Several receiver configurations can be used in the radar. The most commonly used receiver is nothing more than a balanced mixer with the RF port fed by the receive antenna and the LO port fed by the transmitter. The IF port of the mixer drives an audio frequency preamplifier with 50 dB gain, followed by an anti-aliening filter and an Analog to Digital Converter (ADC) mounted in the computer. The mixer forms the mathematical product of the transmitter and received signals. This receiver configuration operated at up to 30,000 samples per second when used with a DAC controller sweep oscillator transmitter.
The radar can be treated as an interferometer with the mixer forming an output related return signal at the mixer output can be derived as a function of , the phase difference between the signal and LO mixer inputs.
q= 2pr/lambda Where: r = path length lambda = wave length
The mixer output is the product of the transmitted signal (LO port) and the path delayed replica (received signal) with appropriate loss terms included:
Eo = sin(2p(c/lambda)(t) ( LO signal ) K sin(2p(c/lambda)(t)+q) ( Received signal ) c = propagation velocity t = time K= range and other losses
Using the cosine product rule:
Eo = .5K cos(q+(4p(c/lambda(t) ( Sum frequency ) -.5K cos(q) ( Diff Frequency )
The upper sideband which is in the microwave spectrum is not passed by the audio frequency preamplifier, resulting in the mixer output to the computer being the lower sideband:
Eo = -5K cos(2pr/lambda)Notice that the receiver output signal phase is only a function of the path length and wavelength, and is not a function of time. If the RF frequency I linearly stepped at an arbitrary rate, a sampled cosine wave will be produced at the mixer output. The mixer output can be compressed into an equivalent pulse in the range domain by performing a spectral analysis with a Fast Fourier Transform (FFT). This operation is know as pulse or range compression.
The mixer output corresponds tot he inphase (I) or real signal component of the radar return. The quadrature (Q) signal component can be obtained by a variety of techniques. The classical method uses a second mixer channel fed by a 90 degree hybrid, however other quadrature extraction techniques can provide significant advantages.
The quadrature (Q) component can be derived from a single mixer by using a broad band 90 degree phase shifter at the mixer output if any positive or negative frequencies are present. This is true if the target is nearly stationary, unaliased and at a positive range or can be pulse gated to those requirements. The broadband phase shifter can be readily implemented in software by a Hilbert transform. This configuration provides very high phase accuracy with a minimum of hardware.
The quadrature signal can also be obtained by performing a single sideband upconverion using a computer controller phase shifter ahead of an I channel receiver and then performing a quadrature detection in the computer. This configuration supports CW operations and with over-determined phase shifts can be self calibrating.
The radar achieves a -70 dBsm sensitivity at a 30 ft. Range using a 10 milliwatt transmitter with the single mixer, Hilbert transform receiver. This sensitivity is achieved by using a high pulse compression ratio with the receiver operating in a spread spectrum, matched filter mode. With a transmitter sweep width of 2 GHz, the equivalent of a .5 nanosecond pulse is synthesized resulting in a range resolution of 3 inches. The RF chirp is integrated for 0.2 seconds in the receiver signal processor resulting in a pulse compression ratio of 10. This operation is equivalent to coherently averaging 10 10mw pulses. The result is high sensitivity with simple low power transmitter.
The majority of the radar is implemented as a software based signal processor running in a DEC PDP-11/73 microcomputer. The minimum computer configuration includes a color graphics terminal, a plotter, 2500 Kbytes floppy disks and 128 Kbytes of RAM memory. For extensive ISAR and nearfield processing, a 40 Mbyte Winchester disk and 512 Kbytes or more of RAM are recommended.
The radar program structure is based on state space methods to generate a highly modular program with a clear structure. Central to the state space design is a set of 3 vectors. A minimum and non-redundant set of parameters which define the radar setup and environment form the 1st vector called the state vector. Processed radar returns which are a function of the state and measurement vectors are saved in the derived measurement vector. The state and measurement vectors may be saved to disk for later use. The derived measurement vector can be derived from the state and measurement vectors when required and need not be saved to disk.
The radar signal processor program is written as
a set of modules which communicate through the three data vectors.
These modules include:
The RCS radar program can be used easily reconfigured to operate with a variety of microwave sources such as synthesizers and sweepers and a variety of receivers ranging form simple mixers to SA-1780 receivers. In the following description of program operation, the most common HP-86290B sweeper / simple balanced mixer receiver configuration is assumed.
