DSSR-250C

Baron Services DSSR-250C Processing Algorithms

RVP8 User’s Manual March 2006

Processing Algorithms

5. Processing Algorithms

Note: Optional dual polarization processing algorithms are described in Appendix B.

This chapter describes the processing algorithms implemented within the RVP8 signal processor. The discussion is confined to the mathematical description of these algorithms. Figure 5–1 shows the overall process by which the RVP8 converts the IF signal into corrected reflectivity, velocity, and width. Table 5–1 summarizes the quantities that are measured and computed by the RVP8. The type of the quantity (i.e., real or complex) is also given. Subscripts are sometimes used to denote successive samples in time from a given range bin. For example, s “I” and “Q” time series or “video” sample from the n’th pulse from a given range bin. In cases where it is obvious, the subscripts denoting the pulse (time) are dropped. The descriptions of all the data processing algorithms are phrased in terms of the operations performed on data from a single range bin- identical processing then being applied to all of the selected ranges. Thus, there is no need to include a range subscript in this data notation.

denotes the

It is frequently convenient to combine two simultaneous samples of “I” and “Q” into a single complex number (called a phaser) of the form:

s + I ) jQ

where “j” is the square root of –1. Most of the algorithms presented in this chapter are defined in terms of the operations performed on the “s”’s, rather than the “I”’s and “Q”’s. The use of the complex terms leads to a more concise mathematical expression of the signal processing techniques being used. In actual operation, the complex arithmetic is simply broken down into its real-valued component parts in order to be computed by the RVP8 hardware. For example, the complex product:

s + W Y

is computed as

Real{s}+ Real{W}Real{Y}* Imag{W}Imag{Y

Imag{s}+ Real{W}Imag{Y}) Imag{W}Real{Y

where “Real{}” and “Imag{}” represent the real and imaginary parts of their complex-valued argument. Note that all of the expanded computations are themselves real-valued.

In addition to the usual operations of addition, subtraction, division, and multiplication of complex numbers, we employ three additional unary operators: “||”, “Arg” and “*”. Given a number “s” in the complex plane, the magnitude (or modulus) of s is equal to the length of the vector joining the origin with “s”, i.e. by Pythagoras:

}

| s | + Real{s

The signed (CCW positive) angle made between the positive real axis and the above vector is:

ë+Arg{s}+ arctan

}

5–1

) Imag{s

Imag{s

Real{s

}

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Processing Algorithms

where this angle lies between * p and ) p and the signs of Real{s} and Imag {s} determine the proper quadrant. Note that this angle is real, and is uniquely defined as long as |s| is non-zero. When |s| is equal to zero, Arg{s} is undefined. Finally, the “complex conjugate” of “s” is that value obtained by negating the imaginary part of the number, i.e.,

s*+ Real{s}* jImag{s}.

Note that Arg{s*} = –Arg{s}. The reader is referred to any introductory text on complex numbers for clarification of these points.

Table 5–1: Algebraic Quantities Within the RVP8 Processor

p Instantaneous IF-receiver data sample Real b Instantaneous Burst-pulse data sample Real

I,Q Instantaneous quadrature receiver components Real

s Instantaneous time series phaser value Complex

sȀ Time series after clutter filter Complex T

Zeroth lag autocorrelation of A values Real Zeroth lag autocorrelation of AȀ values Real First lag autocorrelation of AȀ values Complex

Second lag autocorrelation of AȀ values Complex SQI Signal Quality Index Real V Mean velocity Real W Spectrum Width Real CCOR Clutter correction Real LOG (Signal+Noise)/Noise ratio for thresholding Real SIG Signal power of weather Real C Clutter power Real N Noise power Real

Z Corrected Reflectivity factor Real

T UnCorrected Reflectivity factor Real

The following sections cover the various parts of the diagram shown in Figure 5–1, i.e.,

S IF Signal Processing S I/Q processing and clutter filtering S Range averaging and clutter microsuppression S Moment calculations (reflectivity, velocity, spectrum width) S Thresholding for data quality and Speckle Filtering S Reflectivity Calibration S Special algorithms for ambiguity resolution (dual PRF, dual PRT, Random Phase) S Calibration and Testing

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Figure 5–1: Flow Diagram of RVP8 Processing

dBZ

dBT

Speckle Remover

Thresholding

V W

Processing Algorithms

SIG

LOG

SQI

CCOR

FLAGS

dBZ dBT

Calibrate Moments

dBZ

Calculate Output Data

Range Averaging

Micro Clutter Suppression

Clutter Filtering and Autocorrelation by

Time Domain or Frequency Domain Approach

AFC

V W SQI SIG CCOR

R0 R1 (R2) T

Correlate Correlate

Filter

K–bins

CCOR

D/A

FFT

Compute

Frequency

A/D

36 MHz

Burst IF Input Channel

FIR

Decimate

in Time

A/D

IF Signal Input Channel

5–3

(I and Q)

36 MHz

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Processing Algorithms

5.1 IF Signal Processing

The starting point for all computations within the RVP8 are the instantaneous IF-receiver samples p available at a very high sampling rate (typically 36MHz), which makes possible the digital implementation of functions that are traditionally performed by discrete components in an analog receiver. The RVP8’s all-digital approach replaces a great deal of analog hardware, avoids problems of aging and maintenance, and makes it easy to tune-up the receiver and alter its parameters.

