DSI3 Sensor to Master Current Threshold Adaptation for Pattern Recognition

International Journal of Signal Processing Systes Vol., No. Deceber 03 DSI3 Sensor to Master Current Threshold Adaptation for Pattern Recognition David Levy Infineon Austria AG, Autootive Power Train Systes, Villach, Austria Eail: david.levy@infineon.co shows the perforance achieved with the proposed ethod. Section VI suarizes the paper. Abstract The newly released Distributed Syste Interface 3 (DSI3) Bus Standard specification defines 3 odulation levels for which 6 valid sybols are coded. This coplex structure is best decoded with sybol pattern recognition. In order to siplify the pattern recognition correlation calculation, the received differential current is quantized back to 3 levels. This paper describes how the thresholds are estiated and adapted for the ost optiu quantization. The coplete syste was siulated in Matlab script. It will be shown that after 4 sybols, the estiated threshold is 6% away fro the optiu thresholds when the initial currents are 35% off the expected noinal thresholds. This proves fast convergence to the optial threshold and a sall residual error in a syste that includes the ajor distortions and inaccuracies. Index Ters autootive, DSI3, sybol threshold estiation, threshold adaptation I. Figure. Coding exaple. II. decoding, The sensor slave encodes response fraes to the aster with current odulation. The aster supplies the slaves with a quiescent current. The slave odulates this current in a way that the aster has to supply a higher current during data odulation. The DSI3 standard defines three current odulation levels: 0: this current level is identical to the quiescent current supplied by the aster : this current level is IRESP above the quiescent current : this current level is IRESP above the quiescent current The sallest chunk of inforation is called chip, which represents one current level. The iniu duration during which the slave keeps the odulated current at the sae level during data transission is tchip. Three chips are cobined to for a sybol. The slave encodes 4 bits of data in a sybol. An exaple of such a coding is given in Fig. and the coplete coding table is given in Table I. INTRODUCTION DSI3 Bus Standard specification [] is prooted by the DSI consortiu. DSI3 goals are to iprove perforance, reduce cost and proote open standard. Higher perforance is achieved aong others, by increased counication speed fro the slave sensor to the aster. The higher counication speed is achieved by copressed bit encoding. Each incoing saple current is quantized to 3 levels, based on an adapting threshold. The quantized levels are then input to a correlation achine. Thanks to the quantization, the correlation achine can be kept very siple. The correlation echanis is described in another paper. This paper describes a ethod to adapt the threshold to the optiu threshold. The perforance of the proposed ethod is checked with a Matlab siulation. The siulation includes the coplete syste: sensor, harness and decoder. Depending on the load odels the threshold estiation anages to reach an error below 6\% fro the optiu threshold in 4 sybols when starting with an error of 35\%. The organization of the paper is as follow: section II describes the DSI3 bit decoding. Section III describes existing threshold adaptation echaniss. Section IV defines the proposed adaptation echanis. Section V III. PRIOR ART The PSI5 standard [] uses Manchester encoded current odulation for sensor data transfer to the ain unit. The Manchester encoding has two levels and two chips per sybol. The two possible sybols are syetric. The advantage of these properties is that whatever data is transferred, the threshold between the two levels is always siply the average current during the frae. Manuscript received July 6, 03; revised Noveber 4, 03 03 Engineering and Technology Publishing doi: 0.70/ijsps...4-45 BACKGROUND 4

