Module 2. Revealing of tracking signals and radar surveillance Topic 2 Module 2. Revealing of tracking signals and radar surveillance Topic 2.1 THEORY OF TRACKING SIGNALS REVEALING Lecture 2.1.4 FM PM PULSE COMPRESSION. CONSTANT FALSE ALARM RATE.

Pulse compression is a signal processing technique mainly used in radar, sonar and echography to increase the range resolution as well as the signal to noise ratio. This is achieved bymodulating the transmitted pulse and then correlating the received signal with the transmitted pulse.

Pulse Compression Pulse compression is a generic term that is used to describe a waveshaping process. The pulse is frequency modulated, what provides a method for further resolving of targets which may have overlapping returns. Pulse compression is a method which combines the high energy of a long pulse width with the high resolution of a short pulse width. The pulse structure is shown in the figure 1.

Figure 1: separation of frequency modulated pulses

Since each part of the pulse has unique frequency, the returns can be completely separated. This modulation or coding can be either - FM (frequency modulation) - linear (chirp radar) or - non-linear or - PM (phase modulation). The receiver is able to separate targets with overlapping of noise. The received echo is processed in the receiver by the compression filter. The compression filter readjusts the relative phases of the frequency components so that a narrow or compressed pulse is produced. The radar therefore obtains a better maximum range than it is expected because of the conventional radar equation.

Figure 2: short pulse (blue) and a long pulse with intrapulse modulation (green)

The ability of the receiver to improve the range resolution in comparison with the conventional system is called the pulse compression ratio (PCR). For example a pulse compression ratio of 50:1 means that the system range resolution is reduced by 1/50 of the conventional system. The pulse compression ratio can be expressed as the ratio of the range resolution of an unmodulated pulse τ to that of the modulated pulse with bandwidth B. PCR = (c0 · τ /2)/ (c0 / 2B) = B · τ

The compression ratio is equal to the number of sub pulses in the waveform, i.e., the number of elements in the code. The range resolution is therefore proportional to the time duration of one element of the code. The radar maximum range is increased by the fourth root of PCR. The minimum range is not improved by the process. The full pulse width still applies to the transmission, which requires the duplexer to remained aligned to the transmitter throughout the pulse. Therefore Rmin is unaffected.

Pulse compression with linear FM waveform At this pulse compression method the transmitting pulse has a linear FM waveform. This has the advantage that the wiring still can relatively be kept simple. However, the linear frequency modulation has the disadvantage that jamming signals can be produced relatively easily by so-called „Sweeper”. The block diagram on the picture illustrates, in more detail, the principles of a pulse compression filter.

The compression filter are simply dispersive delay lines with a delay, which is a linear function of the frequency. The compression filter allows the end of the pulse to „catch up” to the beginning, and produces a narrower output pulse with a higher amplitude. Filters for linear FM pulse compression radars are now based on two main types. - Digital processing (following of the A/D- conversion). - Surface acoustic wave devices.

View of the Time-Side-Lobes

Time-Side-Lobes The output of the compression filter consists of the compressed pulse accompanied by responses at other times (i.e., at other ranges), called time or range sidelobes. The figure shows a view of the compressed pulse of a chirp radar at an oscilloscope and at a ppi-scope sector. Amplitude weighting of the output signals may be used to reduce the time sidelobes to an acceptable level. Weighting on reception only results a filter „mismatch” and some loss of signal to noise ratio. The sidelobe levels are an important parameter when specifying a pulse compression radar. The application of weighting functions can reduce time sidelobes to the order of 30 db's.

Pulse compression with non-linear FM waveform The non-linear FM waveform has several distinct advantages. The non-linear FM waveform requires no amplitude weighting for time-sidelobe suppression since the FM modulation of the waveform is designed to provide the desired amplitude spectrum, i.e., low sidelobe levels of the compressed pulse can be achieved without using amplitude weighting.

Matched-filter reception and low sidelobes become compatible in this design. Thus the loss in signal-to-noise ratio associated with weighting by the usual mismatching techniques is eliminated. A symmetrical waveform has a frequency that increases (or decreases) with time during the first half of the pulse and decreases (or increases) during the last half of the pulse. A non symmetrical waveform is obtained by using one half of a symmetrical waveform.

Symetrical waveform

A symmetrical waveform (Output of the Waveform-Generator)

Non-symetrical waveform

Phase-Coded Pulse Compression Diagram of a phase-coded pulse compression

Phase-coded waveforms differ from FM waveforms in that the long pulse is sub-divided into a number of shorter sub pulses. Generally, each sub pulse corresponds with a range bin. The sub pulses are of equal time duration; each is transmitted with a particular phase. The phase of each sub-pulse is selected in accordance with a phase code. The most widely used type of phase coding is binary coding.