This section describes these IF signal processing steps. Please refer to Figure 1-3 for a block diagram of the IF processing that is performed.

5.1.1 FIR (Matched) Filter

The RVP8 implements a digital version of the “matched” filter that is found in the traditional analog radar receiver. The equivalent Finite-Impulse-Response (FIR) filter is designed using an interactive graphical procedure described in Section 4.4. The filter length (number of taps), center frequency, and bandwidth are all adjustable. The design procedure computes two sets of

filter coefficients f

where N is the length of the filter. The input samples pn are centered on the range bin to which the (I, Q) pair is assigned. Note that some of the p i.e., the filter length may be chosen to be greater than the bin spacing. Such an overlap introduces a slight correlation between successive bins, but the longer length allows a better filter to be designed.

and, the instantaneous burst-pulse or COHO reference samples bn. These data are

and f

such that the instantaneous quadrature samples at a given bin are:

I +

N*1

n+0

pn, Q +

N*1

n+0

are likely to overlap among adjacent bins,

The sums above for I and Q are computed on the RVP8/Rx board using dedicated FIR chips (for revisions A and B) that can perform up to 576 million sums of products per second. The Rev C RVP8/Rx uses a more flexible FPGA. The p

and f

are represented as 10-bit (Rev.A/B) or 16-bit (Rev.C) signed integers. A numerical

are represented as 16-bit signed integers, and the

optimization procedure is used to quantize the ideal filter coefficients into their hardware values. The overall spectral purity of the FIR filter will typically be greater than 66dBc (Rev.A/B) and 84dBc (Rev.C).

The reference phase for each transmitted pulse is computed using the same two FIR sums, except with b

substituted for the pn. For a magnetron system the Nbn samples are centered

on the transmitted burst; for a Klystron system they may be obtained from the burst pulse (recommended) or from the CW COHO. If the Klystron is phase modulated by an external phase shifter (as opposed to the RVP8/Tx digital transmitter board), then the samples should be from the modulated COHO.

The f

coefficients are computed as:

+ ln sin

) 2p

SAMP

n *

5–4

N * 1

, n + 0 AAA N * 1

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Processing Algorithms

where fIF is the radar intermediate frequency, f frequency, and l

are the coefficients of an N-point symmetric low-pass FIR filter that is

matched to the bandwidth of the transmitted pulse. The multiplication of the l

is the RVP8/IFD crystal sampling

SAMP

terms by the

sin() terms effectively converts to the low-pass filter to a band-pass filter centered at the radar IF.

The formula for the f The phase of the sinusoid terms, and the symmetry of the l

coefficients is identical except that sin() is replaced with cos().

terms, has been carefully chosen to

have a valuable overall symmetry property when n is replaced with (N–1)–n, i.e., the sequence is reversed:

(N*1)*n

+ l

(N*1)*n

+ ln cos

sin

) 2p

(N*1)*n

SAMP

) 2p

+ f

((N * 1) * n) *

SAMP

n *

N * 1

Thus, the coefficients needed to compute I are merely the reversal of the coefficients needed to compute Q; if you know f

, then you also know f

5.1.2 RVP8/Rx Receiver Modes

The RVP8 supports six fundamental IFD and RVP8/Rx configurations which allow you to choose the best style of IF processing for your particular site. The following table summarizes the options where, BW is the net IF sampling rate (full 72MHz, or halfband filtered 36MHz), DynR is the dynamic range (normal single channel, or extra wide dual channel), Pol is the number of polarizations, Freq is the number of distinct intermediate frequencies, and IFD is the number of IFD’s, along with their corresponding RVP8/Rx cards.

# BW DynR Filt Pol Freq IFD Description – –––– –––– –––– ––– –––– ––– –––––––––––––––––––––– 0 Full Norm Norm 1 1 1 Standard single channel 1 Full Norm Norm 2 2 1 Dual Pol on two frequencies 2 Full Norm Norm 2 1 2 Dual Pol on separate IFDs 3 Half Norm Norm 2 1 1 Dual Pol on single IFD 4 Half Wide Norm 1 1 1 Extra wide dynamic range 5 Half Norm Long 1 1 1 Extra long/fast FIR filters

The first three modes were already supported in the previous RVP7 processor. The last three modes are unique to the RVP8 and bring some exciting additional capabilities to the signal processor. The six receiver modes are summarized below. Please see the Discussion of

Halfband Filtering (Section 5.1.2.1) as it applies to Modes 3-5, and the Discussion of Wide Dynamic Range (Section 5.1.2.2)for additional details on using Mode-4.

Mode-0

: Standard Single Channel This is the most common “vanilla” mode that is used by

single-polarization CW-pulsed radars whose front-end LNA has a dynamic range less than 92dB. The (I,Q) data are computed from IF samples at their full acquisition rate (32MHz for Rev.D IFDs, and 72MHz for Rev.F), and the resulting dynamic range from 14-bit IFD samples is well matched to the RF components.

