#### Pulse Integration

A pulse integrator is a improvement technique to address gains in probability of detection by using multiple transmit pulses. This gain will be achieved by inserted in receiving path radar signal processor adding radar returns (thus the word integrator) from different successive pulse periods. Depending on location of the pulse integrator in the signal processing chain this process is referred to as

**Coherent Integrator**

or

no detect

Figure 1: Location of the Coherent Integrator

**Coherent Integrator**

or

no detect

Figure 1: Location of the Coherent Integrator

Filter

(IF-Amp.)

**Coherent**

Integrator

Integrator

Detector

Device

no detect

Figure 1: Location of the Coherent Integrator

- coherent integration, or
- non-coherent integration

#### Coherent Integration

With coherent integration we insert a coherent integrator, or signal processor, between the matched filter and amplitude detector as shown in Figure 1. The signal processor samples the return from each transmit pulse at a spacing equal to the range resolution of the radar set and adds the returns from N pulses. After it accumulates the N pulse sum it performs the amplitude detection and threshold check.

Thus, for example, if we were interested in a range of 75 Km and had a range resolution of 150 m the signal processor would form 75,000/150 or 500 samples for each pulse. The signal processor would then accumulate (add) each of the 500 samples in 500 summators. After the signal processor has summed the first N pulses it would begin dropping older pulses off of the accumulator as new pulses arrive. Thus, the signal processor will add the returns from the most recent N pulses.

In analog processors the integration (summation, accumulation) is accomplished by filters. (e.g. with Potentialoscopes). It is accomplished by Fast Fourier Transformations (FFTs) in digital signal processors.

The noise on each pulse is zero-mean and Gaussian. The noise samples from each pulse are uncorrelated. Thus the noise out of the coherent integrator has the same statistical properties of the noise out of the matched filter from the IF- amplifier.

We assume that the signal level at the input to the coherent integrator is constant from pulse to pulse. This is indicative of a Swerling Case 0 target Swerling Case 1 target or a Swerling Case 3 target. These signal levels will be added in the integrator. The specific amplitude over the N pulses integrated by the coherent integrator is governed by the probability density function for the specific target type. So we can essentially consider the output of the coherent integrator as the return from a single pulse whose Signal-to-Noise Ratio (SNR) is N times the SNR provided by the radar range equation.

Coherent integration offers no benefit for Swerling Case 2 and Swerling Case 4 targets. This stems from the fact that, that the signal of these targets is not constant from pulse to pulse but, instead, behaves like noise.

#### Non-Coherent Integration

**Noncoherent Integrator**

or

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Figure 2: Location of the Non-Coherent Integrator

**Noncoherent Integrator**

or

no detect

Figure 2: Location of the Non-Coherent Integrator

Filter

(IF-Amp.)

Detector

**Noncoherent**

Integrator

Integrator

Device

no detect

Figure 2: Location of the Non-Coherent Integrator

The Non-Coherent Integrator is placed after the amplitude or square law detector as shown in Figure 2. The name non-coherent integration derives from the fact that, since the signal has undergone amplitude or square law detection, the phase information is lost. The non-coherent integrator operates in the same fashion as the coherent integrator in that it sums the returns from N pulses before performing the threshold check.

In older radars the pulse integration was implemented via the persistence on displays plus the integrating capability of a human operator.

A second implementation is termed an m-of-n detector and uses more of a logic circuit rather than a device that integrates. Simply stated, the radar examines the output of the threshold device for n pulses. If a detect is declared on any m of those n pulses the radar declares a target detection. This type of implementation is also termed a dual threshold detector.

The third type of non-coherent detector is implemented as a summator or integrator. In older radars low-pass filters were used to implement them. In newer radars they are implemented in special purpose hardware or the radar computer as digital summators. They operate as described as coherent integrators.