Ultrasonic Beamforming with Delta-Sigma Modulators

Transcription

1 Proceedings of the 10th WSEAS International Conference on CIRCUITS, Vouliageni, Athens, Greece, July 10-1, 006 (pp ) Ultrasonic Beaforing with Delta-Siga Modulators IOAN LIE *, MIHAIL EUGEN TANASE *, DAN LASCU *, MIHAELA LASCU ** * Applied Electronic Departent, ** MEO Departent Politehnica University of Tiisoara Bd Vasile Parvan, no, Tiisoara, 3003 ROMANIA Abstract: - Delta - Siga ( ) odulation allows delay resolution in ultrasound beaforers to be achieved by siple clock cycle delays applied to the undeciated bitstrea, greatly reducing the coplexity of the signal processing and the nuber of bits in the data path The signal resapling involved in dynaic beaforing, however, disrupts synchronization between the odulators and deodulator, causing significant degradation in the signal-to-noise ratio As a solution a beaforer architecture based on nonunifor oversapling conversion was explored Using this approach, the echo signals received by the transducer array are sapled at tie instants deterined by the beaforing tiing and then digitized by single-bit A/D conversion prior to the coherent bea suation The coded beasus obtained by adding the delayed 1-bit echo signals are then processed through a deciation filter to produce final outputs Key-Words: - Delta-Siga, Beaforer, Ultrasound, Delay 1 Introduction The newer digital ultrasound iaging systes have greatly benefited fro iproveents in seiconductor electronics, which have iproved the speed and accuracy of the necessary data conversion These advanceents have resulted in high quality, -D real-tie iagers Recent advances in seiconductor electronics have ade it possible to develop ultrasound beaforers that can acquire and process data at a sufficiently high rate to produce real-tie 3-D iages Because a significant fraction of a -D data set has to be collected and processed over the course of a single transit event, bea foration ust either occur serially with a great aount of eory and speed or in parallel using duplication of hardware The need for siplicity in the delay calculation forces the need for an A/D converter that saples well in excess of the Nyquist rate to reduce error in calculation of the fine delays Although such a syste is feasible, there is great potential for further hardware reduction An interesting ethod of achieving such a high data conversion rate, while aking ajor siplifications in the signal processing hardware, is the use of a odulator as the A/D converter in the beaforer, as proposed by [1], and developed in [3] When a odulator is operated with a sapling frequency (fs) of 3x the center frequency (fc) of the ultrasound signal or higher the nuber of bits involved in the signal processing is greatly reduced, and the need to interpolate between saples is eliinated It then becoes feasible to achieve parallel bea foration via duplication of hardware, which has been drastically siplified over the conventional case The price of this siplicity is the need for a high speed odulator Although such high speed operation of the odulator ight appear to be wasteful of power, odulators use significantly less power than Nyquist-rate A/Ds operating at the sae speed, because they supply only a single bit of resolution at that speed That single bit of resolution, however, is enough to provide the required delay accuracy, saving the conversion to high resolution until after the coplex beaforer hardware, where it is needed at a uch lower rate Most iportantly, the speed and size of the digital hardware is reduced because of the siplified signal processing and reduced nuber of bits being processed Δ Modulators The oversapling ratio OSR is defined to be the ratio of the sapling frequency f s to twice the signal band edge (the Nyquist rate) OSR = fs/(f B ) = 1/(f B T) (1) where T is the sapling period As the oversapling ratio increases, the quantization noise can be spread over a larger range of frequencies, so the noise power in band changes Using (1) we can write the noise power that lies within the liited signal band (-f B, f B ), as

