Radar receiver
3.3 Receiver and filter
3.3.1 Overview
After traversing the rotating joint, feeder and protection circuits, the echo and clutter signals enter the receiver proper, all at transmitter frequency except for a few specialised racon targets discussed in Chapter 8, which can respond at an offset frequency. Each scatterer delivers a packet of several pulses each scan; Figures 3.2(a) and (b).
If number of pulses in packet = n, scanner azimuth beamwidth = 0 rad and scanner rotation rate = r rpm,
Of 60 \ 0 n = prf x scan time x — = I prf x — I x —
2TT y r J 2n
n
= 9.55 x prf x - pulses per packet. (3.1) For example, Figure 3.2(b) is drawn for lOOOpps, 30rpm and 1° beamwidth, 0 = 0.0175 rad, n = 5.57. The prf is not synchronised with scanner rotation and non- integral n signifies individual packets fluctuate between 5 and 6 pulses. The figure excludes environmental effects such as target roll which may make individual pulses fade quasi-randomly, either sweep to sweep or scan to scan.
It is often sufficient to assume that all pulses within the beamwidth have full scanner gain on transmit and receive, with scanner gain zero elsewhere; Figure 3.2(c).
This rectangular assumption introduces the beamshape loss discussed in Chapter 2, Section 2.7.15, targets slightly off-axis being credited too much gain.
The functions of the receiver are to amplify echoes to a level easily handled by the signal processor, convert them to baseband or video frequency, preserve information content represented by pulse shape and spectrum, introduce as little distortion and
(c) Rectangular beam approximation to (a)
Figure 3.2 Echo pulse packets. Packet received as each scan sweeps across target.
Number of pulses in packet proportional to prf. Rectangular approxi- mation assumes all returns in beamwidth encounter full scanner gain, all other returns being ignored
additional noise as possible and control bandwidth by filtering, so delivering the optimum signal to noise ratio (SNR).
Target and clutter scatterer motions have similar velocities, giving similar Doppler frequency spectra and precluding use of the moving target indication (MTI) technique so common in aeronautical and military radar. The signal to clutter (but not signal to noise) ratio is almost independent of receiver bandwidth, but not of transmitter pulse- length, which alters the illuminated footprint. The echo spectrum replicates that of the transmitter, possibly trivially modified by dispersion in a waveguide feeder, Chapter 2, Section 2.6, which would cause the higher frequency components to lead slightly.
Echoes may be as low as -12OdBW (10"12W, 1 pW), 16 orders of magnitude feebler than transmitter power, a huge ratio equivalent to a penny to a major State's gross domestic product for a century.
Chapter 4 will show that, speaking very generally, echo strength follows the inverse fourth power law, rising as range is halved by a factor of 24 = 16(12 dB).
n pulses per beamwidth, here n = 5.57 Azimuth beamshape loss (shaded) (b) Short range, high prf 2000 pps, rotation 30 rpm
Pulse envelope set by scanner pattern
Scanner half-power
0 First scan (a) Long range, low prf
15 ms 1000pps, rotation 30 rpm 2.0 s Second scan Time
PowerPowerPower
For example, a 0.001 m2 target at 1 km returns the same echo power as a 10 m2 target at 10 km. To reduce the dynamic range of echoes, overall gain is made to rise with time from the instant of pulse transmission, full gain being reached at fairly long range, say 10-20 km, equivalent to 65-130 |xs. Swept gain, discussed further in Chapter 12, is introduced by insertion early in the receiver of a swept gain attenuator, often formed by a PIN diode attenuator preceding or immediately following the initial microwave amplifier, to prevent later stages developing cross-modulation output components when a small echo is surrounded by high clutter spikes.
Conventional printed circuit boards are too lossy at microwave frequency, so the input circuits use microstrip, a form of transmission line printed as a metal- strip conductor pattern, with surface-mounted components, on a low-loss sapphire or alumina substrate backed by a metallic ground plane. The substrate is about the size of a couple of postage stamps and a millimetre thick. Microstrip propagates rather like an opened-out coaxial cable.