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Processing Algorithms

Mode-1: Dual-Pol On Two Frequencies This was the original dual-Pol configuration used by the RVP7 several years ago. A single IFD A/D converter receives the “H” and “V” channels using two distinct intermediate frequencies. Two different STALOs are required in this configuration, making the RF/IF components a bit more expensive, but only one IFD is required.

Mode-2

: Dual-Pol On Separate IFDs This mode was introduced into the RVP8 in 2003, and

provides dual polarization data using two IFDs connected to two RVP8/Rx cards in the same PCI chassis. A single intermediate frequency is used, hence only one STALO is required.

Mode-3

: Dual-Pol On Single IFD This is the recommended dual polarization mode for all new

RVP8 installations. The “H” and “V” channels are fed into the Primary and Secondary IFD inputs using a single intermediate frequency. System cost and complexity are both optimized in this design since only a single IFD, RVP8/Rx card, and STALO are required to process both polarization channels.

Mode-4

: Extra Wide Dynamic Range Radars having very high performance front-end LNAs

can preserve the full benefit of that investment by running two separate IF signals into the Primary (HiGain) and Secondary (LoGain) IFD inputs. A nominal channel separation of 25–30dB might be used to achieve an overall dynamic range of up to 110dB.

Mode-5

: Extra Long/Fast FIR Filters This mode is intended for pulse compression systems

that require unusually long filters (up to 80μsec), or finer range resolution in order to employ higher compressed bandwidths without the risk of missing echoes between bins. For example, a 30μsec pulse could be processed at an incoming range resolution of 50 meters and then range averaged down to 150meter output spacing.

5.1.2.1 Discussion of Halfband Filtering Modes 3-5

Traditionally, the IFD used by the RVP7 and RVP8 has sent raw 14-bit A/D samples from its Burst and IF inputs directly to either the RVP7/Main or RVP8/Rx cards for FIR filtering and conversion into complex (I,Q) values. The IFD would function simply as a waveform sampling device (hence the acronym IF

Digitizer), and all of the front-end signal processing

took place downstream of it. This model has changed with the introduction of the Rev.F IFD which has the ability to carry

out several billion multiply-accumulate cycles per second. This means that IF samples from multiple signals can be preprocessed entirely within the IFD and then encoded without loss onto the fixed bandwidth of its digital downlink. The new receiver modes 3 through 5 rely on this hardware capability and use a method known as “Halfband Filtering” to effectively double the downlink data rate.

Section 2.2.7 of the RVP8 User’s Manual contains a detailed account of how A/D quantization noise affects the dynamic range of the IFD. Briefly, for the Rev.F A/D converter which runs at 72MHz, the contribution of A/D quantization noise within any given 1MHz interval is 72 times smaller than the total noise of the converter itself. This is an important property of all wideband sampling systems: the noise floor after processing, and hence the dynamic range, are improved by increasing the fundamental A/D sampling rate.

Normally the IFD sends 72MHz A/D samples from a single input channel directly down to the RVP8/Rx PCI card. The samples are sent at full speed in order to realize maximum reduc-

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tion of the final (I,Q) noise floor. But suppose we wanted to send two A/D waveforms down the same data link by interleaving the samples together. Each channel would have to be down-sampled to 36MHz in order to fit within this format, but that would cause its (I,Q) noise floor to increase by 3dB.

To avoid this, we do not create the 36MHz streams merely by discarding every other A/D sample, but rather, by passing the original 72MHz data through a halfband digital filter and then discarding every other point of this filtered A/D stream. The difference is important. Since the halfband filter has removed all of the A/D quantization noise from half of the original Nyquist interval, there will be no increase in noise density within the passband of the (I,Q) filter when the halfband stream is down sampled to 36MHz. Thus, the A/D noise that would normally have folded into the (I,Q) data at 36MHz is first removed by the halfband filter so that we’re left with a 36MHz stream having the same dynamic range of the original 72MHz samples.

The IFD halfband filter is a 49-Tap equiripple FIR filter having 40dB of stopband rejection and 0.175dB of passband ripple. The passband extends either from 0–16.5MHz when configured as a lowpass filter, or 19.5–36MHz when configured for highpass. The RVP8 automatically selects the correct type of filter depending on the intermediate frequency specified in the Mb menu. The halfband filter has linear phase and is therefore non-dispersive. This means that it is totally suitable for handling compressed pulses and other wideband Tx/Rx waveforms.

Processing Algorithms

5.1.2.2 Discussion of Wide Dynamic Range Mode-4

When a two channel IFD is used as an extended dynamic range receiver there are some important decisions to make with respect to setting up the RF/IF levels that drive the IFD.

The first of these is the amount of signal level separation between the high gain and the low gain IFD inputs. There is an absolute minimum and absolute maximum channel separation that still allows the IFD to capture the full dynamic range of the receiver. If a signal level separation is made that is outside of these absolute limits valuable receiver dynamic range will be lost.

