#  Radar Basics

#### Intrapulse Modulation and Pulse Compression Uin
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Figure 1: Input and output signals of a pulse compression stage, the received signal in noise is hardly noticeable, so the pulse compression results in a clear echo signal. Uin
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Figure 1: Input and output signals of a pulse compression stage, the received signal in noise is hardly noticeable, so the pulse compression results in a clear echo signal. Uin
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Figure 1: Input and output signals of a pulse compression stage, the received signal in noise is hardly noticeable, so the pulse compression results in a clear echo signal.

## What is an Intrapulse Modulation?

#### Intrapulse Modulation and Pulse Compression

Pulse compression is a method for improving the range resolution of pulse radar. This method is also known as intra-pulse modulation (modulation on pulse, MOP) because the transmitted pulse got a time-dependent modulation internally. In publications the inaccurate term Chirp–Radar is often taken (which only describes a part of the possible modulation methods). Pulse compression combines the energetic advantages of very long pulses with the advantages of very short pulses. The range resolution of a simple pulse-modulated radar depends on the pulse duration. Two reflective objects located within the spatial extent of the pulse are only displayed as one target. To improve the range resolution for a relatively long transmission pulse duration, the transmission pulse is modulated internally. Now a frequency comparison can be made in the received echo, for example, which makes it possible to localize the reflecting object within the pulse.

Several modulation methods can be applied. There are pulse compression methods:

The Pulse Compression Ratio (PCR) is the ratio of the time length of the uncompressed transmitted pulse to the length of the compressed pulse.

The noise is always broadband and the noise pulses have a statistical distribution. The frequency-synchronous part of the noise (i.e. noise at the same frequency as the modulated received signal) is rather low compared to the echo signal. Therefore, the non-frequency synchronous part of the input noise is reduced by the filters. This way an output signal is still obtained even if the input signal has long since been lost in the noise and would thus be lost for simple demodulation. Compared to the non-modulated pulse, an additional gain is thus obtained, the pulse compression gain or pulse compression factor, which is approximately equal to the Pulse Compression Ratio (PCR). Figure 2: short pulse (blue) and a long pulse with intrapulse modulation (green) Figure 2: short pulse (blue) and a long pulse with intrapulse modulation (green)

For a linear (i.e. not divided into discrete single pulses) frequency modulation of the transmit pulse, the bandwidth B of the transmit pulse with the pulse duration τ is decisive. For further calculations, the time-bandwidth product is introduced, the derivation of which results from the ratio of the different range resolutions:

 PCR = (c0 · τ /2) = B · τ (1) (c0 / 2B)

The range resolution of a pulse modulated radar is therefore a multiple (by a factor of the Pulse Compression Rate PCR) of the range resolution of an intra-pulse modulated radar:

 Rres = c0 · (τ / 2) = PCR · c0 /2 B (2)
##### Pulse Compression Gain

With the help of pulse compression, a relatively long transmission pulse with comparatively low peak power can achieve a better, longer range than the basic radar equation would suggest. This is because pulse compression can still detect echo signals that have already disappeared in the noise before pulse compression. The probability is very low that a noise pattern similar to the intra-pulse modulation will occur in such a way that this noise also forms an output signal during pulse compression.

In the radar equation, the advantage of intrapulse modulation and pulse compression must be seen as an increase in range. In the equation the pulse compression ratio PCR or N is often entered directly, i.e. the transmitted pulse length and the length of the compressed pulse. This then results in a pulse power multiplied by the transmission pulse duration, i.e. a transmission pulse energy. This is divided by the minimum possible received power PE min multiplied by the duration of the compressed pulse, together also an energy. The pulse compression ratio is sometimes also called Pulse Compression Factor K, because it is entered directly as a factor in the radar equation under the fourth root:

 K = T·B = N = Τ where Τ = length of the transmitted pulse B = bandwidth of the transmitted pulse τc = length of the compressed pulse (3) τc   (4)

However, this requires a largely lossless pulse compression, which can never be achieved in practice. For this reason, it is better to use the quantity Pulse Compression Gain, which is to be determined by measurement and takes into account the conversion losses. Alternatively, the pulse compression loss can also be used separately (called loss for the mismatch of optimal filters Ln).

The disadvantage of this method, however, is that the blind range of the Chirp-radar is very much worse. As long as the transmitter is working, nothing can be received, because the duplexer blocks the receivers during this time. Only with the use of ferrite circulators is it possible to transmit and receive simultaneously. However, these ferrite circulators can only be used for relatively low transmitting powers.

##### Pulse compression with linear frequency modulation

With this pulse compression method, the transmission pulse is frequency modulated linearly. This has the advantage that the circuit can still be kept relatively simple. However, the linear frequency modulation has the disadvantage that interference can be generated relatively easily by so-called “sweepers”. In the following circuit example, the principle is illustrated using five frequencies present in the transmission pulse. filters for one partial frequency
delay lines for the time duration
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time duration of
a frequency component

Figure 3: Block diagram (an animation as explanation of the mode of operation) filters for one partial frequency
delay lines for the time duration
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time duration of
a frequency component

Figure 3: Block diagram filters for one partial frequency
delay lines for the time duration
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time duration of
a frequency component

Figure 3: Block diagram (an animation as explanation of the mode of operation)

The transmission pulse is divided into several time intervals with an assumed constant frequency. Special filters for exactly the frequency in the respective time interval result in one output signal each, which is added to an output pulse in a cascade of delay lines and adding stages.

