CLUTTER EFFECT ON DETECTION RANGE

Clutter may arise from a surface area on the Earth (land or sea), from a volume in the atmosphere (precipitation, chaff, insects, or aurora), or from discrete objects on or above the surface (prominent surface features, birds, or meteors). The gen-eral method of range calculation for all types of clutter is discussed here, and ap-plied in following sections to each individual type.

3.2.1 Range-Ambiguous Clutter

Energy from clutter in the spatial resolution cell at a range R_c equal to the target range R is one source of interference that competes with the signal entering the

F_{rdrc i} = range-dependent response factor for clutter (see Section 1.6.2);

L_{c i} = atmospheric attenuation for clutter (see Sections 7.2 and 7.3).

The total clutter input energy C₀ is the sum of C_i over all ambiguities containing

3.2.2 Types of Radar Waveforms

Radar waveforms are defined [1] as belonging to one of four types, for each of which a different clutter analysis is necessary.

 Low-PRF (LPRF) Waveform:

A pulsed-radar waveform whose pulse-repetition frequency is such that targets of interest are unambiguously resolved with respect to range.

While targets of interest lie within the unambiguous range, clutter may origi-nate beyond that range (i > 0). The energy received from each ambiguity is multiplied by the factor (R/R_{c i})⁴ = R⁴/(R + iR_u)⁴, relative to clutter at target range R, and may contribute to interference even for i > 0, especially if it is not reduced by the clutter improvement factor applicable to clutter at range R.

 Medium-PRF (MPRF) Waveform:

A pulsed-radar waveform whose pulse-repetition frequency is such that targets of interest are ambiguous with respect to both range and Doppler shift.

For this waveform, clutter at R_c < R (for which i < 0), as well as at R_c  R, contributes to interference. The contributions from short-range ambiguities exceed that from R_c = R by a large factor when (R + i_minR_u) << R.

 High-PRF (HPRF) Waveform:

A pulsed-radar waveform whose pulse-repetition frequency is such that targets of interest are ambiguous with respect to range.

The HPRF, chosen to avoid Doppler ambiguities, exceeds the MPRF, intro-ducing more range ambiguities and increasing the input interference, espe-cially from clutter at range R_{c i} << R.

 Continuous-Wave (CW) Waveform:

The CW radar is defined as a radar that transmits a continuous-wave signal that may be phase-modulated. The spatial resolution cell for an unmodulated CW waveform is bounded by the antenna beam and extends to a maximum range t_oc/2, where t_o is the dwell time of the antenna beam. The input clutter energy in any given environment is greater than that of an HPRF waveform, although use of separate transmitting and receiving antennas may reduce clut-ter from very short ranges. CW waveforms with periodic phase modulation

Radar Equations for Clutter and Jamming 59 having repetition interval t_r produce range ambiguities at intervals R_u identical to those of pulsed radars with PRI = t_r.

3.2.3 Clutter Detectability Factor

The detectability factor D_x used in the radar equations of Chapter 1 is the required ratio of the signal energy to the spectral density of white Gaussian noise. Clutter differs from noise in two ways: (1) it is not random from pulse to pulse, and hence its spectrum consists of discrete lines within the signal bandwidth; and (2) its am-plitude distribution may spread beyond that of the Rayleigh distribution that char-acterizes the sum of in-phase and quadrature Gaussian noise components. Hence, a different clutter detectability factor D_xc must be used.

3.2.3.1 Clutter Spectrum and Correlation Time

The spectra of different types of clutter (see Chapter 9) are characterized by the mean radial velocity relative to the radar and the spread of each spectral line. Ve-locity parameters are used in preference to the mean and spread of Doppler fre-quency because they characterize the clutter independently of the radar frefre-quency.

Spread is measured by the standard deviation _v in velocity that results from random motion of the clutter scatterers, antenna beam scanning, and projection of the mean radial velocity on the antenna pattern. The spread affects the number n_c of independent clutter samples available for integration, which can be expressed as a function of the correlation time t_c of the clutter at the radar input and the ob-servation (dwell) time of the radar beam [2, p. 117]:

1 ^o 1 2 2 ^{v o}

c c

t t

n n

t

     

 (3.6)

where n is the number of noise samples integrated. When clutter appears in more than one range ambiguity, different values _{v i} and t_{c i} are found for each range R_i.

3.2.3.2 Clutter Correlation Loss

In the absence of Doppler processing, the clutter detectability factor depends on nc, rather than the number n of target pulses integrated. The increase in required energy ratio is described by the clutter correlation loss L_cc:

   

0

0 c 1

cc

L D n

 D n  (3.7)

Note that this loss does not reduce the effect of clutter, but rather increases it to reflect the increase in signal-to-clutter ratio required for target detection, as com-pared to white Gaussian noise.