International Journal of Signal Processing Systes Vol., No. Deceber 03 TABLE I. DATA TO SYMBOL MAPPING Data st chip nd chip 3 rd chip 0 0 0 3 0 4 0 0 5 fit best to the DSI3 because the triodal distribution is a GMM with three Gaussian coponents. The authors focus on the siple GMM which consists of two coponents, but also describe the extension to a general GMM. The first step consists in finding the ean and variance of each Gaussian coponent, using the expectation-axiization (EM) algorith. Unfortunately, the EM algorith, described in reference [9], is uch too coplex to ipleent in hardware on signals sapled an order of agnitude faster than /t chip rate. 6 7 0 8 0 9 0 0 0 3 0 0 4 0 5 The adaptive quantizer, proposed by Jayant [3], adapts its step size by a factor depending on the knowledge of which quantizer slot was occupied by the previous signal saple. Unfortunately the choice of this ultiplication factor depends on the input signal type. Jayant considered Gauss-Markov inputs with different correlation factors fro one saple to the next and derived the optiu ultiplication factors for these types of inputs. The DSI3 case is unfortunately not a Gauss-Markov signal, and therefore, it would require an extensive set of siulations to find the optiu ultiplication factors. In references [4] and [5], it is assued the input data to be Gaussian. The DSI3 statistics would show a triodal distribution, because the current has a uch higher probability to be close to one of the three allowed current levels. The ethods for adaptive quantization proposed cannot be used for DSI3 current odulation decoding. In reference [6], Ortega proposes an adaptive quantizer that estiates the input probability function distribution (pdf). Based on this function, it tunes the quantizer paraeters optially and coputes the next tie the pdf has to be re-estiated. The pdf estiation consists in assuing that the probability that a saple is greater than the highest quantization level or saller than the lowest one is zero. Unfortunately this assuption is ipossible for a two-level only quantizer, which is our case. Reference [7], a Wireless sensor dedicated adaptive quantization is proposed. It requires running the Variational algorith and calculating the Fisher Inforation atrix for every saple. These coplex operations are not suitable for DSI3 where the chip duration can be as low as.75µs. Reference [8], adaptive quantization for signals of Gaussian ixture odel (GMM) is proposed. This would IV. Figure. Block Diagra. THRESHOLD ADAPTATION ALGORITHM The receiver has to reove the quiescent current and to quantize the current levels. The quiescent current is reoved by an estiation of the DC current when no data odulation takes place. The quantization is achieved by coparing to thresholds. One threshold is for differentiating between level 0 (corresponding to the quiescent current) and level (corresponding to I RESP above the quiescent current). The other threshold is for differentiating between level and level (corresponding to I RESP above the quiescent current). The values of those thresholds have to be estiated and continuously adapted. The quantized saples are used by the correlation achine which recognizes expected patterns. Thanks to the quantization, the correlation achine only needs to eorize bits per saple instead of the coplete current, and the correlation is a siple coparison rather than the theoretical ultiplication. The block diagra is shown in Fig.. The correlation echanis is detailed in a separate paper. The algorith outputs a set of threshold estiations for each sybol detected by the correlation echanis. The beginning of the first sybol in the frae is the first tie the differential current level threshold is crossed. The beginning of the subsequent sybols is detected by the correlation echanis. The average easured current for the duration of the sybol, µ, is given in (), n s I [ i] () ns i where n s is the nuber of current saples in the detected sybol and I [i] is the easured differential current of saple i. n s ay vary fro sybol to sybol due to channel phase distortion or clock isatch between sensor and aster. As can be seen fro Table I, the average current varies per sybol. Therefore, the recognized sybol, received 03 Engineering and Technology Publishing 4

International Journal of Signal Processing Systes Vol., No. Deceber 03 fro the correlation echanis ust be used to calculate the expected current. The expected average current, µ e, is given in (), e ( nc I[ s ] nc I[ s ]) () 3 where n c and n c are the nuber of chips at level and, respectively, for the recognized sybol. For exaple, for data (second line in Table I), n c = and n c =. I [s-] and I [s-] are the previous sybol calculated differential currents for for level and level respectively. The error, ε, is siply the difference between the easured and expected current. e (3) The error can also be split to error on level, ε, and error on level, ε, as shown in (4). ( nc nc ) (4) 3 Assuing that there is no saturation effect on the currents for the range considered, we have: I[ s] I[ s] (5) (6) By reoving ε and ε fro equations (), (3), (4), (5) and (6), we obtain the error on differential current level, as a function of the easured average current and the previous current level, as shown in (7): 3 I [ s] nc nc A siilar approach is used to extract ε : 3 I [ s] nc nc With the errors on both current levels, the new current levels can be updated. A conservative approach is used, to avoid that any wrongly recognized sybol by the correlation echanis would sharply ipact the current level estiations. For this purpose, a first order Infinite Ipulse Response (IIR) is used to filter the updated current, as shown in (9) and (0), where α is a positive real uch saller than. The saller α, the ore conservatively the currents are updated, with a negative ipact on the convergence to the optial currents. (7) (8) I [ s] I [ s ]( ) a( I [ s ] ) I [ s ] (9) I [ s] I [ s ] (0) The thresholds after saple s was received, T 0 [s] and T [s], between current levels 0 and and current levels and, respectively, are the iddle values between the current levels, as shown in () and (): I[] s T0[] s () I[ s] I[ s] I[ s] I[ s] T [ s] I[ s] () Figure 3. Δ extree current deviations. Figure 4. Influence of α on Δ. V. PERFORMANCE ESTIMATION The noinal value of I RESP is defined in [] to be A, therefore, the noinal value of T is 8A. In reference [], the sensors are allowed to deviate by.5% fro the noinal value. The cobined line attenuation and the receiver gain error also create a deviation fro the noinal value of another 0%. The total error fro sensor current odulation to the input to the quantizer can reach overall +35% to -30%. We then have that the expected threshold between levels 0 and, E 0 [s], can have any value between 0.35I RESP and 0.675I RESP. The expected threshold between levels and, E [s], can have any value between.05i RESP and.05i RESP. The perforance can be easured by introducing the difference between the expected threshold, E [s] and T [s], Δ [s], for every saple: [ s] T [ s] E [ s] (3) The first siulations were run in a siplified syste: there is no signal distortion between the sensor and the aster, no quiescent current and the correlation echanis always recognizes the correct sybol. In Fig. 3, the current level I RESP was set to the extree values and the noinal value, with α= -3. For the extree 03 Engineering and Technology Publishing 43