The TR cell recovery characteristic, if applicable, is also utilised and sometimes the protective PIN diode is biassed. Swept gain is adapted to the current clutter input, augmented by the operator's swept gain or sensitivity time control (STC, Chapter 12, Section 12.7.2). The control is advanced to reduce sea clutter, which primarily occurs at short range.
The microwave amplifier is specially designed for low noise, usually using a pair of GaAs FET (gallium arsenide field effect transistor) stages. It feeds the mixer. Complete receiver front ends, sometimes integrated with the transmit microwave components, are often procured by radar manufacturers from specia- list suppliers. After the initial microwave low noise amplifier (LNA, alternatively known as a microwave integrated circuit, MIC) and the mixer, the IF signal is further amplified, then detected to give an output at baseband, as shown in Chapter 2, Figure 2.10(c).
Although several controls, Figure 3.3, are provided to optimise target detection, we cannot always assume that they have been set to suit the target in question. For example, the operator may be primarily concerned with a nearby echo, while keeping an eye on more distant traffic, accepting some reduction in its detectability.
3.3.2 Receiver noise
If targets reflected steady echoes and no noise or interference returns intruded, we could increase receiver amplification until targets of interest at indefinitely long range registered a strong echo, or we could reduce transmitted power and save money. As usual, life is less easy. Thermal noise can never be avoided. Together with unwanted clutter from precipitation and the sea, noise limits the smallest echo detectable by any given radar. The noise limit is dictated by the fundamental laws of physics. Design imperfections may prevent achievement of the theoretically possible performance, but under no circumstances can that performance be exceeded. Nonetheless, the Writer of the laws of physics has been kind to the marine radar community, enabling small and relatively cheap effective radars to be produced with sufficient performance for most purposes.
Figure 3.3 Main controls of a modern radar. Simplicity of use, with all settings shown on alpha-numeric panels of display. Reproduced by permission of Kelvin Hughes Ltd, Ilford UK
Beside noise fluctuations, the echo usually fluctuates also. The detection task boils down to maximising detection of wanted targets while minimising unwanted false alarms from the intruders; both usually fluctuating in strength.
The fundamentals of thermal noise summarised here are fully discussed in Chapter 11, Section 11.2. Thermal noise arises when current flows in a resistor of any kind, including semiconductors and feeders, so all the receiver components con- tribute some noise. The first amplification stage dominates the noise performance of the whole system because its noise is amplified most. Great care is therefore taken to minimise noise sources prior to amplification, and the noise generated within the first stage of the receiver.
Noise is a random variation of voltage, hence power, uniformly distributed through all frequencies as 'white noise' unless restricted, as it always is in practice, an observation bandwidth being implicit in all statements of noise. The sine wave, pulse or pulse train waveforms already considered follow definite patterns. Once we have 'cracked the code' we can state with confidence the instantaneous voltage at any time, past or future. Noise is different; it is random and there is no 'code'. Noise is often best described in terms of power density - power per unit bandwidth. Figure 3.4 shows (a) a sample of noise within a wide bandwidth, (b) the same sample after fil- tering to a narrow bandwidth (with the same noise power density), and then (c) after re-amplification to the former power level, event X being represented by Y after a bandwidth-dependent delay. The number of separate noise events per second is the reciprocal of the bandwidth; the rounded form of (c) shows the event rate to be less than (a). Another sample would look the same in general form but quite different in detail, just as no two sea waves are identical. The instantaneous voltage amplitude has Gaussian or normal statistical distribution; Figure 3.5 is the probability density function, discussed further in Chapter 11, Section 11.2. Occasionally spikes have several times the rms amplitude. Noise is the antithesis of a sine wave's -Jl times rms
Voltage relative to rms
Figure 3.5 Probability, Gaussian noise or clutter. There is a small but finite probability that noise and clutter events may substantially exceed the rms voltage. Until the statistics are detailed in Chapter 11, noise powers and voltages are to be understood to be average or rms values, subject to Gaussian distribution unless specifically stated otherwise.
