Search/Track Radar

A Search/Track radar detects and tracks point targets. The signal return from a point target is inversely proportional to the fourth power of target range and directly proportional to the target's radar cross section (RCS). Real targets have widely differing radar cross sections from different aspect angles. The Search/Track page relates to the search and track settings of the radar, including the setting of PRF (pulse repetition frequency) and its impact on range and/or velocity ambiguity.

See the Technical Notes for search/track radar constants and equations.

Range and azimuth resolution computations

The range resolution computation is based on the pulse width and bandwidth. STK selects the larger resolution value.

The azimuth resolution computation is based on the antenna beamwidth. In the case of elliptical beams, STK selects the smaller beam values.

Waveform tab

On the Waveform tab, choose one of the following Waveform types:

Continuous Wave
Fixed PRF

The availability of certain report and graph elements depends on whether or not you enable search/track mode.

To model Main Lobe Clutter and Side Lobe Clutter filters, select the Doppler Filters tab.

Continuous Wave type

A Continuous Wave (CW) radar has separate receivers and transmitters, with the transmitter always on. It uses frequency modulation to resolve the range of a target. The PRF of a CW radar is effectively infinite, so that all targets are unambiguous in velocity, no matter how fast they move.

For a continuous wave system, the integration occurs over a continuous time period. For a perfect integrator, the integrated CW SNR_T = T_int SNR₁. Recall that SNR₁ for CW radars is based upon a one-second pulse width.

The following parameters are available for Continuous Wave radar:

Continuous Wave Setting	Description
Modulator	Use Signal PSD. If you select this check box, STK computes the power spectral density based on the radar's operating mode, S/T pulsed, or continuous wave. For a pulsed waveform, the computed PSD is ±n null points on the RF spectrum. You can select the value of n; the default value is 15. The pulsed signal spectrum follows a sinc pattern. The first null point is at the 1/ pulse width. For example, the default value for the pulse width is 1.0e^-7 seconds. The computed spectrum is ±150 MHz for the default value 15 for n. The spectrum sample rate is adaptive and based on the spectrum bandwidth used by the signal. This ensures that the sampling of the spectrum is at a sufficient rate for accuracy. The S/T continuous mode models the carrier to be a pure sinc wave. By enabling PSD analysis, you can change to an impure carrier with a Gaussian power density distribution. The spectrum spreads to ±6 sigma over the bandwidth specified in the Power Spectral Density and RF Spectrum Filters group on the Radar Basic System properties page. PSD Analysis use enhances the fidelity of the radar performance analysis. STK computes the amount of RF power at the radar's transmitter and the transmitter filter due to the signal spectrum characteristics and the bandwidth. On the receive side of the radar, the received power computes based on the incoming signal spectrum, the receive side filter characteristics, and the bandwidth. PSD analysis also improves the radar performance analysis under jamming. The received jamming power computes on the basis of the jammer signal spectrum, bandwidth, the radar's receive side filter and the bandwidth. The jamming power represents the unwanted signal power as seen by the radar's receiver. The pulsed radar signal spectrum is a train of sinc-shaped spectrums. The envelope of the peak amplitudes of these sinc spectrums also follow a sinc characteristic curve. A SincEnvSinc filter is available as a filter type to do match filtering on the radar signals. PSD Limit Multiplier. Use PSD Limit Multiplier to extend the bandwidth of the PSD used in spectral overlap computations with the receive radar spectral filter. The bandwidth of the PSD can be computed by the equation: BW = 2 / Pulsewidth * n where n is the PSD limit multiplier.
Analysis Mode	Select either an integration analysis based on the desired signal-to-noise ratio (Goal SNR) or a Fixed Time and enter an appropriate value.

Continuous Wave Setting

Description

Modulator

Use Signal PSD. If you select this check box, STK computes the power spectral density based on the radar's operating mode, S/T pulsed, or continuous wave.

For a pulsed waveform, the computed PSD is ±n null points on the RF spectrum. You can select the value of n; the default value is 15. The pulsed signal spectrum follows a sinc pattern. The first null point is at the 1/ pulse width. For example, the default value for the pulse width is 1.0e^-7 seconds. The computed spectrum is ±150 MHz for the default value 15 for n. The spectrum sample rate is adaptive and based on the spectrum bandwidth used by the signal. This ensures that the sampling of the spectrum is at a sufficient rate for accuracy.