The radar uses a pair of data buffers in the computer memory to store 2 radar returns. One radar return includes the object under evaluation along with a clutter environment, the other return is of the clutter environment only. The 2 returns may be vector subtracted resulting in a coherent MTI suppression of the clutter signal component. The 2 data buffers can be loaded by the radar hardware, a radar signal simulator or from copies of the 2 data buffers previously saved to disk.
The instantaneous frequency of the microwave sweep oscillator is controlled by a Digital to Analog Converter (DAC) located in the computer. Simultaneously, the radar return is acquired by an Analog to Digital Converter (ADC) and moved into 1 of the 2 data buffers for MTI clutter suppression. The data acquisition process is initiated in phase with the 60 Hz power line to coherently reject power line interference if present. The signal acquisition occurs at up to 30,000 samples per second.
At this point the target + clutter, clutter or MTI enhanced target return may be plotted, listed or statistically analyzed. A warning message is displayed if the ADC has saturated. The 2 data buffers are saved to disk for processing at a later time.
If aspect, ISAR or nearfield processing is required, the radar acquires a set of measurements of the target over a range of aspect angles. The target aspect is controlled by the computer through the use of a software based servo loop. The servo senses the target aspect using a resolver or optical encoder and generates target rotator velocity commands to minimize the servo error.
A simulated radar return may be generated and added to existing data in the measurement vector. The target simulator is used to support target modeling, software development and operator training. The simulator can simulate point, clutter and sphere targets. The sphere backscatter, simulator models the Raleigh, resonance and optical response regions.
The point target simulator operates by transforming a simulated target attached to a target rotator model into the radar reference frame. The mixer input at the RF lower band edge is then computed as a complex phasor with the amplitude based on the radar range equation and the phase based on the total path length. The derivative of this phasor with respect to frequency is then computed. The two phasors are used to initialize a Cordic difference equation for which the solution is the desired radar return.
Amplitude and frequency errors in the radar return due to RF source errors can be corrected by a complex multiplication between the radar signal and a complex weighting function. This operation is similar to SAR focusing, except this operation :focuses" the pulse compressor.
The radar signal as functions of RF frequency and range area Fourier transform pair. The I channel receiver output for a point scatter during a linear RF sweep will appear to be a constant frequency sine wave. A Fast Fourier Transform is used to convert the constant frequency to an equivalent sin(x)/x pulse in the range domain. A convolutional window (typically Handing) is applied in the range domain to reduce the range side lobes of the compressed pulse. A range loss prewhitening filter is then used to convert quasi-monostatic received power into RCS. The RCS may now be plotted as a function of range.
To determine the target RCS or phase properties as a function of the microwave frequency, additional processing is required. A range gate centered in the region of interest is applied to the Fourier transformed data. The rangegate is a range band pass filter and is implemented as a vector product between the range domain radar signal and a window vector.
The quadrature (Q) channel of the radar signal is derived to simplify the amplitude and phase demodulation process. The quadrature signal when combined with the in phase (I) signal is known as a pre-envelope or analytic signal and can be derived by a broad band 90 degree phase shifter if negative frequency components are not present.1.2 The broad band 90 degree phase shifter is implemented as a Hilbert transform in the range domain by:
H(r) = -j sgn(r) G(r)
The range gated, Hilbert transformed, range domain analytic signal is inverse Fourier transformed, resulting in a range filtered frequency domain analytic signal.
The real and quadrature Fourier domain signals can be processed simultaneously by combining the Hilbert and inverse Fourier transforms. The real and imaginary signal components are orthogonal allowing the previous equation to be summed with G(f) resulting in:
= 2 G(r), r<0 G(r) + j H(r) = G(o), r=0 = , r=<0
This equation states that a complex return can be recovered by taking a single sided inverse Fourier transformed of the range gated data. The resultant complex return is a rotating phasor. The analytic signal allows the instantaneous demodulation of the amplitude, phase and time delay information present in the radar signal. The amplitude and phase can be recovered by converting the analytic signal to polar form. The magnitude of signal is the instantaneous RCS of the target as a function of frequency.
The phase of the analytic signal carries additional information about the target. If a point target with a Raleigh response is measured and the phase shift due to path length is subtracted from the return, the residual phase shift is due to sweeper non-linearity, antenna dispersion and similar effects. The complex reciprocal of this signal with Raleigh correction can be used as a normalizing function to correct radar returns for antenna dispersion, sweeper power and frequency linearity errors.