S The absolute minimum separation of the channels is equal to the total dynamic

range of the receiver minus the dynamic range of a single channel of the IFD. Generally, the total dynamic range of the receiver is set by the LNA. For example, if we are considering a 1μsec pulse (1MHz bandwidth), the dynamic range of the LNA may be about 105dB, and the dynamic range of a single channel of the IFD is about 84dB (from –78dBm to +6dBm). In this case, the minimum separation would be 21dB. At minimum separation, the overlap of the low gain channel and the high gain channel will be maximized, and that overlap is equal to the dynamic range of a signal channel of the IFD minus the separation. In this case, the overlap is ( 84dB – 21dB ) = 63dB.

S The absolute maximum separation of the channels is simply the dynamic range

of a single channel of the IFD. In the above example this would be 84dB. At

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maximum separation, the overlap of the low gain channel and the high gain channel is zero -- we begin using one as soon as the other has begun to saturate.

We see that there can be a large difference between the absolute minimum and maximum signal level separations; thus additional criteria must be considered to choose an optimum value that is between these diverse limits.

Choosing a proper separation value is a tradeoff of several factors. If the separation value is too low, the IFDs may end up operating very close to their noise floors. And if the separation is too high, then the overlap between the two channels is reduced which makes it dif ficult for the IFD to make a smooth transition as it combines the data from both channels. Too high a separation may also result in receiver components that are not practical to build.

As a rule of thumb, channel separations in the 22–30dB range provide a good balance of the above criteria. In the case of a 1μsec pulse this results in an overlap interval of approximately 55-63dB, which is sufficient for good IFD transitions and also leads to receiver components that are practical to build.

Once a separation value has been chosen, one must consider how to build the receiver to achieve this. The basic receiver will take the form of an LNA and a mixer followed by a splitter resulting in a low gain channel and a high gain channel. W e know the gain dif ference in the two channels (the separation value), but we must find the actual gain to use in each channel.

Processing Algorithms

If we consider the total system dynamic range as generally set by the LNA (105dB in the above example), we can estimate the minimum detectable signal input to the LNA as well as the maximum usable linear level at the IFD. If the LNA has a noise figure of 1dB and we are using a 1μsec pulse, the minimum detectable signal at the LNA input is –113dBm, and thus the maximum signal is 105dB above this, or –8dBm. If we add to these number the gain of the LNA and the conversion loss of the mixer (and any other losses experienced through the power splitter for the low gain and high gain channels), we can use this information to determine the signal values of the components in these two channels.

For example, if the LNA has a gain of 17dB, the mixer has a conversion loss of 7dB, there is 1dB miscellaneous losses and 3dB loss in the power splitter, then the signal level at the output of the power splitter is ( –113 + 18 – 7 – 1 – 3 ) = –106dBm for the minimum signal, and and –1dBm for the maximum signal. In the low gain channel, we need to bring the –1dBm up to the maximum input value of the IFD (+6dBm). To do this we need about 8dB of amplification (7dB plus one more deciBel to account for the anti–alias filter loss of the IFD). If we assume 25dB of channel separation, on the high gain channel we require about +33dB of amplification. Finally , this tells us that on the low gain channel, the minimum and maximum signals presented to the IFD are ( –106 + 8 ) = –98dBm and ( –1 + 8 ) = 7dBm. For the high gain channel, the signal levels are ( –106 + 33 ) = –73dBm and ( –1 + 33 ) = +32dBm. Note that as +32dBm is above the maximum input level tolerated by the IFD, the amplifier on the high gain channel must limit its output to less than +16dBm. Thus an amplifier with an output saturation value of between +10dBm and +15dBm should be used.

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5.1.3 Automatic Frequency Control (AFC)

AFC is used on magnetron systems to tune the STALO to compensate for magnetron frequency drift. It is not required for Klystron systems. The STALO is typically tuned 30 or 60 MHz away from the magnetron frequency. The maximum tuning range of the AFC feedback is approximately 7MHz on each side of the center frequency. This is limited by the analog filters that are installed just before the signal and burst IF inputs on the IFD. It is important that the system’s IF frequency is at least 4MHz away from any multiple of half the digital sampling frequency, i.e., 18, 36, 54, or 72MHz.

The RVP8 analyzes the burst pulse samples from each pulse, and produces a running estimate of the power-weighted center frequency of the transmitted waveform. This frequency estimate is the basis of the RVP8’s AFC feedback loop, whose purpose is to maintain a fixed intermediate frequency from the radar receiver.

The instantaneous frequency estimate is computed using four autocorrelation lags from each set of Nb 36MHz), but becomes noisy within 10% of each end. Since the span of the burst pulse samples is only approximately one microsecond, several hundred estimates must be averaged together to get an estimate that is accurate to several kiloHertz. Thus, the AFC feedback loop will typically have a time constant of several seconds or more.

samples. This estimate is valid over the entire Nyquist interval (e.g., 18MHz to

Most of the burst pulse analysis routines, including the AFC feedback loop, are inhibited from running immediately after making a pulsewidth change. The center-of-mass calculations are held off according to the value of Settling time (to 1%) of burst frequency estimator, and the AFC loop is held off by the Wait time before applying AFC (Mb Section 3.2.6). This prevents the introduction of transients into the burst analysis algorithms each time the pulsewidth changes.