The S/T continuous mode models the carrier to be a pure sinc wave. By enabling PSD analysis, you can change to an impure carrier with a Gaussian power density distribution. The spectrum spreads to ±6 sigma over the bandwidth specified in the Power Spectral Density and RF Spectrum Filters group on the Radar Basic System properties page.

PSD Analysis use enhances the fidelity of the radar performance analysis.

STK computes the amount of RF power at the radar's transmitter and the transmitter filter due to the signal spectrum characteristics and the bandwidth.

On the receive side of the radar, the received power computes based on the incoming signal spectrum, the receive side filter characteristics, and the bandwidth. PSD analysis also improves the radar performance analysis under jamming. The received jamming power computes on the basis of the jammer signal spectrum, bandwidth, the radar's receive side filter and the bandwidth. The jamming power represents the unwanted signal power as seen by the radar's receiver.

The pulsed radar signal spectrum is a train of sinc-shaped spectrums. The envelope of the peak amplitudes of these sinc spectrums also follow a sinc characteristic curve.

A SincEnvSinc filter is available as a filter type to do match filtering on the radar signals.

PSD Limit Multiplier. Use PSD Limit Multiplier to extend the bandwidth of the PSD used in spectral overlap computations with the receive radar spectral filter. The bandwidth of the PSD can be computed by the equation:

BW = 2 / Pulsewidth * n

where n is the PSD limit multiplier.

Analysis Mode

Select either an integration analysis based on the desired signal-to-noise ratio (Goal SNR) or a Fixed Time and enter an appropriate value.

The per-pulse signal-to-noise ratio (SNR) values generated for CW radars are based upon a one-second pulse width.

Fixed PRF type

Radar systems often use multiple pulse integration to increase the signal-to-noise ratio. This processing occurs either coherently (as in PD radars) or noncoherently. When the integration is perfect, the integrated SNR equals the number of pulses integrated multiplied by the single pulse SNR (SNR_M = M SNR₁). One method to model perfect integration is the constant efficiency method, represented by SNR_M = M SNR₁, where ranges between 0.0 and 1.0. Another method makes use of a characteristic of noncoherent integration, whereby the integrated gain tends toward SNR_M = M SNR₁, where ranges between 0.0 and 1.0. Or you can use an integration gain file that specifies the integration gain for a given number of pulses integrated.

The following parameters are available for fixed PRF radar:

Pulse Definition
Modulator
Probability of Detection
Pulse Integration
Specs

Pulse Definition

Fixed PRF Parameter	Description
(Fixed) PRF / Unambiguous Range / Unambiguous Velocity	Select one of these parameters to control, and enter its value. STK will derive the values of the other two parameters from the parameter that you control. The default control parameter is PRF, with a default value of 1.0 kHz. The Velocity is ambiguous where the true target velocity is greater than the unambiguous velocity value computed by radar. The Range is ambiguous where the true target range is greater than the unambiguous range computed by radar. Pulse Doppler radars are generally ambiguous in range and/or Doppler. The unambiguous range is given by c/2fR, where c is the speed of light and fR is the PRF. The Unambiguous Velocity constraint denies access when the velocity is ambiguous (i.e., it enforces a high PRF mode). The Unambiguous Range constraint denies access when the range is ambiguous (i.e., it enforces a low PRF mode). Thus, instead of specifying a fixed PRF value, you may want to specify a target range or velocity that requires unambiguous data.
Pulse Width / Duty Factor	Select one parameter to control, and enter its value. STK will derive the value for the other parameter. Pulse Width is the width of the transmitted pulse. The uncompressed RF bandwidth can also be taken as the inverse of the Pulse Width. Duty Factor is the duty cycle of a radar beam, which is the ratio of the pulse width to the pulse-repetition period. The default value for Pulse Width is 0.1 microseconds.
Number of Pulses	Enter the number of pulses in the modulating pulse sequence. This value is only used for signal PSD analysis. The number of pulses does not affect Maximum Pulses on the Pulse Integration tab.

Fixed PRF Parameter

Description

(Fixed) PRF / Unambiguous Range / Unambiguous Velocity

Select one of these parameters to control, and enter its value. STK will derive the values of the other two parameters from the parameter that you control. The default control parameter is PRF, with a default value of 1.0 kHz.

