Signal processing basics - Radar receiver

Radar receiver

3.6 Signal processing basics

Waveform (f) shows baseband signal (d) after differentiation. Peak echo amplitude has fallen, but clutter has fallen further permitting a lower threshold (g). All echoes except E4 are now detectable, with a couple of false alarms. Strong echo E6 occupies considerable time, equivalent to radial length. It might represent an islet or a racon response. When the radar is operated conventionally, all parts of the echo are detected and displayed as an axial trace. Engaging the differentiator suppresses nearly everything but the leading edge, perhaps with a faint suspicion of the remainder from enhanced noise, E6'. Display quality is reduced. The extended nature of the echo is no longer apparent, neither can the shape of its paint reveal the aspect of a large target. At the end of the echo, voltage overshoot (not shown) in the baseband amplifier circuit may cause a faint blip which might be mistaken for another target.

The figure is drawn for differentiator timeconstant half a pulselength to emphasise the principle. In practice the timeconstant is usually about one pulselength. All radars provide a differentiator or FTC on/off control, usually with control of timeconstant, giving the operator more scope to balance detectability against display quality. As differentiation degrades echo plots, it should be disengaged in clear conditions. Its value lies in its ability to break up solid clutter. Sea clutter is less solid than that from precipitation - the structure of individual sea-waves is often visible as striations on the display - so differentiation is less effective against sea than precipitation clutter.

3.6 Signal processing basics

3.6.1 The task

The data stream at the receiver output contains a serial jumble of thermal noise and clutter returns, mixed up with any target echoes. All modern radars use extensive digital signal processing to remove as much noise and clutter as possible before reaching the display. Processing optimises detection of wanted echoes and minimises false alarms. Information theory sets definite limits to what can be achieved.

The processing strategies of individual radar suppliers are not normally disclosed and doubtless differ in detail, but the competitive nature of the market dictates that they all achieve performance close to the theoretical limit for the target and clutter scenario.

This section gives a broad outline of the signal processing section of the radar;

quantitative analysis following in Chapter 12. Automatic tracking aids, discussed in Chapter 13, use the detected echo positions to form tracks of individual targets.

From these likely future positions are extrapolated and closest points of approach are predicted.

The processor's task is to extract the maximum information - matter informative to the user - from the undigested stream of data; that is, to maximise the probability of detection, PD, and minimise the probability of false alarms, PpA- Data once discarded is irretrievably lost, so must be retained until as much information as possible has been wrung from it. PD and PFA are interlinked with the relative strength of the wanted signal to unwanted noise, the all-important signal to noise and clutter ratio (SNR).

It is impossible to have high PD and low PFA with low SNR. The processor plays a big part in the effort to maximise SNR. Detectability is affected by the random or partly

random manner in which echoes, noise and clutter fluctuate with time, necessitating statistical treatment in Chapter 12.

Prior to the processor, we have already encountered several features which use the precepts of information theory to maximise the echo at the expense of its competitors:

• high transmitter power, attention to feeder loss and low receiver noise figure improve the ratio of echo to thermal noise;

• narrow scanner beamwidths - high gain - minimise the amount of clutter illuminated;

• receiver bandwidth is restricted to reduce thermal noise;

• swept gain reduces necessary dynamic range of components;

• available dynamic range may be increased by logarithmic amplifiers, automatic gain control, etc.;

• differentiation breaks up solid clutter.

3.6.2 Po and P^A for target perception

The detection process in its widest sense contains several steps, with operator intervention in each. The target in question may not be the one of primary interest to the operator, who therefore may not optimise the controls for it. The steps are:

• generation of a prospective target plot in the signal processor - the operator chooses the radar band if both 3 and 9 GHz are available, then sets gain and other controls;

• display of the plot - the operator chooses an appropriate range scale;

• display of track - the operator may choose whether a plot is to be tracked;

• operator perceives paint as being a valid plot or track, not clutter.

The last step is mental, with electrotechnical implications. The eye has good pattern recognition capability and under optimum conditions can perceive faint target plots, if they persist, in quite severe clutter. When viewing a display containing noise or clutter, the operator consciously or subconsciously applies a mental threshold, whose consistency depends on motivation, fatigue and circumstance; the threshold may be higher in mid-ocean than when anxiously searching for a liferaft. Conditions are rarely optimum: the operator has other tasks, may be fatigued or stressed, cannot devote full attention to the display, or may not have the luxury of time for long observation of a barely visible plot before having to make the navigation decision.