Doppler-based signal processing increases the number of independent sam-ples in (3.6), which depends on the spectrum of the clutter at the processor output, thus reducing L_cc relative to that applicable to the input clutter. Methods of calcu-lating n_c and L_cc for systems using Doppler processing are given in Chapter 9. The loss L_{cc i} is applied to increase in the effective spectral density for each ambiguity.

3.2.3.3 Clutter Distribution Loss

The second source of increased clutter detectability factor is the broader amplitude distribution of some clutter. The detectability factors calculated for noise are based on a detection threshold that is high enough to meet the specified false-alarm probability on the exponentially distributed noise power, adjusted for inte-gration. The probability density function (pdf) of volume clutter is approximately exponential, as is surface clutter when viewed at high grazing angles. But the pdf spreads as the grazing angle decreases, and can be modeled as a Weibull distribu-tion having a spread parameter a_w  1. The spread varies from aw = 1 for the ex-ponential distribution to a_w  5 for extreme cases.

This factor increases the clutter detectability factor D_xc by a clutter distribu-tion loss L_cd. This loss applies to a two-parameter constant-false-alarm-rate (CFAR) processor that controls the threshold using estimates of both the mean and spread of input clutter. It is defined as the ratio of the threshold y_b required to ob-tain a specified false-alarm probability P_fa with the actual clutter distribution to that required for the exponential distribution (see Section 4.2.2). For clutter with a Weibull distribution:

where P_w^1( p,a_w) is the inverse function of the integral of the Weibull distribution for probability p with spread parameter a_w and P_^1( p) is the inverse function for the incomplete gamma function. The width of the pdf varies over range ambigui-ties, and separate values of L_{cd i} are applied as factors to find the effective spectral density at each range R_i.

Given the large loss that results when Weibull clutter with a_w >> 1 is input to a two-parameter CFAR processor, many radars supplement the CFAR process with a clutter map that suppresses clutter peaks (and targets) in the resolution cells where they are observed over several scans. Since these peaks are relatively sparse, even in regions of strong clutter, the loss is confined to individual map cells and the average loss in detection probability caused by target suppression is

Radar Equations for Clutter and Jamming 61 relatively small. The peaks can be considered discrete clutter, effects of which are described in Section 3.5, rather than by the clutter distribution loss of (3.8).

3.2.3.4 Clutter Detectability Factor

The clutter detectability factor, denoted here by D_xc, is defined [1] as:

The predetection signal-to-clutter ratio that provides stated probability of detection for a given false alarm probability in an automatic detection circuit. Note: In MTI systems, it is the ratio after cancellation or Doppler filtering.

The losses Lcc from Section 3.2.3.2 and Lcd from Section 3.2.3.3 give corrections that are applied to the detectability factor D_x to account for the difference between clutter and noise statistics:

xc x cc cd

D D L L (3.9)

3.2.4 Effective Spectral Density of Clutter

To form the effective input spectral density I0 e in (3.2), the input clutter compo-nent C_0i is adjusted for use with a common detectability factor D_x. The adjustment required for clutter in ambiguity i is

0_{e i i} ^{xc i} _i ^{cc i cd i} (W/Hz)

where I_m is the MTI improvement factor, defined [1] as:

The clutter power ratio at the output of the clutter filter divided by the signal-to-clutter power ratio at the input of the signal-to-clutter filter, average uniformly over all target velocities of interest. Synonym: clutter improvement factor.

The synonym in the definition covers CW and pulsed Doppler as well as MTI radars, and will be used here. The improvement factor for different processing methods is discussed in Section 9.6. It may vary over the individual ambiguous regions, but an average value I_m can be used to express the effective output spec-tral density of clutter as

Adjustment of effective clutter spectral densities for clutter losses, before summation is carried out, and averaging of the improvement factor as in (3.11),

permits C_{0 e} to be added directly to N₀ in (3.2), and the sum is used with a common value of D_x in the radar equation to solve for detection range.

3.2.5 Detection Range with Clutter

The effective clutter energy given by (3.11) is added to the noise spectral density N₀ to obtain the effective interference energy I_0e in the environment of clutter and noise. This allows the detection range R_mc in clutter to be expressed as:

     

performed during the observation time to. Since many terms on the right-hand side of this equation are range-dependent, R_mc must generally be found graphically or by root-finding. Exceptions to this general rule, where this equation may be writ-ten in closed form for surface and to volume clutter, are given in Sections 3.3.5 and 3.4.6.

The graphical procedure is to plot separately the signal energy E from (1.25) and required energy I_{0 e}D_x(n) = (N0 + C_{0 e})D_x(n) as functions of target range R.

The detection requirement is met at ranges for which E  I_{0 e} + D_x(n) and the longest such range is R_mc. The root-finding procedure is to express E and I_{0 e}D_x(n) as separate functions of R, and create a computer program to find the largest R at which the two expressions are equal:

 

0

   

mc rootR e x

R  E R I R D n  (3.13)

where root_x[·] is the value of x at which the equality within the brackets is met.

In document Radar Equations for Modern Radar (Page 77-82)