Continuous Wave Settings | Fixed PRF Settings | Doppler Filters

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.

Choose one of the following Waveforms:

Continuous Wave
Fixed PRF

The availability of certain report and graph elements depend on whether you enable search/track mode.

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

Continuous Wave

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 Settings	Description
Modulator	Use Signal PSD. If enabled, 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 is computed to ±n (n is user selectable, default value is 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 (e.g., the default value for the pulse width is 1.0e^-7 seconds; the spectrum is computed to ±150 MHz for the default value 15 for n. The spectrum sample rate is adaptive and is based on the spectrum bandwidth used by the signal. This insures that the spectrum is sampled at a sufficient rate for accuracy. The S/T continuous mode models the carrier to be a pure sinc wave. By enabling PSD analysis, this can be changed to an impure carrier with a Gaussian power density distribution. The spectrum is spread 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 will enhance the fidelity of the radar performance analysis. STK will compute 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 is computed 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 SincEnvSinc filter is available as a filter type to do match filtering on the radar signals. PSD Signal Multiplier. The PSD limit multiplier is used 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 Settings

Description

Modulator

Use Signal PSD. If enabled, 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 is computed to ±n (n is user selectable, default value is 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 (e.g., the default value for the pulse width is 1.0e^-7 seconds; the spectrum is computed to ±150 MHz for the default value 15 for n. The spectrum sample rate is adaptive and is based on the spectrum bandwidth used by the signal. This insures that the spectrum is sampled at a sufficient rate for accuracy.

The S/T continuous mode models the carrier to be a pure sinc wave. By enabling PSD analysis, this can be changed to an impure carrier with a Gaussian power density distribution. The spectrum is spread 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 will enhance the fidelity of the radar performance analysis.

STK will compute 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 is computed 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 SincEnvSinc filter is available as a filter type to do match filtering on the radar signals.

PSD Signal Multiplier. The PSD limit multiplier is used 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

Radar systems often use multiple pulse integration to increase the signal-to-noise ratio. This processing is carried out 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. Alternatively, 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

Pulse Definition

Fixed PRF Parameter	Description
(Fixed) PRF / Unambiguous Range / Unambiguous Velocity	Select and, if desired, enter a value for PRF, Unambiguous Range or Unambiguous Velocity; values for the other two parameters will be derived values. The Velocity is ambiguous where the true target velocity is greater than the ambiguous velocity value as computed by radar. The Range is ambiguous where the true target range is greater than the ambiguous range as computed by radar. Pulse Doppler radars are generally ambiguous in range and/or Doppler. The unambiguous range R_U is given by c/2f_R, where c is the speed of light and f_R 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, in lieu of specifying a fixed PRF, it may be desirable to specify a target range or velocity for which unambiguous data is required and derive the other values; e.g., if an unambiguous target range is specified, the values for PRF and unambiguous velocity can be derived. The default value for PRF is 1.0 kHz.
Pulse Width / Duty Factor	Select and, if desired, enter a value for Pulse Width or Duty Factor; the value for the other parameter will be a derived value. The duty cycle of a radar 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	Number of pulses in the modulating pulse sequence.

Fixed PRF Parameter

Description

(Fixed) PRF / Unambiguous Range / Unambiguous Velocity

Select and, if desired, enter a value for PRF, Unambiguous Range or Unambiguous Velocity; values for the other two parameters will be derived values.

The Velocity is ambiguous where the true target velocity is greater than the ambiguous velocity value as computed by radar. The Range is ambiguous where the true target range is greater than the ambiguous range as computed by radar.

Pulse Doppler radars are generally ambiguous in range and/or Doppler. The unambiguous range R_U is given by c/2f_R, where c is the speed of light and f_R 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, in lieu of specifying a fixed PRF, it may be desirable to specify a target range or velocity for which unambiguous data is required and derive the other values; e.g., if an unambiguous target range is specified, the values for PRF and unambiguous velocity can be derived. The default value for PRF is 1.0 kHz.

Pulse Width / Duty Factor

Select and, if desired, enter a value for Pulse Width or Duty Factor; the value for the other parameter will be a derived value.

The duty cycle of a radar 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

Number of pulses in the modulating pulse sequence.

Modulator

Type	Description
Use Signal PSD	If enabled, 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 is computed 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 (e.g., the default value for the pulse width is 1.0e^-7 seconds; the spectrum is computed to ±150 MHz). The spectrum sample rate is adaptive and is based on the spectrum bandwidth used by the signal. This insures that the spectrum is sampled at sufficient rate for accuracy. The S/T continuous mode models the carrier to be a pure sinc wave. By enabling PSD analysis, this can be changed to an impure carrier with a Gaussian power density distribution. The spectrum is spread 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 will compute 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 is computed 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	The PSD limit multiplier is used 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 enabled, 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 is computed 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 (e.g., the default value for the pulse width is 1.0e^-7 seconds; the spectrum is computed to ±150 MHz). The spectrum sample rate is adaptive and is based on the spectrum bandwidth used by the signal. This insures that the spectrum is sampled at sufficient rate for accuracy.

The S/T continuous mode models the carrier to be a pure sinc wave. By enabling PSD analysis, this can be changed to an impure carrier with a Gaussian power density distribution. The spectrum is spread 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 will compute the amount of RF power at the radar's transmitter and the transmitter filter due to the signal spectrum characteristics and the bandwidth.

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

The PSD limit multiplier is used 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 swerling 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. The Clutter Geometry Range of CFAR Cells option is recommended for use with this CFAR type. This allows clutter in the cells before and after the current cell that will be evaluated during computation of CFAR and the probability of detection. For information on parameters that can be 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	The threshold is not adjusted to keep the CFAR constant. Pdet is computed accordingly. For information on parameters that can be set with this option, see Probability of False Alarm.
Ordered Statistics Constant False Alarm Rate (OS-CFAR)	Clutter power in the reference cells is ordered in descending order and sub-selected to compute CFAR threshold. The Clutter Geometry Range of CFAR Cells option is recommended for use with this CFAR type. This allows clutter in the cells before and after the current cell that will be evaluated during computation of CFAR and the probability of detection. Parts of the CA-CFAR and OS-CFAR algorithm that have been enhanced by Dr. Chen Chin of Defence Research and Development Canada (DRDC). For information on parameters that can be 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	The probability that a target is declared to be present when in fact none exists. Enter a value in the range 0-1.
CFAR Reference Cells	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	Available only when the integration analysis mode is Goal SNR. Enter the desired value for maximum pulses.
Integration Type	Perfect. If M is the number of pulses integrated, SNR₁ is the per pulse SNR, and SNR_M is the integrated SNR, 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, SNR_M = M SNR₁, where 0.0<<1.0. 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, SNR_M = M SNR₁, where 0.0<<1.0. 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. (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

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

Integration Type

Perfect. If M is the number of pulses integrated, SNR₁ is the per pulse SNR, and SNR_M is the integrated SNR, 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, SNR_M = M SNR₁, where 0.0<<1.0. 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, SNR_M = M SNR₁, where 0.0<<1.0. 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. (Not available for Fixed Pulse Number integration mode.)

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: 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 the user sets for filtering may affect the value of access constraints, since targets lying within the filter bandwidth are not detectable under normal circumstances. If this filter is selected, enter the appropriate bandwidth in the Doppler velocity unit. The default value is 0 m/s.
Side Lobe Clutter (SLC)	Side lobe clutter bandwidth is the bandwidth about the altitude line. If this filter is selected, enter the appropriate bandwidth in the Doppler velocity unit. The default value is 0 m/s.