Pulse Coherent Doppler Processing and the ADV Correlation Coefficient

Transcription

1 SonTek Technical Notes 6837 Nancy Ridge Drive, Suite A San Diego, CA 911 Telephone (619) Fax (619) Internet: inquiry@sontek.com Pulse Coherent Doppler Processing and the ADV Correlation Coefficient The information presented in this document applies to all SonTek Acoustic Doppler Velocimeter systems: the 10 MHz ADV, the 5 MHz ADVOcean, and the 16 MHz MicroADV. Each of these systems use the same signal processing algorithms and record the same type of data; they differ primarily in the acoustic frequency used and the mechanical packaging of the instrument. Throughout this document, they are referred to collectively as the ADV. With each sample, the ADV records nine values: three velocity components, signal strength for each of three receivers, and correlation coefficient for each of three receivers. Naturally, velocity data are of primary interest; the other data are used primarily as data quality parameters. Signal strength is a measure of the strength of the return reflection from the water; it can be accessed as signal amplitude in internal logarithmic units called counts (1 count = 0.43 db) or as signal to noise ratio (SNR) in db. Correlation coefficient is a quality parameter that is a direct output of the Doppler velocity calculations. Correlation is expressed as a percentage: perfect correlation of 100% indicates reliable, low noise velocity measurements; 0% correlation indicates that output data is dominated by noise with no coherent signal used for velocity calculations. Correlation is used to monitor data quality during collection, and to edit data in post processing. Ideally, correlation should be between 70 and 100%. Values below 70% indicate that the ADV is operating in a difficult measurement regime, the probe is out of the water, the SNR is too low, or that something may be wrong with the ADV. In some environments (highly turbulent flow, aerated water), it may not be possible to achieve high correlation values. Low correlation values affect the short term variability of velocity data, but do not bias mean velocity measurement. For mean velocity measurements, correlation values as low as 30% can be used. The above description provides general guidelines when using the correlation data as a quality parameter. To understand the exact meaning of the correlation coefficient, and all factors affecting it, requires a detailed discussion of ADV Doppler processing. An introduction is provided in this document; additional references are provided at the end. Pulse Coherent Doppler Processing The ADV measures velocity using a technique called pulse coherent Doppler processing. The system sends two short acoustic pulses and samples the return signal from each pulse as it passes through the sampling volume. Pulse coherent Doppler estimates velocity by measuring the change in phase of the return signal from two acoustic pulses. To illustrate this, consider the simplified case of a transmit/receive acoustic transducer and a single acoustic target moving with speed U relative to the transducer (see figure 1). Pulse Coherent Doppler Processing and the ADV Correlation Coefficient (November 1997) 1

2 At time T = 0, the transducer sends a short pulse. It samples the return signal at time T = dt, corresponding to the reflection of the pulse from the sampling volume. The system measures the phase of the return signal, φ 1. This phase is a function of the location X 1 of the acoustic target. At some time later T = T 1, the transducer sends a second pulse, identical to the first. It samples the return from this pulse at time T = T 1 + dt, corresponding to the return signal of the second pulse from the sampling volume. The phase return from the second pulse is a function of the new location X Figure 1 Pulse Coherent Doppler Measurements of the acoustic target. The speed of the target during the time between the two pulses is determined from the measured phases by the following relation. U = (X - X 1 ) / T 1 = λ (φ - φ 1 ) / (4 π T 1 ) When measuring water velocity, the acoustic return is not the reflection from a single target but the superposition of the reflections from the many individual particles. These acoustic scatterers are contained in the ADV sampling volume which is defined by the beam geometry, the transmit pulse length, and the receive window. If all scatterers maintain their relative positions with respect to each other, so that the strength and relative phases of the individual reflections do not change from one pulse to the next, they maintain what is called phase coherency. In this case, the single reflector analogy applies, and the velocity of the scatterers can be estimated from the phase measurements. In general, phase coherency is only partially maintained between the two pulses. The return signal from the second pulse is not just a phase shifted replica of first return, but contains a certain amount of random noise. This can be thought of as noise added to the coherent return signal of each pulse. S 1 ' = S 1 + N 1 S ' = S + N Here S 1 ' and S ' are the return signals from the two pulses, S 1 and S are the coherent portion of the signal, and N 1 and N are the random noise added to each signal. The effect of this noise is to add a random error to the measured phases, and hence to the measured velocities. A measure of this noise is the ratio of the coherent signal power to the total power, which can be expressed by the following relation. Pulse Coherent Doppler Processing and the ADV Correlation Coefficient (November 1997)

