# Radar Technology - Signals and Range Resolution

The performance of a radar depends on a multitude of things such as antenna pattern, transmitter power, receiver sensitivity and noise level. These quantities mostly define a radar's accuracy. Another important performance figure is resolution, the ability to recognise two objects as separate entities, rather than merging them into one (bigger) object. A radar's data sheet features two figures for its resolution because there are two distinct cases: targets can be close to each other in range, and they can be close to each other in angle. Angular resolution depends on the antenna pattern, whereas range resolution is defined by the properties of the radar's signal, which is often referred to as the 'waveform'. A few typical waveforms and their properties are discussed below.

### The Simple Pulse

Early radars used a so-called 'simple pulse', that is, the signal could be represented as a slice cut out from a sine wave and typically consists of several thousand cycles. If you were to simulate the signal on a piano then you would simply hit one key (and after some time, the brake):

|.,_,.·´‾`·.,_,.·´‾`·.,_,.·´‾`·|

Let's take a pulse duration of 20µs as an example. As with all electromagnetic waves, radar signals travel at the speed of light, c. Thus, when the last portion of the pulse leaves the antenna, the first portion of the pulse has already travelled a distance of 20µs×3×108m which is 6,000m. The pulse stretches over 6,000m in space and it yields echoes that are also 6,000m long.

Imagine the situation of two targets being illuminated by the simple pulse depicted above. If they happen to be, say, 10,000m apart then their echoes will be received one after the other. The critical point is when the targets are separated by less than 3000m, because the signal from target 2 must travel an additional distance of 6000m and, after reflection, appears right at the end of the echo from target 1. If the targets are even closer together then the echoes will partially overlap.

3000m (------------------------------~~~~~~~~~~>T2 <~~~~~~~~~~ ---------<~~~~~~~~~~~~~~~~~~~~T1 echo from T1 echo from T2

There is no way of telling the end of one echo pulse from the beginning of the next, and they get merged into one. Hence the simple pulse can resolve two targets only if they are separated by a minimum distance of 0.5×(pulse duration)×(speed of light). This is a rather poor figure but that's why the signal is called 'simple pulse.'

Obviously, the resolution would be better if the pulse were shorter, but there's a lower limit to pulse duration: a certain amount of signal energy is required to detect an echo in the first place. The energy carried by the pulse is calculated as (transmitter power)×(pulse duration). Therefore, cutting pulse duration in half would necessitate doubling transmitter power in order to keep the signal's energy constant. The problem with that is that transmitter power cannot be increased at will because of cost and other constraints.

But there are other opportunities. If the end of a pulse could be 'painted' in some way so that it was different from the pulse beginning then the problem of overlapping echoes could be solved. Another solution would be to somehow 'compress' the pulse after it has been received. One way of both 'painting' and 'compressing' the pulse is frequency modulation.

### Frequency Modulation and Pulse Compression

Synonyms for this type of signal are:

• chirp - because if you could hear it, it would sound like the 'chirp' of a bird
• FMOP, Frequency Modulation on Pulse
• LFMOP, Linear Frequency Modulation on Pulse - a special case of FMOP

FMOP is characterised by a constant variation of the pitch of the signal. Think of a trombone-slide performed by Glenn Miller1 and you get the idea. FMOP can be simulated on a piano by 'wiping' a finger over a selected range of keys. Doing so at constant speed produces an LFMOP signal, which is an 'up-chirp' if you're going from left to right, or a 'down-chirp' if you're going the other way. The difference between the lowest and the highest frequency (or the number of keys on the piano) is the bandwidth of the signal, and bandwidth translates into range resolution2.

FMOP signals on a piano: _____________________O____O_______O____________ ____________________O______O_______OO _________ ___________________O________O________OOO_______ __OOOOO___________O__________O__________OO_____ _________________O____________O___________O____ (Simple pulse) Up-chirp Down-chirp Non-linear FMOP

So, what's the trick?

The propagation speed of a wave depends on the properties of the medium in which the wave travels. Media such as air and water exhibit constant propagation speeds, regardless of the frequency. But there are devices such as Surface Acoustic Wave (SAW) chips that are different. They can be built such that propagation speed is proportional to frequency - in other words, the higher the frequency of a signal, the faster it travels through the chip.

Hence, if you pass an up-chirped signal through such a device then the following happens:

• The lower frequency part at the beginning of the echo pulse is received first, but travels more slowly than the rest of it.

• The higher frequency part of the echo is received last, but travels at the highest speed.

• Provided that the device is properly matched to the signal, all signal components arrive at the output at the same time.

• Overlapping echoes consist of the high frequency end of the first echo and the low frequency beginning of the second, which are subject to different propagation velocities and get separated.

The result is a pulse that is significantly shorter than the signal that was radiated into the air. It is also much stronger because all components are added. The pulse was literally compressed - hence the term 'pulse compression.' Compression factors of a few 100s can be achieved in practical application. Thus, a pulse of 20μs duration yields 3000m range resolution if it is not compressed, and somewhere around 50m using pulse compression.

Interestingly, bats have been using this type of signal for millions of years.

### Barker Code

It should be possibly to compare a signal with optimum range resolution capability with a time-shifted replica and produce:

• A peak output if the 'master' and the copy are identical, and...

• ...no output if they are identical but there's a time delay between them.

Such an ideal signal doesn't exist. However, there are some types that approximate the feature, and the Barker code is one of them. Barker codes yield maximum output if the two copies match precisely, and either zero or a constant minimum value in other cases. The 'comparison' that takes place in the receiver is called correlation. A correlator compares two signals by:

• Looking at one bit of each input line at a time
• Multiplying these bits

The bitstreams of the 'master copy' (M) and the echo (E) are encoded as '1' and '-1' as long as the signal is present at all, and '0' if not. Here's an example for the Barker code with length 13, correlated with itself at different delay times:

Case 1: No time shift

Master: 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 0 0 Echo: 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 0 0 Products: 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 Sum: 13 Case 2: Time shifted by 1 bit Master: 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 0 0 Echo: 0 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 0 Products: 0 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 0 0 Sum: 0 Case 3: Time shifted by 2 bits: Master: 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 0 0 Echo: 0 0 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 Products: 0 0 1 1 1 -1 -1 -1 -1 -1 1 1 1 0 0 Sum: 1

For any amount of delay (zero delay and 12 cases each for positive and negative delay), Barker codes yield either 0, 1, or N as the result of correlation. N is the length of the code, and there's a limited repertoire of Barker codes: only six codes are known, and the one with 13 bits that was used in the example is the longest of them.

The Barker code is usually employed by phase-shift keying: the transmitter is switched onto full power for the duration of the pulse, which is split into N segments, one for each bit of the Barker code. For every '-1' in the code sequence, the transmitter signal is inverted, which is equal to a 180° phase shift.

### Noise

Random noise is another signal that, if sent through a correlator, can be expected to yield a pronounced peak value for zero delay, and very little response otherwise. The drawback of Barker codes is that the maximum peak value is only 13. Random (or rather, pseudo-random) signals can be made as long as desired, and the peak value after correlation increases by the same amount. Hence, a radar's range resolution capability can be matched to almost any requirement when noise-type signals are employed.

### Other Entries in This Project

#### Electronic Combat

1American band-leader and composer.2More background can be found in the Entry on Fourier Transformation.