Pulse-Doppler signal processing is a radar and CEUS performance enhancement strategy that allows small high-speed objects to be detected in close proximity to large slow moving objects. Detection improvements on the order of 1,000,000:1 are common. Small fast moving objects can be identified close to terrain, near the sea surface, and inside storms. This signal processing strategy is used in pulse-Doppler radar and multi-mode radar, which can then be pointed into regions containing a large number of slow-moving reflectors without overwhelming computer software and operators. Other signal processing strategies, like moving target indication, are more appropriate for benign clear blue sky environments. It is also used to measure blood flow in Doppler ultrasonography.
Environment Pulse-Doppler begins with coherent pulses transmitted through an antenna or transducer. There is no modulation on the transmit pulse. Each pulse is a perfectly clean slice of a perfect coherent tone. The coherent tone is produced by the local oscillator. There can be dozens of transmit pulses between the antenna and the reflector. In a hostile environment, there can be millions of other reflections from slow moving or stationary objects. Transmit pulses are sent at the pulse repetition frequency. Energy from the transmit pulses propagates through space until they are disrupted by reflectors. This disruption causes some of the transmit energy to be reflected back to the radar antenna or transducer, along with phase modulation caused by motion. The same tone that is used to generate the transmit pulses is also used to down-convert the received signals to baseband. The reflected energy that has been down-converted to baseband is sampled. Sampling begins after each transmit pulse is extinguished. This is the quiescent phase of the transmitter. The quiescent phase is divided into equally spaced sample intervals. Samples are collected until the radar begins to fire another transmit pulse. The pulse width of each sample matches the pulse width of the transmit pulse. Enough samples must be taken to act as the input to the pulse-Doppler filter.
Sampling
The local oscillator is split into two signals that are offset by 90 degrees, and each is mixed with the received signal. This mixing produces I(t) and Q(t). Phase coherence of the transmit signal is crucial for pulse-Doppler operation. In the diagram, the top shows phases of the wave-front in I/Q. Each of the disks shown in this diagram represent a single sample taken from multiple transmit pulses, i.e. the same sample offset by the transmit period (1/PRF). This is the ambiguous range. Each sample would be similar but delayed by one or more pulse widths behind those that are shown. The signals in each sample are composed of signals from reflections at multiple ranges. The diagram shows a counterclockwise spiral, which corresponds with inbound motion. This is up-Doppler. Down-Doppler would produce a clockwise spiral.
Windowing The process of digital sampling causes ringing in the filters that are used to remove reflected signals from slow moving objects. Sampling causes frequency sidelobes to be produced adjacent to the true signal for an input that is a pure tone. Windowing suppresses sidelobes induced by the sampling process. The window is the number of samples that are used as an input to the filter. The window process takes a series of complex constants and multiplies each sample by its corresponding window constant before the sample is applied to the filter.
Detailed explanation of windowing Dolph–Chebychev windowing provides optimal processing sidelobe suppression.
Filtering Pulse-Doppler signal processing separates reflected signals into a number of frequency filters. There is a separate set of filters for each ambiguous range. The I and Q samples described above are used to begin the filtering process. These samples are organized into the m × n matrix of time domain samples shown in the top half of the diagram. Time domain samples are converted to frequency domain using a digital filter. This usually involves a fast Fourier transform (FFT). Side-lobes are produced during signal processing and a side-lobe suppression strategy, such as Dolph–Chebyshev window function, is required to reduce false alarms . All of the samples taken from the Sample 1 sample period form the input to the first set of filters. This is the first ambiguous range interval. All of the samples taken from the Sample 2 sample period form the input to the second set of filters. This is the second ambiguous range interval. This continues until samples taken from the Sample N sample period form the input to the last set of filters. This is the furthest ambiguous range interval. The outcome is that each ambiguous range will produce a separate spectrum corresponding with all of the Doppler frequencies at that range. The digital filter produces as many frequency outputs as the number of transmit pulses used for sampling. Production of one FFT with 1024 frequency outputs requires 1024 transmit pulses for input.
Detection Detection processing for pulse-Doppler produces an ambiguous range and ambiguous velocity corresponding to one of the FFT outputs from one of the range samples. The reflections fall into filters corresponding to different frequencies that separate weather phenomenon, terrain, and aircraft into different velocity zones at each range. Multiple simultaneous criteria are required before a signal can qualify as a detection.
Constant false alarm rate processing is used to examine each FFT output to detect signals. This is an adaptive process that adjusts automatically to background noise and environmental influences. There is a cell under test, where the surrounding cells are added together, multiplied by a constant, and used to establish a threshold.
Threshold criterion { C e l l ( n ) >
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