The Velocity is ambiguous where the true target velocity is greater than the unambiguous velocity value computed by radar. The Range is ambiguous where the true target range is greater than the unambiguous range computed by radar.
Pulse Doppler radars are generally ambiguous in range and/or Doppler. The unambiguous range is given by c/2fR, where c is the speed of light and fR is the PRF.
The Unambiguous Velocity constraint denies access when the velocity is ambiguous (i.e., it enforces a high PRF mode). The Unambiguous Range constraint denies access when the range is ambiguous (i.e., it enforces a low PRF mode).

Thus, instead of specifying a fixed PRF value, you may want to specify a target range or velocity that requires unambiguous data.

Pulse Width / Duty Factor

Select one parameter to control, and enter its value. STK will derive the value for the other parameter.

Pulse Width is the width of the transmitted pulse. The uncompressed RF bandwidth can also be taken as the inverse of the Pulse Width.
Duty Factor is the duty cycle of a radar beam, which is the ratio of the pulse width to the pulse-repetition period. The default value for Pulse Width is 0.1 microseconds.

Number of Pulses

Enter the number of pulses in the modulating pulse sequence. This value is only used for signal PSD analysis.

The number of pulses does not affect Maximum Pulses on the Pulse Integration tab.

Modulator

Type	Description
Use Signal PSD	If you select this check box, STK computes the power spectral density based on the radar's operating mode, S/T pulsed, or Continuous Wave. For a pulsed waveform, the PSD computes to ±15 null points on the RF spectrum. The pulsed signal spectrum follows a sinc pattern. The first null point is at the 1/ pulse width. For example, the default value for the pulse width is 1.0e^-7 seconds; the spectrum computes to ±150 MHz. The spectrum sample rate is adaptive and based on the spectrum bandwidth used by the signal. This ensures that the sampling of the spectrum is at a sufficient rate for accuracy. The S/T continuous mode models the carrier to be a pure sinc wave. By enabling PSD analysis, you can change this to an impure carrier with a Gaussian power density distribution. The spectrum spreads to ±6 sigma over the bandwidth specified in the Power Spectral Density and on the Receiver's RF Filter tab of the Radar Basic Definition properties page. PSD Analysis use will enhance the fidelity of the radar performance analysis. STK computes the amount of RF power at the radar's transmitter and the transmitter filter due to the signal spectrum characteristics and the bandwidth. On the receive side of the radar, the received power computes based on the incoming signal spectrum, the receive side filter characteristics, and the bandwidth. PSD analysis also improves the radar performance analysis under jamming. The received jamming power is computed on the basis of the jammer signal spectrum, bandwidth, the radar's receive side filter, and the bandwidth. The jamming power represents the unwanted signal power as seen by the radar's receiver. The pulsed radar signal spectrum is a train of sinc-shaped spectrums. The envelope of the peak amplitudes of these sinc spectrums also follow a sinc characteristic curve. A SincEnvelopeSinc filter is available as a filter type to do match filtering on the radar signals.
PSD Limit Multiplier	Use the PSD limit multiplier to extend the bandwidth of the PSD used in spectral overlap computations with the receive radar spectral filter. The bandwidth of the PSD can be computed by the equation: BW = 2 / Pulsewidth * M where M is the PSD limit multiplier.

Type

Description

Use Signal PSD

If you select this check box, STK computes the power spectral density based on the radar's operating mode, S/T pulsed, or Continuous Wave.

For a pulsed waveform, the PSD computes to ±15 null points on the RF spectrum. The pulsed signal spectrum follows a sinc pattern. The first null point is at the 1/ pulse width. For example, the default value for the pulse width is 1.0e^-7 seconds; the spectrum computes to ±150 MHz. The spectrum sample rate is adaptive and based on the spectrum bandwidth used by the signal. This ensures that the sampling of the spectrum is at a sufficient rate for accuracy.

The S/T continuous mode models the carrier to be a pure sinc wave. By enabling PSD analysis, you can change this to an impure carrier with a Gaussian power density distribution. The spectrum spreads to ±6 sigma over the bandwidth specified in the Power Spectral Density and on the Receiver's RF Filter tab of the Radar Basic Definition properties page.

PSD Analysis use will enhance the fidelity of the radar performance analysis.

STK computes the amount of RF power at the radar's transmitter and the transmitter filter due to the signal spectrum characteristics and the bandwidth.

On the receive side of the radar, the received power computes based on the incoming signal spectrum, the receive side filter characteristics, and the bandwidth. PSD analysis also improves the radar performance analysis under jamming. The received jamming power is computed on the basis of the jammer signal spectrum, bandwidth, the radar's receive side filter, and the bandwidth. The jamming power represents the unwanted signal power as seen by the radar's receiver.