Motion of a point target will change the received phase. A 3.6 degree phase shift corresponds to a change in target range of 0.005 lambda or at X-band approximately 0.006 inches. Very precise measurements of phase centers and phase flatness can be made by target phase measurements. This capability is useful in range alignment applications and range stability checks.
Complex targets can appear to be at varying range as a function of the instantaneous transmitter frequency the target group delay or instantaneous range as a function of RF frequency can be measured.
Inverse Synthetic Aperture Radar (ISAR) produced images of the target region can be a useful tool in locating scattering regions on the target. ISAR images are produced by rotating the target and processing the resultant doppler histories of the scattering centers.3 If the target rotates in azimuth at a constant rate through a small angle, scatters will be approaching or receding from the radar at a rate depending only on the cross range position. The cross range position is distance normal to the radar line of sight with the origin at the target axis of rotation. The rotation will result in the generation of cross range dependent doppler frequencies which can be sorted by a Fourier transform. This operation is equivalent to the generation of a large synthetic aperture phased array antenna formed by the coherent summation of the receiver outputs for varying target / antenna geometry's. For small angles, an ISAR image is the 2 dimensional Fourier transform of the received signal as a function of frequency and target aspect angle.
If the target is rotated through large angles, the doppler frequency history of a scatter will become non linear, following a sine wave trajectory. This doppler history can not be processed directly by a Fourier transform because of the smeared doppler frequency history which results in the loss of cross range resolution. The maximum rotation angle which can be processed by an unmodified Fourier transform us determined by the constraint that the aperture phase error across the synthesized aperture should vary by less than an arbitrary amount, usually 45 degrees. This occurs when the synthetic aperture to the target range is less than required by the 2D2/lambda limit where D id the required lateral extent of the target. At this point the synthetic aperture is within the target nearfield region and requires focusing. The focusing is accomplished by applying a phase correction to the synthetic aperture.
The radar signal processor program uses several different algorithms to produced fully focused ISAR transforms. For very large scan angles, up to 360 degrees, the radar performs a direct integration in the region of interest. Cordic difference equations are used in conjunction with a band limited decimation of the range gated radar return to substantially improve computational efficiency. The radar image can be viewed during the integration process. Note that with large scan angles, 2 dimensional CW imaging becomes possible because the cross range axis rotates with the target aspect angle.
Fully focused 2 dimensional images can be produced for objects of arbitrary width and depth and if a height which does not violate the 2D2/lambda limit. Objects suited to these requirements include missiles and aircraft. If targets have excessive height, a 3 dimensional ISAR image is required. The fully focused 2D ISAR image is a planar representation of the RCS scattering centers in complex form, with phase front distortion removed.
Errors in the ISAR imaging process generally result
in defocusing and geometry errors in the image. ISAR transform
MULTIPATH: Multiple reflections can result in ISAR imaging distortions such as the classic ghost image trails from jet aircraft tail pipes.
The ISAR transform converts RF data as a function of aspect and frequency to an image consisting of RF data as a function of range an cross range. The ISAR images can be gated in both the range ad cross range dimensions, to select a region of interest. An inverse ISAR transform can be computed resulting in 2 dimensionally gated RF data as a function a frequency and aspect. The earlier described radar target simulator essentially performs the inverse operation of the ISAR transform and can be considered to be an Inverse ISAR transform.
A technique for transforming radar data acquired at a given location in space to another location in space (i.e., the form the near-field to the far-field) is to form a fully focused ISAR image of the target region and then use that image as a target model. The target model can be evaluated directly to be passed to the radar simulator and then be reprocessed by the radar.
The classical method of transforming a set of FMCW radar measurements to an ISAR image is the unfocused or planar wave-front 2 dimensional Fourier transform. N inverse 2 dimensional Fourier transform will convert a focused ISAR image to the equivalent far-field returns.
If processed over the appropriate aperture angles, the image contains the required information to reconstruct the target response at certain other positions in space which could include the far-field. The ISAR image represents a scattering plane which can be illuminated by a radar. The energy at any arbitrary point in space ca determine as a consequence of Huygens principle. The validate and limits of this technique are determined by the planar approximation of the target region.
If a forward and then an inverse ISAR transform of a target environment is performed with the same geometry and frequency parameters, no change to the radar signals will occur. This is true even for multipath and dispersive environments since transforms neither add or delete any information, they only change the reference frame. As the state vectors (geometry, frequencies, etc.) are changed between the forward and inverse ISAR transforms, the derived radar signal accuracy will degrade gradually.