Design Trade-offs in a Code Division Multiplexing Multiping Multibeam Echo-Sounder B. O Donnell B. R. Calder Abstract Increasing the ping rate in a Multibeam Echo-Sounder (mbes) nominally increases the along-track sounding density. Existing multiping mbes use Frequency Division Multiplexing (fdm) to resolve ambiguous ranges; an alternate method that potentially avoids increasing (or sub-dividing) system bandwidth is Code Division Multiplexing (cdm). A cdm mbes would transmit even if an echo was being received and would resolve range ambiguities through the properties of the transmitted signal shapes. This theoretically allows higher ping rates, but requires us to consider receiver blanking (i.e., the need to temporarily stop recording to transmit), which can reduce the total sounding density and hence the advantage of the scheme. This problem may be partly alleviated through active ping timing control, jittering transmit times so that receiver blanking occurs preferentially during non-specular echoes. Then, a detec- Center for Coastal and Ocean Mapping and noaa-unh Joint Hydrographic Center, University of New Hampshire. Address: Chase Ocean Engineering Lab, 24 Colovos Road, Durham NH 03824. E-Mail: briano@ccom.unh.edu. Phone: +1-603-862-0564. E-Mail: brc@ccom.unh.edu. Phone: +1-603-862-0526. Address and affiliation as above. tion might still be possible, albeit with a potentially increased uncertainty. This paper addresses trade-offs in a potential cdm mbes design. We consider here the implications of a cdm scheme on increased sounding density, losses due to receiver blanking, recovery of soundings with better processing (and potentially increased uncertainty), and the computational complexity implied by the processing scheme, with the goal of assessing the potential benefits, and limitations, of such a design. 1 Background and Assumptions Multibeam Echo-Sounder (mbes) sonars have been used since the 1970s to create high resolution maps of the seafloor. Since then there have been a number of improvements leading to increases in across-track and along-track sounding density [1]. Larger receive arrays with their smaller across-track beamwidths, in addition to more sophisticated signal processing has increased and uniformly distributed across-track sounding density, while dual ping modes have increased the along-track sounding density. Existing dual ping modes use Frequency Division 1
Multiplexing (fdm) to differentiate between pings. Two pings are transmitted in rapid succession, one the echo from a previous ping is received, and thus the receivers would need to be periodically shut off when down towards nadir, the other steered forward in the the mbes transmits. along-track direction, resulting in interleaved swaths from pings in the two separate frequency bands. Some mbes are configured to transmit in different sectors to compensate for vessel motion or for multiple bounce echoes. Each of the sectors, for each of the two pings is assigned its own frequency band further subdividing limited bandwidth causing a loss of range resolution in each sector. Piezoelectric transducer arrays are already being used at their maximum practical bandwidths of 10-20% of the center frequency. Increasing the bandwidth will add cost and reduce source levels; thus there is no easy way to extend these dual ping fdm mbes into transmitting at three or four times their base rate. The subsequent sections in this paper discuss the consequences of the increased ping rate and receiver blanking, as well as the justification for specific system design choices that should result in an along-track sounding density that increases linearly with ping rate, and the likelihood of missing small objects objects on the seafloor when periodically blanking the receivers. The increased ping rate intentionally causes range ambiguities which are resolved by time-frequency coding the transmitted pings from a precomputed code dictionary. In a fdm mbes the pings are separated through time-domain frequency filtering. The frequency bands for each ping are distinct enough to separate two different pings, even when they arrive at the same time. In a cdm mbes signals occupy the same bandwidth and thus time-domain frequency filtering cannot be used. While some cdm implementations used in radar and communications can separate signals that overlap in both frequency and duration [2], these signals have a much larger time-bandwidth product than the signals that would be used in a cdm mbes. In a sonar system therefore in order for the pings to be separated they must not overlap in time. Increasing the duration would be be deleterious to minimizing the effects of receiver blanking, and just as in a fdm mbes the total usable bandwidth is limited. Echoes in the outer beams are typically the longest in duration, and are the first to overlap as the ping 2 Increased Ping Rate A Code Division Multiplexing (cdm) mbes design presented in this paper sidesteps the bandwidth limitations that occur when increasing the ping rate in a fdm mbes by deviating from some mbes design assumptions. A cdm mbes would ping rapidly at approximately periodic intervals, even before the entirety of rate is increased. The echo durations mostly depend on the along-track and across-track beamwidths, and so these array parameters are the major limiters of the maximum ping rate. A model of the echo duration has been developed that uses the minimum and maximum ray paths in each receive beam, based on the test tank derived beamwidths for a modern mbes operating at 400 khz. The model has been validated 2
