Principles of Modern Radar - Volume 2 1891121537

134 CHAPTER 4 MIMO RadarFIGURE 4-7Two-way angularpoint spreadfunctions. Thephased arrayresolves targets inangle using onlyreceive degrees offreedom. For theorthogonalwaveform cases, thefilled configurationprovides enhancedsidelobeperformance and thesparse configurationprovides improvedangular resolution.Relative Gain (dB)0−10−20−30−40−50Point Spread FunctionsPhased Array (Filled)Orth. Waveforms (Filled)Orth. Waveforms (Sparse)−60−10 −5 0 5 10Azimuth (deg)The (angular) point spread function (PSF) quantifies the angular resolution capabilityof an array antenna system. Suppose that a target is present and located at some angle θ.To evaluate the PSF at angle θ 0 , a beamformer designed for this angle of interest θ 0 isapplied to data containing a target at angle θ. This quantifies the degree to which a targetlocated at θ will obscure a target located at θ 0 .Comparing the transmit PSF of the phased array to the orthogonal waveforms inFigure 4-6, we see that the phased array (regardless of spoiling) provides no angularresolution on transmit. If, on the other hand, orthogonal waveforms are used and theradar can preserve its transmit degrees of freedom, then angular resolution is possible ontransmit.The PSF is related to the ambiguity function that is familiar from the radar literature.The standard radar ambiguity function describes the response due to a target with a particularrange and Doppler in nearby range and Doppler bins. This idea was extended to theMIMO case in [15], where an ambiguity function in terms of range, Doppler, and angle isdeveloped.Let us now reconsider the sparse configuration presented in Figure 4-2. The (twoway)PSF for the sparse array using orthogonal waveforms is presented in Figure 4-7.As predicted by the virtual array analysis, the sparse array is able to provide enhancedresolution since it provides an effectively larger array than the filled configuration. Note thatorthogonal waveforms are required to use the sparse configuration; otherwise, the sparsitywould introduce undesirable grating lobes. The filled configuration provides improvedsidelobe performance, since a taper is effectively applied to the aperture as a result ofoverlapping virtual phase centers.These results demonstrate the ability of a radar to use orthogonal waveforms to improveperformance. Even if truly orthogonal waveforms are not practical, this analysismay be repeated for a given set of waveforms using the appropriate signal correlationmatrix to quantify the impact of this nonorthogonality with the framework that has beendeveloped.