Principles of Modern Radar - Volume 2 1891121537

13.5 Measurement of the Scattering Matrix 619line of sight. One may define a target-centered Cartesian coordinate system in which thetarget axis is the z-axis, so that the roll angle defines the azimuth φ, and the aspect anglebecomes θ. For monostatic RCS measurements, however, it is convenient to use the radarcoordinate system as the reference [3]. The scattering matrix in (13.60) assumes a linearpolarization basis; it can be transformed to circular polarization basis using a simplelinear transformation (cf. (13.32)). In sequential measurement of the scattering matrix,linear vertical and horizontal polarization signals are transmitted in sequence, and bothco-polarized and orthogonally polarized returns from the target are received. Reciprocityimplies that S HV = S VH . Furthermore, for rotationally symmetric targets, if the line ofsight or aspect direction is aligned with the target axis of symmetry, then the orientationangle becomes the roll angle, and it turns out that S HV = S VH = 0, and S HH = S VV .As described in Section 13.3, there are two ways of characterizing scattering: (a) thecomplex voltage-type scattering matrix S in which the absolute phase of the target return(or each matrix element) is needed; and (b) the real power-type Kennaugh matrix K, whichdoes not depend on the absolute target phase. Only the measurement of S is addressedin this chapter. The reader is referred to [35] for measurement of the Kennaugh matrix.The absolute phase of a target depends on its local position, aspect, surface structure,and the radar frequency. Relative phases, on the other hand, are phase differences amongthe individual scattering coefficients where any one may act as phase reference for theothers. The scattering matrix with absolute phase (SMA) is sensitive to target displacementalong the line of sight, while the scattering matrix with relative phase (SMR) is not.From a measurements point of view, the difference between the two scattering matrixtypes is profound. Determination of the SMA requires the ability to measure absolutephase, while the SMR can be obtained by amplitude and relative phase measurementsonly. Relative phase measurements provide a means to achieve background subtractionof the environmental effects either experimentally (using a CW nulling technique) orcomputationally (using vector subtraction derived from auxiliary measurements) [35]. Inpower- or amplitude-only measurements, such as the Kennaugh matrix, the target returnsfor several transmit antenna polarization states are considered [35]. In conventional RCSmeasurements, just like in radar, the scattering matrix is measured by considering bothamplitude and phase of a linearly polarized transmit channel, and only amplitude of thelinearly polarized receive channel. Furthermore, by reconfiguring the transmit antennapolarization, all the important parameters of the target return can be measured [14]. Thismeasurement, termed by Huynen as the linear restricted scattering matrix (LSM) [35],should not be confused with Kennaugh matrix, although the latter, in principle, can bederived from the former. Measurement of SMR is addressed next.The direct method of measuring the scattering matrix effectively implements (13.60).The measurement of SMR requires two orthogonal transmitter polarizations being radiatedindependently in sequence, while amplitude and phase of the scattered return for each areobserved simultaneously on dual-polarized orthogonal receiver channels. In general, anyarbitrary pair of orthogonal illuminating polarizations can be used (e.g., right and leftcircular polarizations as well as vertical and horizontal). Instrumentation requirementsinclude the ability to measure both amplitude and phase of the radar return, the capabilityof transmitting two orthogonally polarized signals in sequence, and that of receiving andrecording the orthogonal components of the elliptically polarized returns simultaneously.For measurement of returns in low signal-to-noise ratio (SNR) environments or to minimizethe effects of multipath and clutter, it is important to provide high isolation betweenthe radar transmit and receive channels. This requires low-loss filters, circulators, and