Because noise is random, all that can be said is that, averaged over a time interval much longer than the event rate:
• power, measurable on a wattmeter, will average a certain amount;
• the statistical distribution of instantaneous voltage will be Gaussian.
Figure 3.4 Noise voltage waveform. Passage of wide-band noise (a) through a narrow-band low-pass filter (b) reduces amplitude. When amplitude is restored (c), the original amplitude distribution is restored, although the narrow bandwidth makes changes sluggish. Events such as X occasionally considerably exceed the rms, irrespective of bandwidth.
Bandwidth reduction imposes a short delay, to Y
True range of event Apparent range Time (proportional to range)
(b) After narrow-band filter (right-hand scale) (Series of 840 events, Gaussian distribution)
(c) Narrow-band noise amplified to 1V rms (heavy line) (a) Wide-band noise, 1 V rms
Probability
It can never be quite certain whether any event such as X represents a noise spike or a target echo. Precipitation clutter amplitude is noise-like with Gaussian distribution, although the spectrum is set by the transmitter. Sea clutter is also rather similar. Under adverse conditions clutter power far exceeds noise.
At the receiver input average noise power, Pn, is
Pn = HkT0BW (3.2a)
where k is Boltzmann's constant (1.381 x 10~23 J/K), T0 is absolute temperature (conventionally taken as 290 K, 17°C. K stands for Kelvin; measured from the abso- lute zero of temperature. Degrees Celsius or centigrade = Kelvin — 273.3; degrees Fahrenheit = 1.8 K — 460) and B is the bandwidth under consideration, hertz. Excess over the lowest noise power theoretically attainable for the bandwidth is described by the receiver noise factor, n. The equation is frequently put in decibel terms, where noise figure N= lOlogn:
Pn = N + 10 log B - 204 dBW. (3.2b)
Because clutter rather than noise often dominates detection performance, the bother of cryogenic cooling to reduce T0 has not been found worthwhile. Increasing amplifier gain to increase a weak signal also increases the noise and does not improve SNR. Great care is therefore taken to minimise the noise factor of the first amplifier stage. Although noise sets a definite limit to the useful sensitivity of all amplifiers, even before bandwidth is limited, noise power is never remotely high enough to damage the amplifier. Putting £ = 106 MHz (1000 GHz) gives JcT0B = 4 x 10~9 W, whereas the most sensitive electronic devices can generally withstand 1Ox 10~3 W without difficulty.
Beside internally generated noise, the scanner gathers galactic noise, approxi- mately equal to the noise contribution of a resistor of the same value as the radiation resistance of the scanner (a few hundred ohms) and usually insignificant.
Mixers have rather poor noise figure so are often preceded by a specialised microwave low noise amplifier with N ~ 3.5 dB. The noise contributions of the mixer and succeeding stages, and of the scanner, feeder protection system and swept gain attenuator at its maximum gain setting, are usually accounted for by assuming the input stage has a rather poorer noise figure and generates all the noise. The noise figure so defined is properly the system noise figure, 'system' often being omitted.
Although radar data sheets usually quote the system noise figure less the installation- specific feeder, sometimes called the overall noise figure, occasionally the first stage noise figure is given; if so, the overall figure will be slightly (~ 1.5 dB) higher. Attain- able noise figures are mildly frequency dependent, the 14 GHz band being a couple of decibels worse than the 3 GHz band, with the 9 GHz band intermediate. Placing the low noise amplifier adjacent to the scanner in effect prevents the feeder receive-leg attenuation from degrading the system. Reducing receiver gain by insertion of swept gain attenuation of course increases the system noise figure. This is immaterial since only relatively large echoes need be detected at such times. If radar has to share its frequency allocations with telecommunication services, additional telecomms mod- ulated continuous wave signals will be received. Their format will appear noise-like and may degrade the radar system noise figure by about 1 dB.
As an example of practical performance, a receiver having 5 dB overall noise figure and bandwidth 13 MHz (10 log 13 = 11.1) has equivalent input noise power 5 - 144+11.1 = -127.9dBW.