Additional information about using AFC can be found in Sections 2.2.11, 2.4, and 3.2.6.

5.1.4 Burst Pulse Tracking

The RVP8 has the ability to track the power-weighted center-of-mass of the burst pulse, and to automatically shift the trigger timing so that the pulse remains in the center of the burst analysis window of the Pb plot. This means that external sources of drift in the timing of the transmitted pulse (temperature, aging, etc.) will be tracked and nulled out during normal operation; so that fixed targets will remain fixed in range, and clean Tx phase measurements will always be available on every pulse.

The Burst Pulse Tracker feedback loop makes changes to the trigger timing in response to the measured position of the burst. Timing changes will generally be made only when the RVP8 is not actively acquiring data, in the same way that AFC feedback is held off for similar “quiet” times. However, if the center-of-mass has drifted more than 1/3 the width of the burst analysis window, then the timing adjustment will be made right away. Also, there will be an approximately 5ms interruption in the normal trigger sequence whenever any timing changes are made.

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The Burst Pulse Tracker and AFC feedback loop are each fine-tuning servos that keep the burst pulse “centered” in time and frequency. These servos have been expanded to include a combined “Hunt Mode” that will track down a missing burst pulse when we are uncertain of both its time and frequency. This coarse-tuning mode is especially valuable for initializing the two fine-tuning servos in radar systems that drift significantly with time and temperature.

When the radar transmitter is On but the burst pulse is missing, it may be because either of the following have happened:

S It is misplaced in time, i.e., the Tx pulse is outside of the window displayed in the Pb

plotting command. In this case, the trigger timing needs to be changed in order to bring the center of the pulse back to the center of the window.

S It is mistuned in frequency, i.e., the AFC feedback is incorrect and has caused the burst

frequency to fall outside of the passband of the RVP8 anti-alias filters. In this case the AFC (or DAFC) needs to be changed so that proper tuning is restored.

The Hunt Mode performs a 2-dimensional search in time and frequency to locate the burst; searching across a +

20msec time window, and across the entire AFC span. If a valid Tx pulse (i.e., meeting the minimum power requirement) can be found anywhere within those intervals then the Burst Pulse Tracker and AFC loops will be initialized with the time and frequency values that were discovered. The fine servos then commence running with a good burst signal starting from those initial points.

Depending on how the hunting process has been configured in the Mb menu, the whole procedure may take several seconds to complete. The RVP8’s host computer interface remains completely functional during this time, but any acquired data would certainly be questionable. GPARM status bits in word #55 indicate when the hunt procedure is running, and whether it has completed successfully. The BPHUNT (Section 6.26) opcode allows the host computer to initiate Hunt Mode when it knows or can sense that a burst pulse should be present

5.1.5 Interference Filter

The interference filter is an optional processing step that can be applied to the raw (I,Q) samples that emerge from the FIR filter chips. The intention of the filter is to remove strong but sporadic interfering signals that are occasionally received from nearby man-made sources. The technique relies on the statistics of such interference being noticeably different from that of weather.

For each range bin at which (I,Q) data are available, the interference filter algorithm uses the received power (in deciBels) from the three most recent pulses:

, P

n*2

where:

+ 10log

If the three pulse powers have the property that:

n*1

, and P

) Q

* P

n*1

n*2

t C1 and ŤPn* P

5–10

n*1

u C2 (Alg.1)

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Processing Algorithms

then (In,Qn) is replaced by (I

n*1,Qn*1

). Here C1 and C2 are constants that can be tuned by the user to match the type of interference that is anticipated, and the error rates that can be tolerated. For certain environments it may be the case that good results can be obtained with

+ C2; but the RVP8 does not force that restriction.

This 3-pulse algorithm is only intended to remove interference that arrives on isolated pulses, and for which there are at least two clear pulses in between. Interference that tends to arrive in bursts will not be rejected.

Two variations on the fundamental algorithm are also defined. The CFGINTF command (Section 6.23) allows you to choose which of these algorithms to use, and to tune the two threshold constants. You may also do this directly from the Mp setup menu (Section 3.2.2).

* P

n*1

* P

n*1

Where LinAvg() denotes the deciBel value of the linear

n*2

t C1 and Pn* P

t C1 and Pn* LinAvg( P

n*1

u C2 (Alg.2)

n*1

, P

) u C2 (Alg.3)

n*2

average of the two deciBel powers. The Alg.2 and Alg.3 algorithms also include the receiver noise level(s) as part of their decision criteria. Whenever power levels are intercompared in the algorithms, any power that is less than the noise level is first set equal to that noise level. This makes the filters much more robust and properly tunable, so that interference is more successfully rejected on top of blank receiver noise.

Optimum values for C

and C2 will vary from site to site, but some guidance can be obtained

using numerical simulations. The results shown below were obtained when the algorithms were applied to realistic weather time series having a spectrum width = 0.1 (Nyquist), SNR = +10dB, and an intermittent additive interference signal that was 16dB stronger than the weather. The interference arrived in isolated single pulses with a probability of 2%.

