Radar Basics

What is an Intrapulse Modulation?

Intrapulse Modulation and Pulse Compression

Pulse compression is a method for improving the range resolution of a 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 term “chirp radar” is often used. It is an abbreviation of Compressed, High-Resolution Pulse, CHIRP). Pulse compression combines the energy 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 within the pulse's spatial extent are displayed as a single target sign. To improve range resolution with a relatively long transmit pulse duration, the transmit pulse is modulated internally. Now, for example, a frequency comparison can be performed on the received echo, thereby enabling localization of the reflecting object within the pulse.

Several modulation methods can be used for this purpose. There are pulse compression methods:

• frequency modulated (or called Frequency Modulation on Pulse, FMOP)
  • with linear frequency modulation,
  • with non-linear frequency modulation,
  • with time-dependent coded frequency modulation (e.g. the Costas code) und
• phase modulated (or called Phase Modulation on Pulse, PMOP)
  • with time-dependent coded pulse-phase modulation.

The pulse compression ratio (PCR) is the ratio of the duration of the uncompressed transmission pulse to the duration of the compressed pulse.

The noise is always broadband, and the noise pulses have a statistical distribution. The frequency-synchronous component of the noise (i.e., noise at the same clock rate as the modulated received signal) is relatively small compared to the echo signal. Therefore, the non-frequency-synchronous component of the input noise is reduced by the filters. This ensures that an output signal is still obtained even when the input signal has long since been lost in the input noise and would thus be lost for simple demodulation. Compared to the unmodulated pulse, this yields a gain—the pulse compression gain or pulse compression factor — which is approximately equal to the temporal 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 the classic short transmission pulse with a pulse duration of τ, the range resolution is

(1)

• c₀ = speed of light = 3·10^8 m/_s
• τ = transmitted pulse duration
• R_res = range resolution

When using pulse compression, the compressed pulse duration must be used here; alternatively, due to the dependence B = 1/τ on the transmitted pulse bandwidth, the bandwidth can be used instead:

(2)

• τ_c = compressed pulse duration
• B = bandwidth of the transmitted pulse

For linear (i.e., not divided into discrete individual pulses) frequency modulation of the transmitted pulse, the bandwidth B of the transmitted pulse relative to the pulse duration τ is decisive. For further calculations, the time-bandwidth product is introduced, which is derived from the ratio of the range resolutions:

(3)

• PCR = pulse compression ratio
• τ = uncompressed transmit pulse duration

The range resolution of a pulse-modulated radar is thus (by a factor of the pulse compression ratio PCR) times better than that of an intra-pulse-modulated radar, which also results in a pulse compression gain.

Pulse compression gain

With the help of pulse compression, a relatively long transmit pulse with comparatively low peak power can achieve a better, greater range than the basic radar equation would suggest. This is because pulse compression allows echo signals to be detected that had already disappeared into the noise prior to pulse compression. The probability is very low that a noise pattern will occur that resembles the intrapulse modulation to such an extent 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 reflected as an increase in range. In the equation, the pulse compression ratio N is often entered directly, i.e., the transmit pulse length and the length of the compressed pulse. This then results in a pulse power multiplied by the transmit pulse duration, i.e., a transmit pulse energy. This is divided by the minimum possible received power, P_{E min} multiplied by the duration of the compressed pulse, which together also constitute an energy. The pulse compression ratio is sometimes also referred to as the compression factor K, because it is directly entered as a factor in the radar equation under the fourth root and thus improves the maximum range of the radar:

(4)

(5)

(In many publications, the Greek capital letter “Τ” (Τ) is used here as a symbol for the uncompressed pulse length, but this can be confused with the Latin T or the pulse repetition period.)

Most often, the entire fraction under the root is simply multiplied by the time-bandwidth product τ·B instead of by the pulse compression ratio, whereby the bandwidth simultaneously serves as an expression for the noise behavior. However, this presupposes largely lossless pulse compression, which can never be achieved in practice. Therefore, it is better to use the pulse compression gain, a quantity determined by measurement, which takes conversion losses into account. Alternatively, the pulse compression loss can also be reported separately (referred to as L_n, the loss due to the detuning of optimal filters, and typically amounts to about 0.8 dB).

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

adding stages

U_in

U_in

U_out

U_out

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

adding stages

U_in

U_in

U_out

U_out

time duration of
a frequency component

Figure 3: Block diagram

filters for one partial frequency

delay lines for the time duration

adding stages

U_in

U_in

U_out

U_out

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:

U_out

t

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)

U_out

t

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)

• a processor-controlled data processing (after A/D conversion), and
• using Surface acoustic wave (SAW) filters.

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-encoded pulse with a Barker code of length n = 7 n = 7.

Figure 8: Diagram of a phase-encoded pulse with a Barker code of length n = 7 n = 7.

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 τ_c can also be detected, the transmitter and receiver must have a bandwidth of B = 1/τ_c. A phase jump can be programmed between the sub-pulses but does not have to take place at each pulse change.

There are:

• Bi-phase modulation, for example
  • the Barker code, in which the phase jumps occur between 0 and 180°;
  • Bi-phase modulations, whose conditions are not as strict as those of the Barker code;
• Polyphase modulation, for example
  • quadrature phase shift keying, for example, using the Frank Code, in which 4 different phase states are programmed at intervals of 90°;
  • Higher-order phase-shift techniques, such as phase modulation in which 8 different phase angles, each spaced 45° apart, are programmed using a three-bit control word according to Gray code;

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.

The binary code can also consist of a pseudorandom binary sequence (a so-called M-sequence or maximal sequence) that can be easily generated by shift registers (shift registers of length m generate a sequence of length 2m - 1). This coding method could, for example, be used by the practically undetectable noise radar.

Nested codes

An important criterion for the use of codes as phase modulation is the achievable attenuation of the time-sidelobes. All codes can also be combined with and among each other. For instance, the combination of the Frank code (a phase modulation) with the Costas code (a frequency modulation) is said to enable a sidelobe attenuation of over 40 dB. In this case, the individual frequencies of the Costas code are internally phase-modulated once again with the Frank code, but are subject to a common coherent pulse integration of each individual sub-pulse or sub-frequency.