2 Proceedings of the 10th WSEAS International Conference on CIRCUITS, Vouliageni, Athens, Greece, July 10-1, 006 (pp ) σ ey = f B f B f B σe P e(f )df = Pe (f )df = σe (fbt) = () OSR 0 The signal to noise ratio (SNR) of a ulti-bit A/D is found by logarithically copressing the ratio of the signal power to the quantization noise power σ x SNR = 10 log 10 4,77 6,0N (3) V were N is the nuber of bits in the quantizer The relation shows that every extra output bit fro the quantizer provides an extra 6dB iproveent in the SNR An oversapled A/D converter exploits the relation () so that a very high sapling rate is used with a very siple, perhaps single-bit quantizer, to provide adequate SNR Delta siga A/Ds are a subclass of oversapled A/Ds that filter the quantization noise to reduce in-band noise power A first order Δ odulator (figure 1) consists of an integrator, an internal flash ADC or quantizer and a DAC eployed in the feedback path The signal that is quantized is a filtered version of the difference between the input and the analog representation of the odulator output The filter is a discrete tie integrator whose transfer function is z -1 /(1-z -1 ) If the DAC is ideal the odulator output is given by: Y(z)=X(z)z -1 E q (z)(1-z -1 ) (4) so the signal transfer function is STF(z) = z -1 and the noise transfer function is NTF(z) = (1-z -1 ) The output is siply a delayed version of the input plus the quantization noise that has been shaped by a first order high pass filter The peak SNR is given by: 3 N 3 3 SNR peak = 10 log 10 log (OSR) π Thus the peak SNK increases by 9dB or 15 bits when OSR is doubled but we need a relative high OSR, ore than 1000 to achieve a SNR of 16 bits (100dB) with this odulator x[n] u [n] Discret tie integrator v[n1] z -1 DAC 1-bit Fig 1 A first order delta-siga odulator The structure of a second order Δ odulator contains two integrators and a forward path is included in both integrators figure The output of the odulator is given by: 1 Y(z) = X(z)z E (z)(1 z ) (5) where STF(z)=z - and NTF(z)=(1-z -1 ) Copared with the first order NTF, the second order NTF provides ore quantization noise suppression over the low frequency signal band and ore aplification of the noise outside the signal band ie ore power noise is pushed to higher frequencies The peak SNR of the second order architecture is: 3 N 5 5 SNR peak = 10 log 10 log (OSR) 4 π Therefore for every doubling of the OSR, the peak SNR increase by 15 db or equivalent resolution by 5 bits To obtain a SNR of 16 bits we need an OSR of only 116 which is uch saller than the first order case Q v[n] Quantizer e[n] y[n] Discret tie integrator x[n] u 1[n] 1/ z -1 u [n] Discret tie integrator z -1 v[n] quantizer e[n] y[n] DAC Fig A second-order delta-siga odulator Δ odulators with higher-order noise shaping can achieve higher resolution by pushing ore noise power outside the signal band Unfortunately, unlike first and second order odulators it is possible for odulators of third or higher order to go unstable especially when large input signals are applied On the other hand ulti-bit odulators architectures using ulti-bit quantizers reduce the aount of in

3 Proceedings of the 10th WSEAS International Conference on CIRCUITS, Vouliageni, Athens, Greece, July 10-1, 006 (pp ) band quantization noise and iprove the SNR by 6 db for each bit added The drawbacks of this architecture are the requireent for full linearity of feedback DAC and the significant increase of the converter coplexity One of the key benefits of Δ odulators over ulti-bit flash ADCs is the relative siplicity of the Δ ADC ipleentation Based on this the odulator architecture for ultrasound applications will be chose in order to ensure the siplicity and stability requireents and a resolution equivalent to a 10 bits ulti-bit converter which correspond to a 60dB dynaic range An OSR of 3 for a third order odulator assure the desired dynaic range This eans that for a transducer array operating at 35 MHz the odulators and the digital section of the beaforer will be clocked at a frequency around 00 MHz 3 The beaforer architecture 31 Steering and focus delay A ultrasonic bea generated by a phased array can be both focused and steered by properly delaying the transitted and received signals Consider a phased array with N eleents and inter-eleent spacing d = λ /, Fig It is to be focused and steered at point ( r,θ ), where θ is the steering angle and r is the range (r,θ) Fig 3 The geoetry of an array focused to point (r, θ) The one way delay for eleent is given ' ' by: τ = ( r r )/ c (5) where r is distance between eleent and point ( r, θ ), 0 N 1According ' to Law of Cosine, the distance r, is ' r = x r x r sinθ (6) eleent r x s r-s θ d x where x is the position of the th eleent The one way delay is 1 s f τ = r x r xr sinθ = τ τ (7) c s s x sinθ τ = = - steering delay (8) c c f r s x r xr sinθ τ = - focusing delay (9) c The relations 7-9 show a nonlinear dependence of the delays fro the focal point coordinates Only f focusing delay τ is dependent on the point s range r Focusing can be fixed, dynaic, or coposite Fixed focusing synthesizes a focus at only one particular range R, typical in the iddle of the interrogated region In dynaic focusing, the focusing delay is adjusted as function of range r Dynaic focus on reception is coonly used so that depth of field is extended without any reduction of frae rate 3 Delta-Siga beaforer Beaforers based on Δ have two ajor advantages over traditional ulti-bit ethods I Siplifying the ADC structure and the possibility of integrating on the sae chip together with the digital processing blocks The necessary circuits for ipleenting Δ ADC are uch sipler than those used in ulti-bit flash ADC (several operational aplifiers and a coparator in contrast to the 55 coparators used for a 8 bit flash ADC), and this will reduce the resources used for interconnection, the size and energy usage II Precise siple delays can be ensured by anipulating the saples taken with a high sapling rate The coplicated circuits needed for interpolating/deciating are replaced with a conventional FIFO eory that can ensure the delay with the desired resolution before suing Further, the whole area suing is siplified because the first suing level is built with one-bit adders Because of the wide dynaic field required for ultrasound applications, ADC Δ ust be a second or third level odulator in order to keep an adequate signal versus noise ratio To ensure both an adequate signal/noise ratio and an adequately accurate delay we chose a sapling frequency of at least 3 ties higher than the bearing frequency This will give an over sapling factor OSR = 16 In the unifor sapling beaforer, figure 1, the digital output of the odulator is applied to the delay lines These are of variable length, and are ipleented as FIFO eory or as shift registers and dynaically delay