Performance of the three algorithms is summarized in the first three columns of Table 5–2, for which C but with the value of C

and C2 have the common value shown. The fourth column also uses Algorithm #3,

raised by 2dB. The “Missed” rate is defined as the percentage of

interference points that manage to get through the filtering process without being removed. The “False” (false alarm) rate is the percentage of non-interference points that are incorrectly modified when they should have been left alone.

Table 5–2: Algorithm Results for +16dB Interference

Alg.1 Alg.2 Alg.3 Alg.3, C1+=2dB C1,C2 Missed/False Missed/False Missed/False Missed/False ––––– –––––––––––– –––––––––––– –––––––––––– ––––––––––––

6.0dB 17.8% 10.91% 17.8% 4.06% 17.8% 3.48% 10.3% 4.15%

8.0dB 10.5% 6.57% 10.5% 2.42% 10.4% 1.71% 6.1% 1.92%

9.0dB 8.5% 5.09% 8.5% 1.81% 8.3% 1.16% 5.4% 1.28%

10.0dB 7.3% 4.01% 7.3% 1.42% 7.5% 0.79% 5.4% 0.85%

11.0dB 8.9% 3.14% 8.9% 1.06% 8.3% 0.51% 6.5% 0.54%

12.0dB 11.6% 2.53% 11.6% 0.85% 11.3% 0.33% 9.9% 0.35%

13.0dB 17.0% 2.07% 17.0% 0.67% 16.3% 0.22% 15.3% 0.23%

14.0dB 23.5% 1.70% 23.5% 0.54% 22.4% 0.14% 21.6% 0.15%

16.0dB 39.2% 1.21% 39.2% 0.35% 39.6% 0.06% 38.9% 0.06%

20.0dB 67.3% 0.65% 67.3% 0.14% 72.5% 0.01% 72.4% 0.01%

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It is important to minimize both types of errors. If too much interference is missed, then the filter is not doing an adequate job of cleaning up the received signal. If the false alarm rate is too high, then background damage is done at all times and the overall signal quality (especially sub-clutter visibility) may be compromised. We suggest that you try to keep the false alarm rate fairly low, perhaps below 1%; and then let the missed percentage fall where it may.

To summarize the numerical results in Table 5–2:

S The “Missed” rates of Alg.1 and Alg.2 are identical, but the “False” rate of Alg.1 is

much higher. Alg.1 clearly does not perform as well for additive interference, but it is included in the suite for historical reasons.

S The “Missed” error rate for Alg.3 is nearly identical to that of Alg.2, but Alg.3 has a

significantly lower false alarm rate. This is because of the somewhat improved statistics that result when the linear mean of P rather than just P

by itself. We recommend that Alg.3 generally be chosen in

n*1

n*2

and P

is used in the second comparison,

n*1

preference to the other two.

S Alg.3 can be further tuned by allowing the two constants to differ. For example, by

raising C “Missed” rate for an increase in the “False” rate. Lowering C

slightly above C2 (fourth column), we can trade off a decrease in the

would have the opposite

effect.

Keep in mind that optimum tuning will depend on the type of interference you are trying to remove. In the previous example, where the interfering signal is only 16dB stronger than the weather, there was a close tradeoff between the “Missed” and “False” error rates. However, Table 5–3 shows the results that would be obtained if the interference dominates by 26db.

Table 5–3: Algorithm Results for +26dB Interference

Alg.1 Alg.2 Alg.3 Alg.3, C2+=5dB C1,C2 Missed/False Missed/False Missed/False Missed/False ––––– –––––––––––– –––––––––––– –––––––––––– ––––––––––––

6.0dB 17.8% 10.75% 17.8% 3.95% 17.8% 3.44% 17.8% 0.34%

8.0dB 9.9% 6.48% 9.9% 2.31% 9.9% 1.68% 9.9% 0.15%

9.0dB 7.4% 4.99% 7.4% 1.75% 7.4% 1.14% 7.4% 0.10%

10.0dB 5.9% 3.91% 5.9% 1.36% 5.9% 0.76% 5.9% 0.06%

11.0dB 4.8% 3.06% 4.8% 1.06% 4.8% 0.50% 4.8% 0.04%

12.0dB 3.2% 2.37% 3.2% 0.83% 3.2% 0.33% 3.2% 0.03%

13.0dB 2.6% 1.83% 2.6% 0.62% 2.6% 0.20% 2.8% 0.01%

14.0dB 1.9% 1.45% 1.9% 0.50% 1.9% 0.12% 2.6% 0.01%

16.0dB 1.3% 0.90% 1.3% 0.30% 1.3% 0.05% 5.8% 0.00%

20.0dB 3.1% 0.39% 3.1% 0.12% 2.0% 0.01% 31.5% 0.00%

Notice that we can now re-tune the constants and operate with C1+ 13dB and C2+ 18dB (fourth column); which yields a low 2.8% “Missed” rate, and an extremely low 0.01% false alarm rate. Since the false alarm rate is (approximately) independent of the interference power, these filter settings would leave all “clean” weather virtually untouched, i.e., we would have a very safe filter that is intended only to remove fairly strong interference. Such a filter could be left running at all times without too much worry about side effects.

