NCAR/TN-331+STR NCAR TECHNICAL NOTE

i I -

May

1989

Signal Processing for Atmospheric Radars

R. Jeffrey Keeler Richard E. Passarelli

ATMOSPHERIC TECHNOLOGY DIVISION NATIONAL

CENTER FOR ATMOSPHERIC RESEARCH BOULDER, COLORADO

TBSIE OF COTENTS

TABLE OF CONTENTS .....................

.

iii

LIST OF FIGURES ......................... LIST OF TABLES ................... PREFACE.

..

v .

..

.vii

..

i.......................

1.

Purpose and scope .................

2. 2.1 2.1.1 2.1.2 2.1.3 2.1.4 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6

General characteristics of atmospheric radars. Characteristics of processing .......... Sampling ................... Noise ...... ............... Scattering ............... Signal to noise ratio (SNR) .......... Types of atmospheric radars .......... Microwave radars . ........... ST/MST radars or wind profilers ....... FM-CW radars .. .............. Mobile radars ............ .. Lidar ............ ....... Acoustic sounders . ..........

3 3 3 4 5 6 6 7 8 8 9 10 11

3. 3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3 3.3.1 3.3.2 3.3.3

Doppler power spectrum moment estimation . .... General features of the Doppler power spectrum. Frequency domain spectral moment estimation . Fast Fourier transform techniques . .... Maximum entropy techniques .......... Maximum likelihood techniques . ....... Classical spectral moment computation ..... Time domain spectral moment estimation. ..... Geometric interpretations ........... "Pulse pair" estimators ........... Circular spectral moment computation for

13 14 18 18 20 23 25 27 27 28

3.3.4 3.4 3.4.1 3.4.2 3.4.3 4. 4.1 4.1.1 4.1.2 4.1.3 4.2 4.2.1

1

sampled data. . ............. Poly pulse pair techniques ..... Uncertainties in spectrum moment estimators . Reflectivity. ... ............ Velocity. . . ..... . ...... Velocity spectrum width ...........

31 33 .

Signal processing to eliminate bias and artifacts. Doppler techniques for ground clutter suppression Antenna and analog signal considerations. ... Frequency domain filtering. ......... Time domain filtering ............. Range/velocity ambiguity resolution ....... Resolution of velocity ambiguities ...... iii

35 35 36 37 43 43 44 45 46 50 51

4.2.2 4.3

Resolution of range ambiguities ....... Polarization switching consequences .......

55 56

5. 5.1 5.1.1 5.1.2 5.1.3 5.1.4 5.2 5.2.1 5.2.2 5.3 5.4

Exploratory signal processing techniques . .... Pulse compression .... .......... Advantages of pulse compression . ...... Disadvantages of pulse compression. ...... Ambiguity function. .. Comparison with multiple frequency scheme . Adaptive filtering algorithms ......... Adaptive filtering applications ....... Adaptive antenna applications .. ..... Multi-channel processing. ............ A priori information. .............

57 57 58 59 61 63 63 64 68 69 70

6. 6.1 6.2 6.3 6.4

Signal processor implementation ......... Signal processing control functions ..... Signal Z?D conversion and calibration ...... Reflectivity processing ... .......... Thresholding for data quality .........

71 71 74 76 78

7. 7.1 7.1.1 7.1.2 7.1.3 7.1.4 7.2 7.3 7.3.1 7.3.2 7.3.3 7.3.4 7.3.5 7.3.6 7.4 7.4.1 7.4.2 7.4.3 7.4.4 7.4.5

Trends in signal processing. ............ Realization factors ............... Digital signal processor chips ....... Storage media ................. Display technology . .............. Commercial radar processors .......... Trends in programmability of DSP. ........ Short term expectations .......... .... Range/velocity ambiguities ......... Ground clutter filtering .......... Waveforms for fast scanning radars ...... Data compression. ............. Artificial intelligence based feature extraction Real time 3D weather image processing .. ... Long term expectations . ............ Advanced hardware ....... .. Optical interconnects and processing ..... Communications . . . . . . . . . . . . . . . . Electronically scanned array antennas ..... Adaptive systems ...............

81 81 81 82 83 83 84 85 85 86 86 87 87 87 87 88 88 88 88 89

8. 8.1 8.2 8.3 8.4

Conclusions. . ................... Assessment of our past. ............. Recommendations for our future . ........ Acceptance of new techniques ........... Acknowledgements. ..............

91 91 92 93 93

ACRONYM LIST ........................... BIBLIOGRAPHY .......

95

...........

....

iv

.

.