4 Proceedings of the 10th WSEAS International Conference on CIRCUITS, Vouliageni, Athens, Greece, July 10-1, 006 (pp ) the signals These shift registers ust operate at the sapling frequency and contain several hundred cells in order to host the dynaic delays during each bea The length of each delay line depends on the next paraeters: sapling rate, array geoetry, steering angle, axiu iaging depth, carrier frequency When the length of the delay line changes in order to create a new focal zone, the saples ust be repeated, inserted or eliinated at the input, output or even in the iddle of the shift register 1 N Δ ADC Δ ADC Variable delay lines Δ ADC UNIFORM SAMPLING CLOCK Fig 4 Block diagra for an unifor Δ beaforer The delayed saples fro all the array eleents are then digitally sued to for a bea This suing ust be done at the sapling frequency and this requires a set of digital pipeline adders for the whole area Once the bea has been generated by suing the signal it is applied to a low pass filter with to eliinate the quantization noise This superior order filter can be long and coplicated It also has certain power consuption, but only one such filter is required in order to generate a bea In order to use the traditional processing blocks (envelope detection, scan conversion) it is necessary to reduce the sapling rate through the deciation of the filtered saple string The Δ ADC together with the low pass reconstruction filter constitutes a odulator deodulator pair Between the odulator and deodulator can be introduced blocks that executes linear operation without this interfering with SNR The process of creating the ultrasonic bea by the delay-su algorith can be divided into two distinct stages: - Delay the tie lag of the inforation provided by the area eleents - Su - Suing of the delayed eleents Focusing the acoustic waves in a close field requires the delay after a parabolic forula see (7) DECIMATION FILTER Therefore, the bea foring fro ultrasonic signals is done by a non-linear delay operation, followed by the linear suing operation Using the siga-delta with unifor odulation converters for bea foration requires the intercalation between the odulator and deodulator of the non-linear delay process followed by the linear suing process fig 5 Δ conversion with unifor rate DELAY SUMM (resapling BEAMFORMER Filtering/ Deciation (DEMOD) Fig 5 Unifor Δ bea foration The non-linearity of the delay leads to the resapling of the signals delivered by the array eleents that lead to the repeated use of soe saples and soe saples are never used at all The repetition or eliination of saples fro the sigadelta odulators outputs leads to the asynchrony of the odulator / deodulator enseble The preponderance of one or the other echaniss is a function of the ratio between the sapling frequency (f M ) and the foring frequency (f BF ) The siga-delta beaforing with non-unifor rate consists of the extraction of the non-linear delay process fro the odulator / deodulator enseble and placeent of this before the odulator In this way the synchrony of the odulator / deodulator couple is ensured, because between these two blocks only the linear suing operation is intercalated figure 6 Nonunifor Sapling (DELAY) BEAM- Δ Conversion (MOD) SUMM -FORMER Filtering/ Deciation (DEMOD) Fig 6 Non unifor Δ bea foration The digital bea forers that are based on nonunifor sapling create the dynaic focusing by sapling the echo saples at specific oents that ensure the coherent suing operation at the reception The clock for the non-unifor sapling is generated by the delay set stored in a digital eory operated with a unifor clock f M The sapling clock generator creates different nonunifor clock for each area eleent The dynaically delayed saples are then digitized with a set of one-bit siga-delta odulators, before the coherent suing Each odulator is activated