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5.1.6 Large-Signal Linearization

The RVP8 is able to recover the signal power of targets that saturate the IF-Input A/D converter by as much as 4–6 deciBels. This is possible because an overdriven IF waveform still spends some of its time in the valid range of the converter, and thus, it is still possible to deduce information about the signal.

Figure 5–2 shows actual signal generator test measurements with normal A/D saturation (lower line), and with the extrapolation algorithms turned on (upper line). The high-end linear range begins to roll off at approximately +10dBm versus +5dBm, and thus has been extended by 5dB.

12 11 10

9 8 7 6 5 4 3 2 1

0 –1 –2 –3 –4

–4–3–2–10123456789101112

Figure 5–2: Linearization of Saturated Signals Above +4.5dBm (Rev B/C IFD)

The roll off starts at +4.5 dBm for the Rev. B&C IFD, and at +6 dBm for the Rev. D.

5.1.7 Correction for Tx Power Fluctuations

The RVP8 can perform pulse-to-pulse amplitude correction of the digital (I,Q) data stream based on the amplitude of the Burst/COHO input. The technique computes a (real valued) correction factor at each pulse by dividing the mean amplitude of the burst by the instantaneous amplitude of the burst. The (I,Q) data for that pulse are then multiplied by this scale factor to obtain corrected time series. The amplitude correction is applied after the Linearized Saturation Headroom correction.

The mean burst amplitude is computed by an exponential average whose (1/e) time constant is selected as a number of pulses (See Section 3.2.2). A short time constant will settle faster, but will not be as thorough in removing amplitude variations (since the mean itself will be varying).

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Longer time constants do a better job, but will require a second or two before valid data is available when the transmitter is first turned on. The default value of 70 will give excellent results in almost all cases.

Whenever the RVP8 enters a new internal processing mode (time series, FFT, PPP, etc.), the burst power estimator is reinitialized from the level of the first pulse encountered, and an additional pipeline delay is introduced to allow the estimator to completely settle. Thus, valid corrected data are produced even when the RVP8 is alternating rapidly between different data acquisition tasks, e.g., in a multi-function ASCOPE display. The additional pipeline delay will not affect the high-speed performance when the RVP8 runs continuously in any single mode.

For amplitude correction to be applied, the instantaneous Burst/COHO signal level must exceed the minimum valid burst power specified in the “Mb” setup section. If that level is not met, e.g., if the transmitter is turned off, then no correction is performed. Thus, the amplitude correction feature conveniently “gets out of the way” when receiver-only tests are being performed.

The maximum correction that will ever be applied is

5dB. If the burst power in a given pulse

is more than 5dB above the mean, or less than 5dB below it, then the correction is clamped at those limits. The power variation of a typical transmitter will easily be contained within this interval (it is typically less than 0.3dB).

Instantaneous amplitude correction is a unique feature of the RVP8 digital receiver. Bench tests with a signal generator reveal that an amplitude modulated waveform having 2.0dB of pulse-to-pulse variation is reduced to less than 0.02dB RMS of (I,Q) variation after applying the amplitude correction.

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5.2 Time Series (“I” and “Q”) Signal Processing

This section describes the processing of the radar time series data (also called linear “video” or “I” and “Q”) to obtain the meteorologically significant “moment” parameters: reflectivity, total power, velocity, width, signal quality index, clutter power correction, and optional polarization variables.

Recall that the time series synthesized by the FIR filter consist of an array of complex numbers:

where “j” is * 1

[

Im) jQ

1ń2

. The time series, are the starting point for all calculations performed

]

for m + 1, 2, 3, AAA, M

within the RVP8. There are several excellent references on the details of I and Q processing. The reader is referred to Doviak and Zrnic’s text on the subject. The top part of Figure 5–3 shows I and Q values for a simulated time series using the ascope utility.

There are two broad categories of time series signal processing:

S Time Domain Processing using the I and Q samples directly to calculate

“autocorrelations” and then using the autocorrelations to compute the moments. This is used by many systems since the algorithms are very efficient requiring minimal storage and computational power. However, time domain algorithms are generally not adaptive or very flexible.

S Frequency Domain Processing using the I and Q samples to calculate a Doppler power

spectrum and then applying algorithms, such as clutter filtering or 2nd trip echo filtering/extraction, in the frequency domain. The Doppler spectrum is then inverted to obtain the autocorrelation functions and these are used to calculate the moments. The frequency domain is well suited to more complex adaptive algorithms, i.e., where the processing algorithm is optimized for the data.

The RVP8 supports the concept of “major modes” or processing modes to process the time series. Currently the following major modes are supported by SIGMET:

S DFT/FFT Mode is a frequency domain approach which is used for most operational

processing applications. There are a variety of clutter filtering options, including the GMAP algorithms (Gaussian Model Adaptive Processing).

S Pulse Pair Processing or PPP Mode is a time domain approach that is used primarily for

dual polarization applications.

S Random Phase Mode or RPHASE is a frequency domain approach similar to the

DFT/FFT, except that filtering and extraction of both the first and second trip echoes is supported.

