5.1 SUMMARY
This Thesis has examined the possibility o f evaluating the angular spectrum o f the anechoic chamber by the use o f two well-known techniques, namely the Fast Fourier Transform (FFT) and the Multiple Signal Classification (MUSIC). The FFT has vast application as spectrum estimator and is often used as a conq)onent in other signal processes for its fast speed. In this work it was investigated in its canonical form as an angular spectrum estimator. The MUSIC method has been applied as in the original formulation presented by Schmidt and with the addition o f the spatial-smoothing technique developed by Evans to circumvent the existence o f coherent signals. This combination has been widely demonstrated in the literature for angle o f arrival estimation of coherent sources and was here examined as an angular spectrum estimator for a close range emission source located inside the anechoic chamber.
Angular spectrum analysis has been performed in one-dimensional and two-dimensional arenas, preceded by the demonstration o f the related methods in a wide range o f simulated conditions, and followed by comparisons between the two estimation techniques.
The test scenario, conq)rehended by the anechoic chamber and the test equipment setup, have been briefly described with both purposes o f registering the circumstances under which the experimental work has been carried out and o f characterising some operational restrictions found in the data measurement procedure.
5.1.1 One-dimensional angular spectrum estimation
The performance o f the FFT and the MUSIC algorithms have been evaluated for several combinations of incoming simulated signals. These simulations, mostly based on a linear array configuration o f 64 elements and inter element spaciug o f )J6, showed that both algorithms have great potential to work out the angular spectrum in situations similar to the one existing inside the anechoic chamber. However, the angular spectrum estimate
obtained via MUSIC was found to be more accurate. This is because the FFT restricts the resulting signal location on the spatial-spectrum to some discrete angles determined by the array configuration and by the wavelength. Furthermore, the resolution o f MUSIC estimate is higher than the resolution o f the FFT, and the FFT's resolution is additionally deteriorated due to this inflexible spatial-spectrum too. Both algorithms respond somewhat equally to the presence o f weak signals when they are located beside a stronger emission in the angular spectrum The threshold level for the weak signal detection was found to be around 40 dB below the predominant signal level. When noise has been added to the signal, MUSIC spectrum estimation lobes were noticed to reduce in level. When the SNR reaches values below 30 dB there is a gradual dissemination o f spurious pulses along the angular spectrum at random locations. This situation can lead to the loss o f a real signal direction, however the spurious pulses haven't shown any spatial correlation for several runs o f the process.
Although in the simulation's preview MUSIC has shown a better performance, the spectrum evaluation provided by the FFT is also considered satisfactory. Therefore, both techniques have been apphed in the analysis of the experimental data obtained from the anechoic chamber measurement. The spatial-spectrum o f the anechoic chamber has been estimated by these two algorithms and in this processing the following features were noticed and deserve reference:
a) The field measurement shows a phase progression similar to a circular wavefront model and on top o f this shape an undulation is found.
b) In the horizontal plane this ripple has been found to be due to incoming reflections at approximate bearings o f ±60 degrees.
c) Few measurements taken in the vertical direction have revealed the same circular phase shape as the horizontal sets. The ripple however has got a different pattern, leading to side lobes conçonents in positions closer to the main beam.
d) The results o f the two algorithms have been checked for different sampling spacing, driving to reasonably coherent results.
e) Few simulations with different wavelengths have been performed, and although the FFT suggested an apparent move o f the side lobes, when the MUSIC data were examined they appeared to remain in position for the frequency change.
f) Because o f the diflBculty o f performing measurements in the vertical axis, the results obtained from data collected vertically are not so rehable as the ones processed in the horizontal plane.
The shortcomings originated by the positioning unit characteristics prevented the repetition o f the same amount o f measurements done in the horizontal axis for the vertical direction, however the results for both axes sounded reasonable.
From the straight con^arison between the FFT and MUSIC results it has been noticed that the side lobes picked up by the two techniques are basically in conformity on both estimations. However, the FFT evaluation has shown restrictions to work out their correct position, whereas the superresolution method has been able to precisely define it.
Also, throughout the results obtained via FFT, several datasets measured horizontally at different heights have shown a progressive variation in the spectrum shape, but it has not been possible to disclose the cause o f this behaviour. By MUSIC evaluation these changes have been clearly associated to local peaks turning up in the angular spectra along few adjacent horizontal lines. Despite the hypothesis o f noise generated speckles is possible, it has not been given much credit for the non randomly behaviour of these local crests.
5.1.2 Two-dimensional angular spectrum estimation
The 2D-FFT and 2D-MUSIC have been rehearsed for few incoming simulated signals arriving to a planar array o f (64 x 64) elements and with inter element spacings o f X/6 in both axes. It has been shown that the performances or the two-dimensional algorithms has practically matched the respective performances o f the one-dimensional FFT and MUSIC for similar conditions. This way, the 2D-MUSIC turned out to be superior to the 2D-FFT angular spectrum estimation as it did in the linear case. The optimum spatial smoothing factor has also been determined for the 2D-MUSIC.
Experimental data have been evaluated by both two-dimensional methods and the results for the anechoic chamber angular spectrum estimate has been found to agree with the results obtained in separate analysis performed for one-dimensional evaluations. However, the results obtained by the 2D-FFT are again inconsistent to support the existence of side lobes due to wall reflections by themselves. It was via the 2D-MUSIC results that this conclusion was settled.
5.2 FURTHER WORK
It is felt that the following areas can be further explored:
1. The experimental results have been related to vertically polarised signal. Polarisation effects need to be evaluated to conq)letely check for the existence o f other reflections flrom the chamber walls. Two kinds of reflections can be considered. The ones resulted flrom polarisation plane rotation due to reflections and the ones referred to horizontally polarised radiation.
2. Spatial-spectrum estimation is experiencing a fast evolution and some recent pubhcations about methods referred to as "ESPRIT", "MIN-NORM", "CLOSEST", "ROOT-MUSIC", etc. have been demonstrating superior qualities conq)ared to former versions. The use of this algorithms in evaluating the anechoic chamber can eventually reveal more information about this context.
3. The idea o f using the obtained wavefront angular spectrum in a "deconvolution" process in antenna measurements sounds very attractive and can be considered. The inq)lementing viabihty o f this process requires further investigation. The fact that the reflections are perfectly separated fi-om the main beam in spectral domain is a favourable synçtom, however the spread point shape o f these conq)onents can be a critical issue.