An example of an application of linear frequency modulation is the radar AN/FPS-117.

With today's integration possibilities, the high level of circuitry complexity is quite manageable. There are practically two basic possibilities to realize this procedure technically: Uout
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side lobe of antenna
(angularly)
aim
time (range) sidelobes

Figure 4: View of the time sidelobes at an oscilloscope (upper figure) and at B-scope (brightness modulated) Uout
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side lobe of antenna
(angularly)
aim
time (range) sidelobes

Figure 4: View of the time sidelobes at an oscilloscope (upper figure) and at B-scope (brightness modulated)

The circuit in Fig. 3 makes it clear, that if the entire uncompressed pulse is shifted by the Doppler effect, the filter frequencies no longer fit, and losses occur. In practice, several such circuits are therefore often used in parallel, each shifted by a small amount of the Doppler frequency. The signal with the highest signal-to-noise ratio is processed further.

##### Time-Side-Lobes

At the output of the compression filter, sidelobes appear in addition to the target pulse. These sidelobes are offset in time (i.e. in distance) from the main pulse and are called time or range sidelobes. The adjacent graph shows these sidelobes, which are shown once as a function of time (on the oscilloscope) and once as a function of distance (on a section of a brightness modulated display).

Since both the time and amplitude distance are constant, weighting the signal amplitudes can reduce these sidelobes to an acceptable value. However, if this amplitude weighting is only applied on the receive path, it also causes a deterioration of the filter and reduces the signal-to-noise ratio.

The size of these sidelobes is an important parameter of pulse compression radars and can be reduced to a value in the range of -30 dB by this amplitude weighting.

##### Pulse compression with non-linear frequency modulation pulse width
linear FM
non-linear
symmetrically

Figure 5: symmetrically waveform pulse width
linear FM
non-linear
symmetrically

Figure 5: symmetrically waveform pulse width

Figure 7: non-symmetrically waveform pulse width

Figure 7: non-symmetrically waveform

Pulse compression with non-linear frequency modulation has some clear advantages. For example, it no longer requires amplitude weighting for the suppression of the resulting sidelobes, the so-called time-sidelobes, since the form of modulation already fulfills the function of the otherwise necessary amplitude weighting.

A filter adjustment with much steeper edges and nevertheless low time-sidelobes is now possible. In this way, the losses in the signal-to-noise ratio that otherwise occur due to amplitude weighting are avoided.

The symmetrical form of modulation has an increasing (or decreasing) frequency change during the first half of the transmission pulse duration and a decreasing (or now increasing) frequency change during the second half. An asymmetrical form of modulation is obtained when only one half of this symmetrical form is used.

The disadvantages of pulse compression with non-linear frequency modulation are

• a more complicated circuit design and
• a complicated modulation so that each transmitted pulse also gets the same characteristics while maintaining the above-mentioned function of amplitude weighting. Figure 6: A non-symmetrical waveform (Output of the Waveform-Generator) Figure 6: A non-symmetrical waveform (Output of the Waveform-Generator

##### Pulse compression with phase modulation  Figure 8: diagram of a phase-coded pulse compression

The phase-encoded pulse shape differs from the frequency-modulated pulse shape in that the long pulse is divided into smaller sub-pulses of equal length whose carrier frequency does not change. Within this pulse duration of the sub-pulses, the phase is constant. These sub-pulses always represent a range-cell, i.e. the smallest resolvable distance. So that these sub-pulses with the length τc can also be detected, the transmitter and receiver must have a bandwidth of B = 1/τc. A phase jump can be programmed between the sub-pulses but does not have to take place at each pulse change.

This phase jump is usually linked with a binary code. The binary code consists of a sequence of logical states. Depending on this binary code, the phase position of the transmitted signal is switched between 0 and 180°. However, in contrast to the highly simplified picture shown, the transmission frequency is not necessarily a multiple of the frequency of the control pulses. The coded transmission frequency is therefore generally switched disharmoniously at the phase reversal points.

 Length ofcode n Code elements peak sideloberatio, dB 2 +- -6.0 3 ++- -9.5 4 ++-+ ,  +++- -12.0 5 +++-+ -14.0 7 +++--+- -16.9 11 +++---+--+- -20.8 13 +++++--++-+-+ -22.3

Table: Barker Codes

The selection of a suitable code from these so-called 0/π phases is very critical, indeed. Several pulse patterns in the Barker code have proven to be the optimum. This optimum is measured at the level of the expected sidelobes. Only a small number of optimum codes exist, which are listed in the adjacent table. A computer-aided study has examined up to 6 000 different Barker codes and concluded that only the 13 have a maximum signal-to-sidelobes ratio.

It can, therefore, be concluded that no greater number of pulses than this 13 is possible for Barker codes and that the number of 13 subpulses therefore also represents a maximum achievable pulse compression ratio of 13:1!

Recommended video: Paul Denisowski, “Understanding Barker Code”, Educational video of the company Rohde & Schwarz, Munich

##### Nested Barker codes

To take better advantage of the favorable conditions of the Barker codes, it is possible to combine them. For example, an 11-digit Barker code can be used, and within each of these 11 partial pulses, a further 11-digit Barker code is used. This results in a division into a total of 121 sub-pulses. Unfortunately this gives the sidelobes an uneven size.