S Batch Mode during which a small batch of low PRF pulses is transmitted (e.g., for 0.1

degree of scanning) followed by a large batch of higher PRF pulses (e.g., for 0.9 degrees of scanning) to determine which ranges are likely contaminated by second trip echo. This

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was developed to support a US WSR88D legacy requirement. It is not supported in SIGMET’s IRIS software.

The time and frequency domain approaches are described in the sections below.

Figure 5–3: Example of time series and Doppler power spectrum

Doppler Spectrum

White Noise

Time

Ground Clutter

Weather Targets

Spectrum Width

Velocity

Mean Velocity

+VuĆVu

Time series of I and Q and the corresponding Doppler power spectrum obtained from the ascope utility using the built-in simulator. The Doppler spectrum displays the radial velocity on the X-axis over the unambiguous range or “Nyquist” interval and the power in dB

AmplitudeAmplitude

relative to saturation on the y-axis. Note that for illustration, this example

is based on 256 time series points (one point per pulse) which yields 256 spectrum components. This is more than is usually processed in actual operation.

The spectrum shows the three major components of the Doppler spectrum:

Power

* White noise. * Ground clutter at zero radial velocity . * A spectrum of the weather targets

having a Gaussian shape characterized by the weather power, mean velocity and width (standard deviation), i.e., the spectrum moments.

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5.2.2 Frequency Domain Processing- Doppler Power Spectrum

The Doppler power spectrum, or simply the “Doppler spectrum”, is the easiest way to visualize the meteorological information content of the time series. The bottom part of Figure 5–3 shows an example of a Doppler power spectrum for the time series shown in the upper part of the figure. The figure above shows the various components of the Doppler spectrum, i.e., typically there is white noise, weather signal and ground clutter. Other types of targets such as sea clutter, birds, insects, aircraft, surface traffic, second trip echo, etc. may also be present.

The “Doppler power spectrum” is obtained by taking the magnitude squared of the input time series, i.e. for a continuous time series,

m+0

wmsme

*j(2pńM)mk

S(w) + |F{s(t)}|

Here S denotes the power spectrum as a function of frequency ω, and F denotes the Fourier transform of the continuous complex time series s(t). The Doppler power spectrum is real-valued since it is the magnitude squared of the complex Fourier transform of s(t).

In practice a pulsed radar operates with discrete rather than continuous time series, i.e., there is an I and Q value for each range bin for each pulse. In this case we use the discrete Fourier transform or DFT to calculate the discrete power spectrum. Note that in the special case when we have 2 algorithm (FFT), so called because it is significantly faster than the full DFT.

The DFT has the form:

Typically a weighting function or “window” wm is applied to the input time series sm to mitigate the effect of the DFT assumption of periodic time series. The RVP8 supports different windows such as the Hamming, Blackman, Von Han, Exact Blackman and of course the rectangular window for which all spectral components are weighted equally. The typical form of a spectrum

input time series samples (e.g., 16, 32, 64, 128, ...), we use the fast Fourier transform

Sk+ |DFT

{

msm

}

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window is shown in the figure below which illustrates how the edge points of the time series are de–emphasized and the center points are over emphasized. The dashed line would correspond to the rectangular window. Note that the “gain” of the window is set to preserve the total power.

Weight

Time/Sample Index

Rectangular

Figure 5–4: Typical form of a time series window

Even though the window gain can be adjusted to conserve the total power, there is an effective reduction in the number of samples which increases the variance (or uncertainty) of the moment estimates. For example the variance of the total power is greater when computed from a spectrum with Blackman weighting as compared to using a rectangular window. This is because there are effectively fewer samples because of the de-emphasis of the end points. This is a negative side to using a window.

The DFT of the window itself is known as its impulse response which shows all of the frequencies that are generated by the window itself. A generic example is shown in Figure 5–5 below which illustrates that these “side lobe” frequencies can have substantial power. This is not a problem for weather signals alone, but if there is strong clutter mixed in, then the side lobe power from the clutter can obscure the weaker weather signals. The rectangular window has the worst sidelobes, but the narrowest window width. However, the rectangular window provides the

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lowest variance estimates of the moment parameters (in the absence of clutter. More “aggressive” windows have lower side lobe power at the expense of a broader impulse response and an increased variance of the moment estimates.

Window Width

Side Lobes

Power

ĆM/2

Frequency

M/20

Figure 5–5: Impulse response of a typical window

So in summary of the DFT approach and spectrum windows:

S When the clutter is strong, an aggressive spectrum window is required to contain the

clutter power so that the side lobes of the window do not mask the weather targets. The side lobe levels of some common windows are:

Rectangular 12 dB Hamming 40 dB Blackman 55 dB

S More aggressive windows typically have a wider impulse response. This effectively

increases the spectrum width. Rectangular is narrow, Hamming intermediate and Blackman the widest.

S Windows effectively reduce the number of samples resulting in higher variance moment

estimates. Rectangular is the best case, Hamming is intermediate and Blackman provides the highest variance moment estimates.

These facts suggest the best approach is to use the least aggressive window possible in order to contain the clutter power that is actually present- i.e., an adaptive approach is the best.

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