Signal processors bypass most of these limitations.

To optimise perception, the radar has to display the target with high probability of detection (PD) but also low false alarm rate (PFA)- 'High' and 'low' are not always easy to quantify, but the following are often accepted as reasonable for display of the integrated return of a single scan:

PD > 0.5 PpA < 10"6.

PD 0.5 is sometimes called 50 per cent blip/scan ratio, defined as the number of times an echo (blip) is detected divided by the number of sweeps within the packet.

False alarm probability of one in a million may sound very low, but it must be remembered that a noise paint can arise from any of the hundreds of thousands of detection cells on a half dozen sweeps per scan. Psychological or human factors (HF) such as fatigue, use of dim cursive displays, etc. can be partly allowed for in calculations by adjustment of necessary PD-

3.6.3 Digital conversion, detection cells

So far, the radar signals and processes have been analog: 'Designating,1 pertaining to or operating with signals or information represented by a continuously variable quantity, such as spatial position, voltage, e t c ' Older radars were entirely analog, their detection strategy making use of the characteristics of long-persistence display tubes, described in Section 3.10. In the digital technology used in all modern radars, quantities take discrete values: 0, 1, 2, 3 , . . . , expressed as whole binary numbers 000, 001, 010, 0 1 1 , . . . , but nothing in between.

Although analog circuits can perform arithmetical operations such as addition, subtraction and multiplication, it is far more convenient, quick, flexible, cheap, stable and accurate to use digital processing, adopting the technology of the computer industry. The first operation is to digitise the baseband data stream by an analog to digital converter; Figure 3.11. The analog voltage is repetitively sampled to give digital number 'snapshots' best representing the voltages at those instants. If the sampling or clock rate is less than the video bandwidth (undersampling), significant data is lost.

If the clock frequency exceeds video bandwidth (oversampling), there is little loss but more and faster processing capacity is necessary. For pulselength say r = 0.1 |xs, video bandwidth ~0.5/r or 5 MHz so at least 5 x 106 samples/s are taken. Samples may have any amplitude from the noise background up to the echo of a large target.

Together, finite clock frequency and digitising quantum or least significant bit (LSB) introduce a quantising loss.

Apart from a little dead time before each sweep, every instant of the nominal 2.5 s scan time represents a slightly different basic element of surveillance area which may contain a target. In all there are some 10⁷ area elements or detection cells, alternatively called range cells or bins, each identified by a unique address related to range and bearing and together forming a digital frame store. Economies may be made by reusing cells within areas containing insignificant content, but large memory is always needed. The integration process demands a set of detection cells for each beamwidth's worth of bearing, if the cell footprint is not to degrade that of the scanner beamwidth/pulselength. The azimuth might be divided into 512 bearing x 256 range cells = 1 3 1 000 cells, doubled for scan to scan correlation, but modern frame stores may contain over a million addresses. Only in the last years of the twentieth century did such large memory become economically viable. It is usual for cells to have equal angle resolution.

Straddling loss occurs when small targets do not sit central to a cell, but sit astride a pair of cells to record unduly low strengths in each.

1 Shorter Oxford English Dictionary.

Figure 3.11 Signal processing. Digitised data is routed to detection cells within the frame store

3.6.4 Logical process of target detection

Figure 3.11 includes part of a simplified digital frame store, drawn as a matrix in range and bearing. For clarity a cut-down system is depicted. Thirty cells of range are shown, representing, say, from 10 to 14.5 km for pulselength 1 |xs. There are six sweeps in bearing, each sweep advancing by ^ scanner beamwidth, representing 0.65 km mean azimuth bracket at the range in question. Each cell contains thermal noise plus the echo and clutter content of about 150 m x HOm average sea area and the atmosphere above.

For simplicity, cell capacity is shown as a mere 2 bits, content representing 0, 1, 2 or 3 analog baseband voltage units. The figure assumes modest noise or clutter, so most of the cells have count zero; a few have strengths of 1-3.