97

TIST OF FJIGRES

Fig 3.1

of Doppler power spectrum (128 point periodogram) Estimated typical weather echo in white noise. parameters are velocity ~ 0.4 Vax velocity spectrum 10 dB. width ~ .04 Vmax, and SNR

15

Fig 3.2

of the complex representation dimensional Three Radius of helix autocorrelation function as a helix. Ps; proportional to total signal power, Rs(0) is rotation rate of helix is proportional to velocity, V; width of envelope is inversely proportional to velocity Delta function Rn(0) represents spectrum width, W. noise power.

29

Fig 3.3

Periodogram power spectrum plotted on unit circle in the Note velocity aliasing point, the Nyquist z-plane. velocity, at z=-l.

32

Fig 3.4

Comparison of classical and circular (pulse pair) first Classical estimate is determined by moment estimators. linear weighting of spectrum estimate and circular estimate, by sinusoidal weighting.

34

Fig 3.5

Velocity error as function of spectrum width and SNR. normalized to Nyquist interval, Spectrum width is M is number of sample pairs and vn=W/2Vmx=2WTs/X. error is normalized to Nyquist velocity interval, 2va = Small circles represent simulation values 2Vmax. (Doviak and Zrnic, 1984).

39

Fig 3.6

Width error as a function of spectrum width and SNR. normalized to Nyquist interval, Spectrum width is

42

vn=W/2Vmax=2Wrs/X.

M

is

number of sample pairs

and

error is normalized to Nyquist interval, 2Vmax. Small circles represent simulation values (Doviak and Zrnic, 1984). Fig 4.la

Clutter filter frequency response for a 3 pole infinite For impulse response (IIR) high pass elliptic filter. 1 5 rpm and scan rate of ground clutter width of 0.6 ms stop this filter gives about 40 dB suppression. V = 16 ms - (Hamidi band. Vp = pass band cutoff, Vmax = and Zrnic, 1981).

47

Fig 4.lb

Implementation of 3rd order IIR clutter suppression filter; z- 1 is 1 PRT delay. K1 - K4 are filter coefficients (Hamidi and Zrnic, 1981).

48

v

Fig 5.1

Ambiguity diagram for single FM chirped pulse waveform with TB=10. T is range dimension. 0 is velocity dimension. Targets distributed in (r,q) space contribute to the filter output proportional to the ambiguity function. For atmospheric targets, Doppler shift frequencies are typically very small relative to pulse bandwidth (Rihaczek, 1969).

62

Fig 5.2

Prediction error surface for 2 weight adaptive filter. The LMS algorithm estimates the negative gradient of the quadratic error and steps toward the minimum mean square error (mse). The optimum weight vector is W* = (0.65, -2.10). If the input statistics change so that the error surface varies with time, the adaptive weights will track this change (Widrow and Stearns, 1985).

65

Fig 5.3

Adaptive filter structure. The desired response (dk) is determined by the application. The adaptive filter. coefficients (Wk) and/or the output signal (Yk) are the parameters used for spectrum moment estimation (Widrow and Stearns, 1985).

66

Fig 6.1

Block diagram of a typical signal processor.

26

vi

LSTr OF TAHBI Table 1

Comparison of remote sensor sampling schemes and rates.

Table 2

Characteristics of several popular windows when applied to time series data analysis (Marple, 1987).

20

Table 3

Expressions for variance of velocity estimators at high SNR. Assumes Gaussian spectra in white noise, low normalized velocity width (Wn=W/2Vmx) and large M. Expressions apply to both pulse pair and Fourier transform estimators.

38

Table 4

Expressions for variance of width estimators at high SNR. Assumes Gaussian spectra in white noise, low normalized velocity width (Wn=W/2Vmax) and large M. Expressions apply to both pulse pair and Fourier transform estimators.

41

vii

7

PiRFACE

This review of signal processing for atmospheric radars was originally written as Chapter 20 of the book Radar in Meteorology, edited by Dave Atlas (1989) for the Proceedings of the 40th Anniversary and Louis Battan Memorial Radar Meteorology Conference. overview

of

signal

processing

We have attempted to give the reader an techniques

and

the

technology

that

are

applicable to the atmospheric remote sensing tools of weather radar, lidar, ST/MST radars and wind profilers.

This NCAR Technical Note includes the signal processing

relevant references in a single document.

chapter and the

The text has had minor editing

and the references have been slightly expanded over the version published in Radar in Meteorology.

We hope that this Technical Note will assist the many individuals who want a

better understanding of signal processing to achieve that goal.

R. Jeffrey Keeler

Richard E. Passarelli

March 1989

ix

1.

PURPOSE AND SODFE

Signal processing is perhaps the area of atmospheric remote sensing where science and engineering make their point of closest contact. Signal processing offers challenges to engineers who enjoy developing state-of-theart systems and to scientists who enjoy being at the crest of the wave in

observing atmospheric phenomena in unique ways. The primary function of radar signal processing is the accurate, efficient

extraction of information from radar echoes.