The pulsed radar signal spectrum is a train of sinc-shaped spectrums. The envelope of the peak amplitudes of these sinc spectrums also follow a sinc characteristic curve.

A SincEnvelopeSinc filter is available as a filter type to do match filtering on the radar signals.

PSD Limit Multiplier

Use the PSD limit multiplier to extend the bandwidth of the PSD used in spectral overlap computations with the receive radar spectral filter. The bandwidth of the PSD can be computed by the equation:

BW = 2 / Pulsewidth * M

where M is the PSD limit multiplier.

Probability of Detection (Pdet)

STK Radar implements a swirling detection model. The probability of detection is a function of the per pulse SNR (signal to noise ratio), the number of pulses integrated, the probability of false alarm, and the RCS (radar cross section) fluctuation type (taken from the target RCS properties). For a CFAR radar, Pdet is also a function of the number of reference cells.

References for the algorithms that compute probability of detection include:

"Recursive Methods for Computing Detection Probabilities", Mitchell, R.L., J.F. Walker, IEEE Transactions on Aerospace Electronic Systems, Vol. 7, No. 4, July 1971.
"Analysis of CFAR Processors in Nonhomogenous Background", R.P. Gandhi, S. A. Kassan, IEEE Transactions on Aerospace and Electronic systems, Vol 24, No 4, July 1988.

CFAR Type	Description
Cell Averaging Constant False Alarm Rate (CA-CFAR)	Cell Averaging Constant False Alarm Rate (CA-CFAR) accounts for the clutter in the range of cells before and after the cell of interest, within the same azimuth radial. Clutter power in the reference cells is averaged to adjust the CFAR threshold. AGI recommends using the Clutter Geometry Range of CFAR Cells option for use with this CFAR type. This allows clutter in the cells before and after the current cell that is evaluated during computation of CFAR and the probability of detection. For information on parameters that you can set with this option, see Probability of False Alarm and number of CFAR Reference Cells. “Extending Gandhi's CA-CFAR detection probability formula to pulse integration cases”, Dr. Shen Chiu, DRDC, DoD Canada.
Constant False Alarm Rate	A constant false alarm rate (CFAR) processor will adjust the detection threshold based on the noise in reference 'cells' around the cell being examined for the presence of a target. For information on parameters that can be set with this option, see Probability of False Alarm and number of CFAR Reference Cells.
Non-constant False Alarm Rate	Choose this to have STK not adjust the threshold to keep the CFAR constant and to compute Pdet accordingly. For information on parameters that you can set with this option, see Probability of False Alarm.
Ordered Statistics Constant False Alarm Rate (OS-CFAR)	Select this option to have STK organize clutter power in the reference cells in descending order and subselect to compute CFAR threshold. AGI recommends using the Clutter Geometry Range of CFAR Cells option for use with this CFAR type. This allows clutter in the cells before and after the current cell that is evaluated during computation of CFAR and the probability of detection. Parts of the CA-CFAR and OS-CFAR algorithm have been enhanced by Dr. Shen Chiu of Defence Research and Development Canada (DRDC). For information on parameters that you can set with this option, see Probability of False Alarm and number of CFAR Reference Cells. "Extending Gandhi’s OS-CFAR detection probability formula to cases of target-like interference and multiple pulse integration", Dr. Shen Chiu, DRDC, DoD Canada.

You can set the following parameters related to probability of detection:

Parameter	Description
Probability of False Alarm	This is the probability that a target is declared to be present when in reality none exists. Enter a value in the range 0-1.
CFAR Reference Cells	Enter the number of reference cells in an azimuth radial considered for CFAR computation.