Do cells having strength 1-3 represent targets? First, we examine the sweeps of the current scan by eye, for the human mind is good at pattern recognition. Looking at any single sweep in isolation, we may feel little confidence in drawing the line above

Previous scan Frame store Sweep 1

Sweep 2 Sweep 3

Sweep 4 Sweep 5

Sweep 6 Digitised

return strength

Rejected after scan-scan correlation Same target?

Weak target?

Analog video from receiver Thresholding Threshold voltage

Current scan Frame store Candidate B

Sweep 1

Sweep 2 Sweep 3

Sweep 4 Sweep 5

Sweep 6 Range cells Candidate A

Zero range

Analog to digital converter Clock

which we accept a return as valid, or put formally, set the threshold for detection declaration. Figure 3.10(d) shows such a threshold applied to the video signal.

Examining the six sweeps as a set, pulse to pulse integration, gives a clearer picture. Returns of strength 1 seem so far below the strongest returns that we feel sure they must represent noise or clutter and are too feeble to have significant probability of being targets. We discard entirely all cells whose signal strength lies below threshold.

Bearing in mind the steepness of the skirts of Gaussian distribution (Figure 3.5), it seems much more profitable to concentrate on the stronger returns, which are statistically much less likely to represent clutter spikes. Cells labelled 1, 5, 6, 17, 25 and perhaps 30 seem to form a significant cluster (candidate A). Another cluster, candidate B, contains cells 2, 7, 8, 11-14, 19-22, and perhaps 26 and 27. Cells 3, 4, 9, 10, 15, 16, 23, 24, 28, 29 and 31 seem random but might possibly represent small targets. In other words, choice of a low threshold risks numerous false alarms, but a high threshold risks rejection of genuine targets.

Comparison with the previous scan's frame store appears to rule out candidate A because there seems no previous concentration of returns at or near the range and bearing in question - scan to scan correlation is poor. If A is a target, it must be subject to severe fading. Has a weak target at cell 4 been discarded? The claims of candidate B are reinforced: the previous scan contained a cluster at about the same bearing and range. Unless A is a very fast approaching target, only B is probably a valid target and we might well declare it, meanwhile watching future scans for confirmation.

All that can be concluded from the evidence is:

• there is high probability of a target at B;

• there is moderate probability of a fading target at A;

• several other weak targets possibly exist;

• increased SNR would reduce the uncertainties.

3.6.5 Machine detection

The data processing system more or less replicates the mental processes outlined above in a formalised manner. To replace the mind's more subjective assessments, processing uses algorithms, defined and objective mathematical procedures, to squeeze the most information from the evidence quickly, tirelessly and rationally.

We have seen that in isolation it is not possible to state with confidence whether a particular cell content represents signal or a noise/clutter spike. Optimum threshold level is usually computed to be several times average cell occupancy, which on the premise that most cells are devoid of targets, is a measure of the prevailing noise and clutter. The first step is to reject as clutter or noise all cells whose counts lie below threshold, called thresholding. The threshold stage can be analog, thus reducing the load placed on the digital convertor and signal processor. The threshold voltage is set in part by the processor, by reference to the clutter environment (generally assessed by the average cell contents) and partly by the operator's use of the gain control. In the example, the average signal, noise and clutter count is 53 in 180 cells, average 0.29. As the least significant bit in our simplified model is 1, the threshold might

be set at 1 ( I V :0.29 V represents 10.75 dB, a reasonably typical value). Using 0 would let through all the noise and 2 would probably exclude too many genuine echoes.

Signals or hits exceeding threshold form first-stage single-pulse target candidates.

Clearly, detection is optimised by setting the threshold as low as possible consistent with accepting as high a false alarm rate (FAR) as the operator or system can abide.

The noise/clutter density varies with range and other circumstances - Figure 2.6 shows how a squall may occupy only part of the playing area. It is therefore beneficial to juggle the threshold (or receiver gain, which amounts to almost the same thing) to give constant false alarm rate (CFAR). This is accomplished by a combination of methods:

• swept gain, reducing gain at short range in a partially predetermined and partially adaptive manner;

• automatic gain control, averaging relative gain over the whole surveillance area;

• manual gain control, the operator setting IF gain (or threshold/logarithmic clipping levels) to give optimum display of a particular target;

• dedicated CFAR algorithms, which measure the average noise/clutter occupancy of cells near the candidate target, setting local FAR to maximum permissible by swept gain (or swept clipping level with logarithmic amplifiers);

• clutter mapping, where local clutter over each part of the playing area is regularly assessed, threshold being adaptively set for optimum FAR at each part.