A typical pulsed Doppler radar

system samples data at 1000 range bins at 1 kilohertz pulse repetition

frequency

(PRF), generating approximately 3 million samples per second

(typically in-phase (I) and quadrature phase (Q) components from a linear channel and often a log receiver). These "time series", in their raw form, convey little information that is of direct use in determining the state of

the atmosphere.

The volume of time series data is sufficiently large that

storage for later analysis is impractical except for limited regions of time

and space.

The data must be processed in real time to reduce its volume and to convert it to more useful form. In this paper the current state of signal processing for atmospheric radars (weather radars, ST/MST radars or wind profilers, and lidars) shall be discussed along with how signal processing is currently optimized for various applications and remote sensors. The focus shall be on signal processing for weather radar systems but the techniques and conclusions apply equally well to ST/MST radars and lidars. Zrnic (1979a) has given an excellent review of spectral moment estimation for weather radars and Woodman (1985) has done the same for MST radars. Problem areas and promising avenues for future research shall be identified. Finally, we shall discuss the scientific and technological forces that are likely to shape the future of atmospheric radar signal processing. We will differentiate between "signal processing" (the topic of this review) and "data processing" in the following way. "Signal processing" is that set 1

of operations performed on the analog or digital signals for efficiently extracting desired information or measuring some attribute of the signal. For atmospheric radars this information is often referred to as the "base parameter estimates". Fundamental base parameters are: Radar reflectivity factor

Z

dBZ

Radial velocity Velocity spectrum width1

V W

ms- 1 ms-l

In the course of extracting these estimates, signal processing algorithms will improve the signal to noise ratio (SNR) through filtering or averaging,

mitigate the effects of interfering echoes such as ground clutter, remove ambiguities such as range or velocity aliasing, and reduce the input data The end result of an effective signal rate by a significant factor. processing scheme is to provide minimum mean squared error estimates of the base parameters along with the expected error or a measure of the degree of

confidence that can be placed on the estimates (e.g., the SNR). Note that signal processing is primarily used in atmospheric remote sensing as an estimation procedure as well as a detection process as in some aviation applications. The emphasis is on making estimates of atmospheric parameters or meteorological events. "Data processing", on the other hand, takes up where signal processing leaves off -- although the line of demarcation is not razor sharp. Data processing algorithms take the base parameter estimates and further process

them so that they convey information that is of direct use to the radar For example, data processing techniques imply display generation, user. data navigation to a desired coordinate system, wind profile analyses, data syntheses from several Doppler radars or other sensors, applying physical constraints to the measured data, and forecasts or "nowcasts" of severe weather hazards. Many aspects of data processing are covered in other chapters.

1 The width is defined as the square root of the second central moment of the spectral power distribution. 2

2.

There are two main

classes of

Electromagnetic radars systems.

CIRACJERSLR'LCS OF AICMY4SERIC RADARS

GENRA

"radar"

--

electromagnetic

and acoustic.

include microwave, UHF, VHF, infrared and optical

Acoustic radars

The signal

are only briefly described here.

processing techniques employed for all these systems are similar (Serafin and Strauch, 1978).

2.1

ClARACTERISTICS OF IRDCESSING are nearly identical

Although the processing techniques atmospheric

radars,

the

way

in

which

this

for the various

backscattered

or

partially

reflected radiation is sampled, the principle noise sources, and the nature of the scattering mechanisms are different.

2.1.1 Sampling Because electromagnetic less than 1 im, constraints

radars employ wavelengths

from several

meters

to

they must use different sampling techniques. There are two (Ts)

on the sample time spacing

of the backscattered signal.

The first is that the backscattered signal should be coherent from sampleto-sample, i.e., the motion among the scatterers should be small compared to the wavelength so that their relative positions produce highly correlated echoes from sample-to-sample.

The nominal duration of this correlation is

called the coherence time (Nathanson, 1969), i.e.,

T s < tcoh =

(2.1)

/4rW

where the true velocity spectrum width W in ms-1 is a direct measure of the The coherence time is a measure of the

relative motions of the scatterers.

maximum time between successive samples for coherent phase measurements. Thus, signal

for

short wavelength systems,

must be

sampled much more

microwave system.

such as

a

rapidly than

lidar, the backscattered for a

longer wavelength

The autocorrelation function (defined later) can provide

a direct measure of the coherence time of a fluctuating target echo.

3

The second constraint on sampling is that for regularly spaced pulses, the sampling frequency must be at least twice the maximum desired Doppler shift

frequency which reduces the occurrence of velocity aliasing.