Pulse Integration

The following options are presented for selecting and defining the Pulse Integration Mode of your Search/Track radar:

Parameter	Description
Analysis Mode	For a Fixed PRF radar, select either an integration analysis based on the desired signal-to-noise ratio (Goal SNR) or a fixed number of pulses (Fixed Pulse Number).
Maximum Pulses	This is available only when the integration analysis mode is Goal SNR. Enter the desired value for maximum pulses. Maximum Pulses is not affected by the Number of Pulses on the Pulse Definition tab.
Integration Type	Perfect. If M is the number of pulses integrated, SNR₁ is the per pulse SNR, and SNR_M is the integrated SNR, then SNR_M = M SNR₁. Constant Efficiency. If M is the number of pulses integrated, SNR₁ is the per pulse SNR, and SNR_M is the integrated SNR, then SNR_M = M SNR₁, where 0.0<<1.0. This is not available for CW radar. Exponent on Pulse Number. If M is the number of pulses integrated, SNR₁ is the per pulse SNR, and SNR_M is the integrated SNR, then SNR_M = M SNR₁, where 0.0<<1.0. This is not available for CW radar. Integration Gain File. Enter the path and filename of the Integration Gain File or browse for the file by clicking the ellipsis ( ... ) button. This is not available for Fixed Pulse Number integration mode.

Parameter

Description

Analysis Mode

For a Fixed PRF radar, select either an integration analysis based on the desired signal-to-noise ratio (Goal SNR) or a fixed number of pulses (Fixed Pulse Number).

Maximum Pulses

This is available only when the integration analysis mode is Goal SNR. Enter the desired value for maximum pulses.

Maximum Pulses is not affected by the Number of Pulses on the Pulse Definition tab.

Integration Type

Perfect. If M is the number of pulses integrated, SNR₁ is the per pulse SNR, and SNR_M is the integrated SNR, then SNR_M = M SNR₁.

Constant Efficiency. If M is the number of pulses integrated, SNR₁ is the per pulse SNR, and SNR_M is the integrated SNR, then SNR_M = M SNR₁, where 0.0<<1.0. This is not available for CW radar.

Exponent on Pulse Number. If M is the number of pulses integrated, SNR₁ is the per pulse SNR, and SNR_M is the integrated SNR, then SNR_M = M SNR₁, where 0.0<<1.0. This is not available for CW radar.

Integration Gain File. Enter the path and filename of the Integration Gain File or browse for the file by clicking the ellipsis ( ... ) button. This is not available for Fixed Pulse Number integration mode.

Specs

The following options enable you to override the STK-computed resolution values with values from the radar spec sheet and to enable pulse cancellation.

Parameter	Description
Override Computed Resolution values	STK estimates range cell and azimuth resolution from the radar system data: It computes Range Cell Resolution from the pulse width. It sets Azimuth Resolution to the antenna 3dB beamwidth. When these resolution values are available as a part of the radar specifications, AGI suggests that you override the computed resolution values and enter the values from the radar specification data.
Enable Pulse Cancellation	Select this check box to improve the signal-to-noise (SNR) by enabling pulse cancellation of noise and clutter. The valid range for Number of Pulses is 2 through 5. Pulse type can be either coherent or noncoherent.

Parameter

Description

Override Computed Resolution values

STK estimates range cell and azimuth resolution from the radar system data:

It computes Range Cell Resolution from the pulse width.
It sets Azimuth Resolution to the antenna 3dB beamwidth.

When these resolution values are available as a part of the radar specifications, AGI suggests that you override the computed resolution values and enter the values from the radar specification data.

Enable Pulse Cancellation

Select this check box to improve the signal-to-noise (SNR) by enabling pulse cancellation of noise and clutter.

The valid range for Number of Pulses is 2 through 5.

Pulse type can be either coherent or noncoherent.

Doppler Filters

Pulse Doppler (PD) and moving target indicator (MTI) radars are capable of filtering out clutter returns from the ground and other interference sources, such as blowing leaves, moving cars, etc. These sources of clutter enter the radar primarily through the main lobe of the antenna and also from the ground directly underneath the radar. These two sources of clutter are respectively termed the main lobe clutter (MLC) and side lobe clutter (SLC). Side lobe clutter is present across a wide Doppler frequency band, corresponding to the velocity of the radar itself. The predominant component of side lobe clutter for typical applications is at 0 Doppler-shift frequency. For an airborne radar, this is the altitude line.

STK Radar models both Main Lobe Clutter and Side Lobe Clutter filters:

Parameter	Description
Main Lobe Clutter (MLC)	Main lobe clutter bandwidth is the total filter width about the MLC velocity. The value that you set for filtering may affect the value of access constraints, since targets lying within the filter bandwidth are not detectable under normal circumstances. If you select this filter, enter the appropriate bandwidth in the Doppler velocity unit.
Side Lobe Clutter (SLC)	Side lobe clutter bandwidth is the bandwidth about the altitude line. If you select this filter, enter the appropriate bandwidth in the Doppler velocity unit.