5 Proceedings of the 10th WSEAS International Conference on CIRCUITS, Vouliageni, Athens, Greece, July 10-1, 006 (pp ) with his non-unifor clock created by the generator figure 7 Each odulator s exit is a string of onebit data that includes the delayed original signal plus the high frequency quantifying noise These one-bit representations for the echo saples appear at various oents in tie on reception channels because there is no regularity in the signal arrival tie If the tie between two consecutive focal points 1/f BF is grater than the axiu delay between eleents (ax {τ n (r, θ)}), then for every focal point the requested saple in the foring process appears before the saple required for the next focal point The one-bit coded saples that appear at different oents in tie at the odulators exits are aligned by the FIFO buffers on each channel and will be siultaneously sent to the adders that generate the rough version for the fascicle that will contain the su of the delayed echoes plus the quantifying noise The reconstruction filter will eliinate the quantifying noise and will reduce the sapling rate close to the Nyquist rate 1 N Δ ADC Δ ADC FIFO BUFFER Δ ADC SAMPLING CLOCK GENERATOR FIFO BUFFER FIFO BUFFER Fig 7 Structure of a non unifor Δ beaforer r θ DECIMATING FILTER Four beaforing ethods and the corresponding structures were eulated using Matlab scripts: - Conventional ulti-bit beaforer with fixed focus on transission and dynaic focus on reception which was the reference (C FFT_DFR) - Unifor beaforer with fixed focus on transission and dynaic focus on reception (U FFT_DFR) - Unifor beaforer with fixed focus on transission and fixed focus on reception (U FFT_FFR) - Non-unifor beaforer with fixed focus on transission and dynaic focus on reception (N FFT_DFR) For perforance evaluation was used the spectral analysis at the bea level The figures 8 11 show the eulation results Analyzing the diagras we can see the presence of an unexpected noise in the frequency range 0-17MHz for U FFT_DFR The noise level is 30 db greater than for C FFT_DFR The noise appears fro the resapling during dynaic focusing of the delta siga odulated signals The hypothesis is confired by the noise absence fro the diagra of U FFT_FFR In this case due to the fixed focus the noise difference to conventional beaforation is less then 10dB It is obvious that the dynaic focusing for unifor sapling disrupts the synchronization for odulator / deodulator pair The sae noise with 10 db greater than for C FFT_DFR is present in the N FFT_DFR diagra This suggest that the with nonunifor sapling beaforer is a good solution which use the odulation benefits and provide for dynaic focusing a SNR perforance coparable with the conventional ulti-bit beaforer Fro a structural point-of-view, the digital bea forer with a non-unifor siga delta odulation is ade up of two sections: - An analogue section - the siga-delta odulators - The digital section which contains the following entities: Digital controller, FIFO eory, adder and deciating filter 4 Siulation results The based beaforers presented above was eulated in software using real ultrasound data available over the www [4] Fig 8 Spectru of a bea - C FFT_DFR

6 Proceedings of the 10th WSEAS International Conference on CIRCUITS, Vouliageni, Athens, Greece, July 10-1, 006 (pp ) Fig 9 Spectru of a bea - U FFT_DFR solution a beaforer architecture based on nonunifor oversapling conversion was explored Using this approach, the echo signals received by the transducer array are sapled at tie instants deterined by the beaforing tiing and then digitized by single-bit conversion prior to the coherent suation T The perforance of the proposed beaforing solution was evaluated by MATLAB eulations using experiental data The coded beasus obtained by adding the delayed 1-bit echo signals are then processed through a deciation filter to produce final outputs Delta siga ( ) odulation allows delay resolution in ultrasound beaforers to be achieved by siple clock cycle delays, greatly reducing the coplexity of the signal processing and the nuber of bits in the data path The siplifications offered by this technique have the potential for low power and portable operation in advanced ultrasonic iaging systes Fig 10 Spectru of a bea - U FFT_FFR Fig 11 Spectru of a bea - N FFT_DFR 5 Conclusion The signal resapling involved in dynaic beaforing disrupts synchronization between the odulators and deodulator, causing significant degradation in the signal-to-noise ratio As a References: [1] S E Noujai, S L Graverick, M O Donnel,, Phased array ultrasonic bea foring using oversapled A/D converters, U S Patent , April 1993 [] P M Aziz, H V Sorensen, J Van Der Spiegel, An overview of siga-delta converters, IEEE Signal Proces Mag, vol 13, no 1, 1996, pp [3] S R Freean, M K Quick, M A Morin, R C Anderson, C S Desilets, T E Linnenbrink, and M O Donnell, An ultrasound beaforer using oversapling, in Proc IEEE Ultrasonics Syposiu, 1997, pp [4] S Krishnan (1997, Dec), Ultrasound RF data set wire cbb, University of Michigan, MI, cbbshtl[online] [5] T L Szabo, Diagnostic Ultrasound Iaging, Elsevier Acadeic Press, 004 [6] M Kozak and M Karaan, Digital beaforing using non-unifor oversapling delta-siga conversion, Proc IEEE Ultrasonics Syposiu, 1999, pp [7] K E Thoenius Evolution of ultrasound beaforers, Proc IEEE Ultrason Syp, volue, pages , 1996