In this case

the time between samples is governed by,

Ts < tNyq =

(2.2)

4V'

where tNyq is the minimum time between samples such that the desired velocity V' is at least the so-called Nyquist velocity. Since V' is typically much larger than W, the latter constraint usually dominates the sampling requirement. + 25 ms-1 , then T s

In fact, if we assume the desired maximum velocity is

V/100 or PRF = 100/ \ is a useful rule of thumb.

2.1.2 Noise One of the goals of signal processing is to suppress the effects of noise.

The main source of noise in microwave radar is thermal in nature. This noise power is simply

Pn = k Tsys Bsys

(2.3)

where k is Boltzman's constant (1.38 x 10-23 W/Hz/°K), Tsys is the total

system temperature, and Bsys is the total system bandwidth including effects of preselector filters, IF filters, and all other amplifiers in the signal path

(Skolnik, 1970, 1980;

Paczowski and Whelehan, 1988).

With recent

improvements in low noise amplifiers (INA's), little room is left for sensitivity improvement in conventional radar receivers. Presently, most microwave radar systems are sufficiently sensitive that thermal radiation from the earth makes a strong contribution to the receiver input at low elevation angles. ST/MST radar noise, because of its lower frequency, has a large contribution

from environmental,

cosmic and atmospheric

sources,

and

is not easily

quantified (Rottger and Larsen, Chap 21A). Therefore, antenna design and the specific radar location and frequency band of operation define the system noise. 4

Coherent lidar systems utilize detection schemes using optical heterodyning

onto cryogenic detectors with a local oscillator laser having relatively high power mixing with the weak atmospheric return (Jelalian, 1980, 1981a,b). Because of the small wavelengths, quantum effects dominate the detection process associated with random photon arrivals impacting the LD laser. This "shot noise" contribution is a fundamental physical limitation of lidar sensitivity. 2.1.3 Scattering

Atmospheric radars respond to a variety of scattering targets-precipitation, cloud particles, aerosols, refractive index variations, chaff, insects, birds, and ground targets.

Probert-Jones (1962) derived the

familiar radar equation most often used by radar meteorologists for precipitation scattering. A detailed derivation can be found in Doviak and Zrnic (1984), Battan (1973), or Atlas (1964). The received power is Pt G2 02 cTr

3

1k12

Ze L

(2.4)

Pr=

1024 ln2 X 2 R 2 This equation includes L, the product of several small but significant loss terms which are necessary to accurately estimate radar reflectivity factor,

e.g. receiver filter loss, propagation loss, blockage loss, and processing bias. Zric (1978) defines the receiver filter loss as that portion of the input signal frequencies not passed by the finite receiver bandwidth, typically 1-3 dB. The other losses depend on atmospheric conditions and antenna pointing and are enumerated in Skolnik (1980). This equation is correct for Rayleigh scattering of a distributed target that completely fills the resolution volume. Non-Rayleigh targets or partially filled resolution volumes will give received power estimates that cannot accurately

be related to precipitation rate.

Rottger and Larsen (Chap. 21A) and

Huffaker, et al. (1976, 1984) give similar received power expressions for

returns from refractive index variations and from lidar aerosol returns, respectively.

5

required

The

dynamic

range

for

measuring the

backscattered power from

atmospheric targets is very large because:

The effective backscatter cross-sections of atmospheric scatterers span

1.

dynamic ranges of approximately 60 dB for precipitation but much larger if cloud particle, "clear air", and ground target returns are included.

The R

2.

2

dependence of the received power for distributed targets spans

a range of 50 dB between 1 and 300 km.

Microwave

systems

should accommodate the

sum of these

two effects

and

typically can achieve a dynamic range of order 100 dB for power measurements using either a log receiver,

linear receiver with AGC,

or some combination

of these.

2.1.4

Signal to noise ratio (SNR)

The ratio

of the received

signal

power

to the measured

noise power

is

defined to be the signal to noise ratio (SNR):

(2.5)

SNR = Pr/Pn

The SNR is extremely important for analyzing tradeoffs in signal processing. It

is

a key term along with spectrum width and integration time in

analytic

evaluation of spectrum moment errors.

2.2

YPES OF AM[SHFERIC RAIDRS

A summary of the characteristics of the different types of electromagnetic radars in use today for atmospheric research is discussed below. assembles these differences.

6

Table 1

Table 1 Remote Sensor Sampling Comparison

Sensor

Pulse Beamwidth Duration (deg) (~sec)

Wavelength Scatterers

Radar S-band Ka-band mm-band

10cm 1 cm 1 mm

Precipitation Precipitation Cloud

ST/MST (profilers) UHF 75 cm Refractive VHF 6 m index

0.5-3 0.5-2 0.2-1

3-10 3-10

Sample Rate (Hz)

0.25-4 0.25-1 0.25-1

103 104 105

0.2-5 0.2-5

104->102 103->10

Lidar IR Optical

2.2.1

10 gmi