Across-Track Along-Track Maximum Beamwidth Beamwidth Ping Rate 0.5 1.0 7 1.0 2.0 5 1.5 3.0 3 Table 1: Predicted maximum ping rate. The maximum ping rate is limited by the along-track and across-track beamwidths than 3.0 are practical for use in a cdm mbes, where beamwidths in the 0.5 to 1.0 range are best suited Figure 1: An increased ping rate causes the echoes to be closely spaced in time. The horizontal boxes spanning all angles-of-arrival (which appear to be lines because of their short duration), are the times when the receivers are blanked to transmit subsequent pings. using echo durations seen in water column data collected using the same type of mbes, and the results from this model have been extended to determine the upper limit on ping rates for a range of commonly occurring beamwidths. Figures 1 shows the simulated echo duration results with an across-track beamwidth of 0.5 and an alongtrack beamwidth of 1.0, operating at 400 khz and a 7x ping rate, where the baseline 1x ping rate is the time it would take to receive the entire echo out to a pointing angle of 60 on a flat seafloor. Increasing the ping rate causes the echoes to be spaced closer in time, so the ping rate can not be increased indefinitely without causing echoes in the outer beams to overlap. Results from the echo duration simulation are presented in Table 1 where the maximum ping rate is estimated for the minimum inter-ping period that avoids for increasing the maximum ping rate. Note that the maximum ping rate is independent of seafloor depth as the echo duration increases with depth in proportion with the arrival time of each subsequent ping at the receiver array. Additionally, the maximum ping rates are based only on the echo overlap, and do not take into account tuning to compensate for receiver blanking. 3 Effects of Receiver Blanking One of the major challenges in designing a cdm mbes is how to compensate for receiver blanking. Depending on ping rate, the blanking can occur across a number of angular intervals in a single echo, some of which are during the near nadir echo, and others are during larger angles-of-arrival. In the specific example of Figure 1, for example, blanking occurs when echoes are being received from angles around 5, 42 and 55. The effects that receiver blanking has on the echo time-of-arrival estimates vary with angle; Figures 2 and 3 are centered around 5 and 55, and show that blanking during near specular angles-of-arrival results outer beam signal overlap in time. Beamwidths less in most of the echo being missed, while blanking at 3
Figure 2: Receiver blanking around 5. Blanking during specular echoes results in a larger percentage of the echo being missed, which makes it difficult to recover any information about the time-of-arrival. larger angles-of-arrival results in a smaller portion of the echo being missed. When near nadir echoes are blanked, it is difficult to infer what echo might, or might not, have been received during the blanking. While the presence of the remaining echo might be used to constrain the depth range over which the seafloor could exist, computing this is not straightforward and is likely to be computationally intensive. For this reason, we would prefer to avoid blanking during specular reflections if possible, accepting the limitations on an increase in ping rate that this implies, and a potential increase in ping timing complexity (Section 4) to minimize this effect. When receiver blanking occurs during non-specular echoes, the blanking is a much smaller portion of the echo. Here, the time-of-arrival is generally computed from the phase signal derived from a split aperture correlation [3]. In the simplest case, the signal is often modeled as a low order polynomial (generally first Figure 3: Receiver blanking around 55. Blanking during non-specular echoes results in a smaller percentage of the echo being missed, which leaves more intact signal on which a time-of-arrival could still potentially be estimated. or second order), and the zero-crossing of the polynomial is used to determine the time-of-arrival using a Least Squares (ls) estimate. Missing data in the correlator output due to blanking would modify this process, most likely by reducing slightly the signalto-noise ratio of the solution, leading to potentially increased uncertainty in the estimated time-of-arrival, but an estimate could still be formed. In more modern mbes the phase signals in non-specular echoes are processed interferometrically, and multiple estimates of the seafloor s location are made in each beam. Blanking would prevent only a minority of these estimates from being made. 4 Transmit Time Jittering Blanking occurs at angles-of-arrival determined by the depth and the ping rate. Thus, the ping rate can be tuned to cause receiver blanking at larger angles-of- 4
blanking out over a range of across-track distances. This can be achieved by varying the actual transmit times for each ping about the nominal ping period required to support the desired ping rate. The transmit times are found according to the equation T (n) = nt + δ t (n) (1) where T (n) is the transmit time for the n th ping, T Figure 4: Predicted receiver blanking characteristics of a 0.5 across-track beamwidth, 1.0 along-track beamwidth cdm mbes. The ping rate determines which echo angles-of-arrival will be blanked. The color denotes the percentage of the time that the received echo is blanked for that ping rate and angle-of-arrival combination. arrival where it is easier to compensate for blanking. The echo duration simulation described in Section 2 can be run repeatedly to show where receiver blanking will occur at different ping rates, as well as to show the percentage of the time that the echo in an angular beam is blanked. Figure 4 shows all of this information for ping rates between 1x and 8x, and angles-of-arrival between 0 and 60. The image is color coded to show the percentage of the time that the received echo is blanked for that ping rate and angle-of-arrival combination. There are ranges of ping rates for which zero receiver blanking occurs when specular echoes are being received, and it is therefore preferable to ping at these is the nominal period to sustain the desired ping rate, and δ t (n) is the deviation from the nominal ping rate. We suggest a uniform distribution in time δ t (n) U(t 1, t 2 ) (2) where