3.6.6 Clutter map

Particularly with VTS groundfast radar, it is feasible to memorise or map the locations of heavy clutter and adapt detection thresholds to match that locally prevailing, editing out stationary clutter from ground features, and much weather clutter. Much of the benefit of differentiation is obtained without loss of display quality. Clutter mapping is less effective when the radar platform moves rapidly through varying clutter density and is not yet common on marine radars. Even in the most crowded harbour, most cells contain only noise and clutter and are devoid of targets. The clutter map is constructed from the average count (discarding high values which are probably targets) of blocks of cells much bigger than a ship dimensions, taken over a succession of scans. The map is stored digitally and steadily updated at a rate sufficient to track clutter movement, e.g. of a rainstorm driven by the wind. The detection threshold at any part of the surveillance area is automatically adapted to suit the average local clutter by reference to the map.

The map has to be very detailed to store coastal features and the strong clutter from breaking waves on the shoreline. One stratagem confines the playing area within the low-tide line, dumping echoes from elsewhere. This needs to be done with discretion;

a VTS once puzzled why its radar had lost a ship, known to be within the harbour.

The ship turned out to have drifted into the intertidal zone before grounding at high water in fog. Embarrassingly, as the playing area had been defined by the low-water line, the ship could not be displayed.

3.6.7 Detection decision process

The detection threshold is set automatically to suit the prevailing clutter, but always with possibility of operator intervention. But it must be stressed that even the most advanced processing can never give certainty from corrupted and incomplete data having low SNR, as shown by Section 3.6.5.

Figure 3.12(a) reproduces the cell matrix of Figure 3.11 more compactly.

Figure 3.12(b) is after thresholding at 1 voltage unit. Cells having value 0 or 1 are dropped, all others being accepted as hits. Actual strengths are not stored, so the processor is compact, at cost of discarding some data. The detection criterion is some minimum number of hits per scan, sometimes called the m out of n criterion, here three hits out of six sweeps per scan. Candidates A and B each score three hits so would be declared as targets.

The next increase of complexity is scan correlation, storing the previous scan's results, only declaring a target when both register some lower number of hits per scan, say 2. Targets with poor blip/scan ratio are likely to be rejected by scan to scan correlation. By adding further memory, the strength information can be stored, enabling the strength of each hit to be accounted for as shown in Figure 3.12(c).

Again candidate B is declared, but with somewhat higher PQ. The full potential of correlation is not always realised, the designer sometimes being content to suppress interference from other radars using a combination of pulse-pulse timing jitter and a 2 pulse correlator (n = 2).

Coherent systems also store phase data. Echo phasing jitters, particularly when SNR is low. Comparison of amplitudes during a scan with constancy of phasing sweep to sweep raises Pp. Scan to scan correlation can be used as before.

In general we see that, for a given PFA> ^D *^S raised if the following occur.

• Many digitising bits are used. There is less quantising loss. The penalty is additional and faster memory capacity.

• SNR is raised.

• Cell size is reduced, needing bigger scanner aperture and short pulses, high bandwidth with the attendant additional noise, as well as additional processing power.

• Scan to scan correlation is used, again needing more processing power.

• The system is coherent, requiring a more complex transceiver.

Physically big targets sprawl over several adjacent detection cells. Particularly with short pulselength, even small targets may straddle a pair of cells. Probability of the candidate being valid increases when its immediate neighbours exceed average clutter and when the previous scan contained a cluster at or near the same position.

Neither own ship or a target moves significantly during the 10 ms or so of the packet of sweeps within a scan, although their intensities may fluctuate. Receiver noise spikes meanwhile occur at random position. The processor has however to allow for fast targets traversing a couple of cells in the inter-scan period.

Modern radars display targets with remarkably little clutter on the screen, even in adverse conditions. But it is important to realise that because the signal processor has

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