The binary code consists of a sequence of either +1 and -1 The binary code consists of a sequence of either +1 and -1. The phase of the transmitted signal alternates between 0 and 180° in accordance with the sequence of elements, in the phase code, as shown on the figure. Since the transmitted frequency is usually not a multiple of the reciprocal of the sub pulsewidth, the coded signal is generally discontinuous at the phase-reversal points.

False Alarm Rate A false alarm is „an erroneous radar target detection decision caused by noise or other interfering signals exceeding the detection threshold”. In general, it is an indication of the presence of a radar target when there is no valid target. The False Alarm Rate (FAR) is calculated using the following formula: FAR = false targets per PRT/rangecells

Different threshold levels

False alarms are generated when thermal noise exceeds a pre-set threshold level, by the presence of spurious signals (either internal to the radar receiver or from sources external to the radar), or by equipment malfunction. A false alarm may be manifested as a momentary blip on a cathode ray tube (CRT) display, a digital signal processor output, an audio signal, or by all of these means. If the detection threshold is set too high, there will be very few false alarms, but the signal-to-noise ratio required will inhibit detection of valid targets. If the threshold is set too low, the large number of false alarms will mask detection of valid targets.

a) threshold is set too high: Probability of Detection = 20% b) threshold is set optimal: Probability of Detection = 80% But one false alarm arises! False alarm rate = 1 / 666 = 1,5 ·10-3     c) threshold is set too low: a large number of false alarms arises! d) threshold is set variable: constant false-alarm rate

Solutions to the false-alarm problem involve implementation of constant false-alarm rate (CFAR) schemes that vary the detection threshold as a function of the sensed environment.

Principle of a „Cell-averaging CFAR”- wiring

Constant false alarm rate Constant false alarm rate (CFAR) detection refers to a common form of adaptive algorithm used in radar systems to detect target returns against a background of noise, clutter and interference. Other detection algorithms are not adaptive. Non-adaptive detectors are sometimes referred to as clairvoyant ( ясновидящие) detectors.

Principle In the radar receiver the returning echoes are typically received by the antenna, amplified, down-converted and then passed through detector circuit that extracts the envelope of the signal (known as the video signal). This video signal is proportional to the power of the received echo and comprises the wanted echo signal and the unwanted power from internal receiver noise and external clutter and interference.

The role of the constant false alarm rate circuit is to determine the power threshold above which any return can be considered to probably originate from a target. If this threshold is too low, then more targets will be detected at the expense of increased numbers of false alarms. Conversely, if the threshold is too high, then fewer targets will be detected, but the number of false alarms will also be low. In most radar detectors, the threshold is set in order to achieve a required probability of false alarm.

If the background against which targets are to be detected is constant with time and space, then a fixed threshold level can be chosen that provides a specified probability of false alarm. The probability of detection is then a function of the signal-to-noise ratio of the target return. However, in most fielded systems, unwanted clutter and interference sources mean that the noise level changes both spatially and temporally. In this case, a changing threshold can be used, where the threshold level is raised and lowered to maintain a constant probability of false alarm. This is known as constant false alarm rate (CFAR) detection.

Cell-averaging CFAR In most simple CFAR detection schemes, the threshold level is calculated by estimating the level of the noise floor around the cell under test (CUT). This can be found by taking a block of cells around the CUT and calculating the average power level. To avoid corrupting this estimate with power from the CUT itself, cells immediately adjacent to the CUT are normally ignored (and referred to as "guard cells").

A target is declared present in the CUT if it is both greater than all its adjacent cells and greater than the local average power level. This simple approach is called a cell-averaging CFAR (CA-CFAR).

Other related approaches calculate separate averages for the cells to the left and right of the CUT, and then use the greatest-of or least-of these two power levels to define the local power level. These are referred to as greatest-of CFAR (GO-CFAR) and least-of CFAR (LO-CFAR) respectively, and can improve detection when immediately adjacent to areas of clutter.

Sophisticated CFAR approaches More sophisticated CFAR algorithms can adaptively select a threshold level by taking a rigorous account of the statistics of the background in which targets are to be detected. This is particularly common in maritime surveillance applications, where the background of sea clutter is particularly spikey and not well approximated by additive white Gaussian noise. This is a difficult detection problem, as it is difficult to differentiate between spikes due to the sea surface returns and spikes due to valid returns from, for example, submarine periscopes. The K-distribution is a popular distribution for modelling sea clutter characteristics.