3 S i / (S i + N i ). This ratio is the ADV correlation coefficient. For signals with perfect phase coherence, the noise term is zero and the correlation coefficient is 1 (100%). If the noise is much greater than the coherent signal, the correlation coefficient approaches 0. The value of the correlation coefficient is a direct measure of the random errors (Doppler noise) of the velocity data. In practice, the ADV measures the phase change by comparing the return signals from each pulse using a complex auto-correlation function. The phase of the complex auto-correlation gives the phase change of the return signal and hence the velocity, while the normalized magnitude gives the correlation coefficient. The auto-correlation routine performs the analogous function in the time domain that a Fourier transform performs in the frequency domain. The noise in ADV phase measurements is caused by a number of factors, the most important of which are discussed below. When discussing noise in velocity measurements, we measure the noise level by the standard deviation of velocity measurements. Electronics Noise (SNR) Figure illustrates the effect of electronics noise on the accuracy of Doppler velocity measurements. The noise effect is determined by the ratio of the strength of the return signal from the water to the ambient electronics noise level (signal to noise ratio or SNR). The ADV calculates SNR by comparing return signal strength from the acoustic pulse to signal strength when no pulse has been sent. Figure plots the Doppler noise scaling factor versus SNR. As SNR decreases below 5 db, the noise in individual measurements increases by Noise Scaling Factor Doppler Noise Variation with SNR SNR (db) Figure Doppler Noise vs. SNR more than a factor of 0. For SNR values greater than 0 db, electronics noise has essentially no impact on velocity measurements as the scale factor asymptotically approaches 1. For ADV operation, when possible we recommend maintaining a SNR of at least 15 db for highresolution velocity measurements (i.e. sampling at 5 Hz). For mean current measurements (i.e. sampling at 1.0 Hz), a SNR of as little as 5 db can be used. When operating in very clear water, seeding material can be used to increase the SNR. Residence Time During the time between the two pulses, some particles will have moved out of the sampling volume while new particles will have been introduced. The new particles contribute a phase signal completely unrelated (un-correlated) to the phase of the other particles. Hence the phase coherence between the two pulses will decrease over a residence time of order (d / U), where d is Pulse Coherent Doppler Processing and the ADV Correlation Coefficient (November 1997) 3

4 the typical size of the sampling volume and U is the velocity of the particles. If the residence time is large with respect to the pulse lag (the time between two pulses), it will have little effect on velocity measurements. If the residence time is of a similar magnitude to the pulse lag, the de-correlation can have a significant impact on velocity data. Sampling Volume Turbulence Turbulent eddies with spatial scales on the order of the sampling volume size or smaller cause the scatterers within the sampling volume to have a distribution of velocities. In this environment, the particles within the sampling volume will not have the same relative positions for the two pulses. Thus the phase change measured by the ADV (which is the sum of the return from all particles) will have noise associated with the changing relative locations. The extent to which the relative positions of particles in the sampling volume changes decreases the correlation between the two pulses, and increases noise in velocity measurements. Beam Divergence Beam divergence results from the fact that the ADV measures the projection of the water velocity onto the bistatic axis of the acoustic beams. Depending upon the physical location of the scatterers within the sampling volume, the angle between the 3D water velocity and the propagation direction of the pulse will change slightly (since the pulse spreads spherically with distance from the transducer). This change in beam angle causes a distribution of velocities across the sampling volume. This is analogous to the broadening of the velocity distribution caused by turbulence, except that the diversity is caused by changes in the beam angle. Like turbulence effects, the broadening of the velocity distribution caused by beam divergence contributes to de-correlation and increased noise in velocity measurements. Estimating Noise Levels The last three items discussed above (residence time, turbulence, and beam divergence) contribute to an increased distribution of measured velocities. In the frequency domain, this appears at the broadening of the spectrum of the return signal. The width of the spectral peak is known as the Doppler bandwidth (B), and is a fundamental parameter for estimating the noise in Doppler velocity measurements. Brumley et al (1987, unpublished) estimated the contribution of each effect to total Doppler bandwidth. Residence Time: B r = 0. U / d Turbulence: B t =.4 (ε d) (1/3) / λ Beam Divergence: B d = 0.84 sin(ω) U c / λ Doppler Bandwidth: B = B r + B t + B d Where: U = Relative velocity of scatterers d = Half-power sampling volume width ε = Turbulent energy dissipation rate λ = Acoustic wavelength ω = Two-way, half-power beam width U c = Cross-beam velocity component Pulse Coherent Doppler Processing and the ADV Correlation Coefficient (November 1997) 4

5 Estimating Doppler noise for a pulse coherent system is a complicated function including pulse spacing (the time between successive pulses), Doppler bandwidth, and signal to noise ratio. These predictions are accurate only for idealized Doppler systems with continuous sampling of the return signal and infinite resolution. For practical systems, they provide at best a lower bound for instrument noise level. The most important consideration for detailed analysis of ADV data is that noise in velocity data is proportional to the Doppler bandwidth B. Low correlation values are an indication of increased Doppler bandwidth, and hence increased noise levels in the data. References Although there are many papers on the subject of Doppler processing, we do not know of any that deal specifically with the subject of pulse coherent Doppler processing and the correlation coefficient in the context of acoustic Doppler systems. The list below gives a few papers related to this subject. R. Cabrera, K. Deines, B. Brumley, and E. Terray, Development of a practical coherent acoustic Doppler current profiler, Proc. of the IEEE Fourth Working Conference on Current Measurement, Institute of Electrical and Electronics Engineers, New York City, pp , R. Lhermitte and R. Serafin, Pulse-to-pulse coherent Doppler sonar signal processing techniques, J. Atmos. and Ocean. Tech., Vol. 1, No. 4, pp , K.S. Miller and M.M. Rochwarger, A covariance approach to spectral moment estimation, IEEE Trans. on Info. Theory, Vol. IT-18, No. 5, pp , 197. L. Zedel, A.E. Hay, R. Cabrera, and A. Lohrmann, Performance of a single beam, pulse-topulse coherent Doppler profiler, IEEE Journal of Oceanic Engineering, No. 1, pp , D.S. Zrnic, Spectral moment estimates from correlated pulse pairs, IEEE Trans. on Aerosp. and Electron. Systems, Vol. AES-13, pp , Pulse Coherent Doppler Processing and the ADV Correlation Coefficient (November 1997) 5