International Journal of Signal Processing Systes Vol., No. Deceber 03 current levels, we see a transient behavior until there is convergence to zero error. The noinal I RESP stays always without error. The positive and negative extree I RESP currents have an identical behavior. In Fig. 4, we use I RESP 35% below the noinal value, and odify α. A bigger α reduces the settling tie to the zero error. The threshold adaptation algorith is used in conjunction with the rest of the syste depicted in Fig.. The following siulations were run with the coplete syste including the sensor, transitting odulated current, harness, voltage regulation and bit decoding odeled in SiuLink. Four load odels were defined, at the expected worst syste response. The load odels include the sensor serial capacitor, C s, serial resistor, R s, the harness capacitor, C e, and its parasitic serial inductance, L e. The values used for each load odel are suarized in Table II. All test cases have fraes of 3 bits each and t chip =.5µs. expected patterns. Once a high score for one of the expected patterns was reached, the sybol is recognized. Depending on how the load distorted the current, the correlation echanis will take a varying aount of saples to recognize the pattern. Therefore, the sybol boundaries ay include saples fro the previous sybol, causing a wrong estiation of µ. More siulations were run with varying α on load odel 4, with 35% positive error. The results are shown on Fig. 6. As was shown with the ideal case, the convergence speed increases with α. The advantage of keeping a lower α is to have less sensitivity to the load odel. The variation due to incorrect current estiation on a single sybol is reduced with a sall α. TABLE II. VALUES OF PARAMETERS FOR ALL SHOWN RESULTS Load odel index 5 8 9 C s(nf) 40 0 0 5 C e(nf) 35 35 5 5 R s(ω) 0.6..5.5 L e(µh).... Figure 6. Δ with varying α on a typical load odel. Figure 5. Δ for considered load odels. All load odels defined above were siulated with 35% positive error and α= -3. The results are shown in Fig. 5. The variation around the converging threshold current has two causes of error: The capacitive load. As can be seen fro Table I, not all sybols have the sae aount of level transitions fro high to low as fro low to high level. This effect causes either an over estiation of µ (for exaple for data 4, if the last chip of the previous sybol has level ) or an under estiation of µ (for exaple for data 6, if the last chip of the previous sybol has level 0). The Correlation echanis. The pattern recognition is based on checking correlation score between the incoing sybol and all possible VI. CONCLUSION This paper proposed a way to estiate and adapt the thresholds used by a quantizer for DSI3 sensor to aster sybol detection. We listed existing quantization level adaptation ethods. We analytically detailed our ethod for quantization levels based on the feedback of the correlation echanis. The perforance was analyzed both in a siplified environent and a realistic coplete syste. The results show a steady state error which is below 6% fro an initial 35% error and a convergence to this error range within 4 sybols when the syste includes all current distortions and the correlation echanis inaccuracies. REFERENCES [] Distributed Syste Interface 3 Bus Standard Revision.00, DSI3 Consortiu, February, 0. [] Peripheral Sensor Interface for Autootive Applications, PSI5 Steering Coittee, Version.0, June st, 0. [3] N. S. Jayant, Adaptive quantization with a one-word eory, The Bell Syste Technical Journal, vol. 5, no. 7, Septeber, 973. [4] R. Kwok and W. T. K. Johnson, Block adaptive quantization of agellan SAR data, IEEE Transactions on Geoscience and Reote Sensing, vol. 7, no. 4, July 989. [5] Z. Peric, J. Nikolic, A. Mosic, and S. Panic, A switched-adaptive quantization technique using µ-law quantizers, Inforation Technology and Control, vol. 9, no. 4, pp. 37 30, August 00. 03 Engineering and Technology Publishing 44

International Journal of Signal Processing Systes Vol., No. Deceber 03 [6] A. Ortega and M. Vetterli, Adaptive scalar quantization without side inforation, IEEE Transactions on Iage Processing, vol. 6, no. 5, pp. 665-676, May 997. [7] M. Mansouri, I. Ouachani, H. Snoussi, and C. Richard, Craerrao bound-based adaptive quantization for target tracking in wireless sensor networks, in Proc. IEEE Workshop on Statistical Signal Processing, Septeber 009, pp. 693-696. [8] D. G. Jeong and J. D. Gibson, Iage coding with unifor and piecewise unifor vector quantizers, in Proc. Global Telecounications Conference, vol., -5 Deceber 99, pp. 80-84. [9] A. P. Depster, N. M. Laird, and D. B. Rubin, Maxiu likelihood fro incoplete data via the EM algorith, Journal of the Royal Statistical Society, Series B (Methodological), vol. 39, no., pp. -38, 977. David Levy was born in Sarcelles, France on March 7, 970. Levy graduated in Electronics in 993 with honors at UniversitéLibre de Bruxelles, Belgiu, focusing on coputer networks. Levy has several patents and a publication related to WLAN in particular and telecounication in general. He worked in several startup copanies as a Board and Digital Designer until 000. He was the Syste Architect of the MAC layer for an ADSL ode at Alcatel and STMicroelectronics fro 000 to 005. He was the WLAN Syste Architect at Texas Instruents, working on the coplete WLAN transceiver in a chip for obile phones fro 006 to 009. Since 00, he is a Concept Engineer for Autootive Airbag SoC at Infineon, Villach in Austria, focusing on the sensor interface and the Ebedded Safing Engine. Fro 006 to 009 Mr. Levy was an active eber of the Wi-Fi Alliance. 03 Engineering and Technology Publishing 45