t 1 and t 2 are the temporal deviations which result in blanking at the smallest and largest angles-ofarrival desired, typically 35 to 60, although this will not be uniform on the seafloor due to the geometry of the acoustic system. A more complex distribution for δ t (n) could more uniformly space blanking on the seafloor, although determining the optimal distribution with multiple angles being blanked would be difficult. How much or little of this angular region is used is limited by naturally occurring variability of the seafloor. A deviation from the expected depth will result in blanking when the echo is arriving from a different angle than was expected. This angular uncertainty spreads the range of angles over which blanking will occur, and necessitates tuning t 1 and t 2 accord- rates to avoid loss of data in those beams. We hypothesize that blanking over a range of angles rather than ingly. These results hold for up to a 2x ping rate, at a single angle is advisable, as this will spread the however they become more complex as the ping rate 5
increases and more than one angular region of an echo is blanked. Direction of Travel θ R 5 Sounding Density Increase The maximum ping rate is echo-limited to approximately a 7x increase for a sonar with an across-track dθ dφ dr H W beamwidth of 0.5, and an along-track beamwidth of 1.0. As seen in Figure 4, the maximum ping rate is further limited by choosing a ping rate that causes blanking to never occur at specular echoes. This suggests that with the best presently available arrays, a 6x ping rate is achievable using only this method. With slightly larger arrays and their subsequently small beamwidths, the echo-limited bandwidth would increase, and an 8x ping rate could be achievable. Compensation for receiver blanking using ls interpolation limits the number of soundings lost to a small fraction of the total number of soundings in a single ping. Thus, the along-track sounding density increases almost proportionally with the ping rate, and for this proposed cdm mbes the increase in the along-track sounding density is approximately 6x that of a single ping mbes. Further improvement to the along-track sounding density could come from combining design elements of a fdm mbes and a cdm mbes into a single hybrid system. Two frequency bands with a different set of codes for each frequency band might then allow for a doubling of the along-track sounding density seen in a Figure 5: When the receivers are turned off the echo from a volume of space is not recorded. The echo from objects within this volume will be missed. ing density in the 12x to 16x range over the sounding density of a single ping mbes. 6 Blanking Volume ls interpolation works well when the seafloor slope is continuous through the blanking period. Often times this is the case, but abrupt changes in the seafloor could be missed depending on the timing of the echo and the blanking. The size of an object that could be missed in a single ping changes with the echo s angleof-arrival. Figure 5 shows the blanking volume geometry. equations The volume s dimensions are found using the dr = cτ (3) dφ = Rφ T (4) dθ = Rθ R (5) where c is the speed of sound in water, τ is the blanking cdm mbes. This could increase the along-track sound- duration, R is the slant range, φ T is the along-track 6
beamwidth, and θ R is the across-track beamwidth. This geometry can be projected into cartesian coordinates that correspond to the the along-track distance, across-track distance and height of the blanking volume and are described by the equations Along-Track Distance = Rφ T (6) objects will not be missed, or a probabilistic estimate of how often different size objects might be missed is a difficult problem and merits further study. Alternative receiver blanking schemes could also be considered, depending on the importance of the maximum height of the blanking volume, and the permissible level of computation complexity. Blanking the Across-Track Distance = Rθ R cos(θ) (7) Height = Rθ R sin(θ) (8) receivers during specular echoes when the blanking volume height is at a minimum could be considered, however time-of-arrival estimation would present difficult where θ is the echo s angle-of-arrival. The effect of problems as well. dr is small for typical pulse lengths relative to the beamwidths, and has been ignored to simplify the projection into cartesian coordinates. The size of each dimension depends on the threshold used to determine the beamwidth. For a 3 db beamwidth threshold the maximum height of the blanking volume is approximately 3% of water depth, while for a 20 db beamwidth threshold the maximum height of the blanking volume is 10% of water depth. Maximum heights occur at the largest angle-of-arrival (in this case 60 ), and decrease with angle-of-arrival. A cdm mbes will be pinging 6 to 8 times as fast as a single ping mbes, pinging fast enough that multiple echoes from (approximately) the same patch of seafloor 7 Conclusion We have proposed a cdm mbes as an alternative method of increasing the along-track sounding density. While the design results in receiver blanking, a method of minimizing the effects on sounding density has been described, and we expect that any objects missed in one ping are likely to be detected in surrounding pings. This design should increase the along-track sounding density by 6x for the smallest beamwidth transducers available today, and could increase it by 8x for slightly larger arrays. will be observed in surrounding pings. Transmit time jittering and vessel motion will cause the blanking on surrounding pings to be distributed at different acrosstrack distances, and thus an object missed because of receiver blanking on one ping is likely to be detected on surrounding pings. However, either an assurance that Acknowledgements The support of noaa grant NA10NOS4000073 for this work is gratefully acknowledged by the authors. 7
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