise ratio transforms to

,

where  - radar cross-section (RCS);

- normalised point target response (space ambiguity function); 

- energy of the transmitted signal;

- averaged RCS;

- spatial resolution (in range).

For the pseudonoise signals SNR can be written as follows

                                                 (8.4)

or

,

where - signal-to-noise ratio in SAR with pulse signal;

;

- mean-square level of the sidelobes, ;

;

- number of digits within pseudonoise signal.

So as we can see from the above equation signal-to noise ratio in remote sensing systems strongly depends on mean-square level of the sidelobes. Pseudorandom sequence, which modulates transmitted signal, must be selected to maximise (8.4).

8.3.      PSP  image quality, surveillance radar.

We estimate radar image quality by determining errors of the radar cross-section estimation (this equals to �errors of the radar image� ).

For further comparison of radiolocation systems suppose simple signal to pseudonoise conversion which satisfies the following conditions: signal energy and resolution within major lobe reserve the same (that corresponds to, for example, usage of phase-shift keying with symbol duration equal to single radio-frequency pulse duration), time repetition interval of the impulse signal and period of the pseudonoise sequence are equal. An example of these signals are shown in Fig. 8.2.

In surveillance radar, figure 8.3, radar image quality achieved with pseudonoise signal may be unsatisfactory, especially when transmitted PNS signal exceeds length of the pulse signal.

Figure 8.3 Surveillance radar.

Fig. 8.4. Radar cross-section estimation in surveillance radar. 1, 2 - transmitted pulse and pseudonoise signal�s envelopes; 3, 4 - space ambiguity function of the corresponded signals; 5- radar cross-section; 6, 7 - radar cross-section estimation with pulse and pseudonoise signals, correspondingly.

       8.4.     PSP radar image quality, Synthetic Aperture Radar.

In contrast to stationary surveillance radiolocator, spatial coordinates resolution in synthetic aperture system corresponds to (time delay-frequency shift) domain.  

The comparison of the space ambiguity functions  for the pulse and pseudonoise signals are shown in  Fig. 8.5.

As we can see, SAF for the pulse signal is finite in range (OY) and for the PNS is not. Both ambiguity functions will be periodic in time and range domains.

Figure 8.5. Space ambiguity function of the SAR with pulse signal (up) and SAR with pseudonoise signal (down).

For further investigation the fact, that for normalized SAF basic ambiguity principle in radiolocation  for SAR as space-time processing system can be presented as, must be mentioned.

Consider signal-to-noise ratio  as

where  - some point neighborhood of ambiguity function absolute maximum; - radar cross-section value, achieved by side lobes; - by principal maximum.

Modeling results of the primary and secondary algorithms in radar and SAR with different transmitted signals for stochastic surface models were implemented in a way, which was described in details in Section 10. Suppose energy of impulse signal and PNS are equal, PNS is a phase-shift keyed periodic sequence, it�s period is equal to impulse signal repetition period, durations of PRS symbol and pulse are equal, unambiguity measurement conditions are satisfied.

Figure 8.6. Modeling results for the SAR: 1 - radar cross-section behavior ;2, 3 - images achieved with pseudonoise and pulse signal;.

In synthetic aperture radar modelling results prove that distortions of the image achieved with pseudonoise signal are the same as distortions of the image achieved with the pulse signal (with equal conditions - energy, single pulse width, repetition interval etc).

8.5.     Conclusion

Images achieved with pseudonoise signals in synthetic aperture radar have no significant distortions in comparison with pulse signals. Statistical characteristics of the radar cross-section estimation errors do not differ from the same errors for the impulse signal.

But pseudonoise signals allow to achieve high noise immunity, to increase resolution, to provide low noise level for other radio-electronic systems, to achieve signal hiding, to decrease requirements to the peak power level of the transmitter, and also to provide additional information transfer to transmitters located in scanned area (by radar signal modulation).

These facts prove advisability of pseudonoise signals usage in monostatic, bistatic and multiposition synthetic aperture radar.

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C(c) Alexander V Ksendzuk