Fuzzy Logic Estimator for Variant SNR Environments

Fuzzy Logic Estimator for Variant SNR Environments Rosa Maria Alsina Pagès, [email protected] Clàudia Mateo Segura, [email protected] Joan Claudi Socoró Carrié, [email protected] Grup de Recerca en Processament Multimodal (GPMM) Enginyeria i Arquitectura La Salle – Universitat Ramon Llull

INTRODUCTION The acquisition system is one of the most sensitive stages in a Direct Sequence Spread Spectrum (DS-SS) receiver (Peterson, Ziemer & Borth, 1995). There are several schemes to deal with this problem, as serial search and parallel algorithms (Proakis, 1995). Serial search algorithms are slow to converge but their computational load is very low; on the other hand, parallel systems converge very quickly but their computational load is very high. The acquisition scheme used in our system is the multiresolutive structure presented in (Moran, Socoró, Jové, Pijoan & Tarrés, 2001), which combines high speed of convergence and low computational load. Nevertheless, the multiresolutive structure has some drawbacks. The decisional system that evaluates the acquisition stage is a key process in the overall system performance. This becomes more important when dealing with time-varying channels, where signal to noise ratio (called SNR) is not constant. Several factors contribute to the performance of the acquistion system (Glisic & Vucetic, 1997): uncertainty about the code phase, channel distorsion and variations, noise and interference, and data randomness. This led us to think about the possibility of using fuzzy logic to solve this complex acquisition estimation (Zadeh, 1973). A fuzzy logic acquisition estimator had already been tested and used in our research group to control a serial search algorithm (Alsina, Morán & Socoró, 2005) with encouraging results, and other applications to this field can be found in bibliography as (Bas, Pérez & Lagunas, 2001) or (Jang, Ha, Seo, Lee & Lee, 1998). Several previous works have been focused in the development of acquisition systems for non frequency selective channels with fast SNR variations (Moran, Socoró, Jové, Pijoan & Tarrés, 2001) (Mateo & Alsina, 2004).

BACKGROUND In 1964, Dr. Lofti Zadeh came out with the term fuzzy logic (Zadeh, 1965). The reason was that traditional logic could not answer to some questions with a simple yes or no. So, it handles the concept of partial truth. Fuzzy logic is one of the possibilities to imitate the working of a human brain, and so to try to turn artificial intelligence into real

intelligence. Zadeh devised the technique as a method to solve problems for soft sciences, in particular those that involve human interaction. Fuzzy logic has been proved to be a good option for control in very complex processes, when it is not possible to produce a mathematical model. Also fuzzy logic is recommendable for highly non-linear processes, and overall, when expert knowledge is desirable to be performed. But it is not a good idea to apply if traditional control or estimators give out satisfying results, or for problems that can be modelled in a mathematical way. The most recent works in control and estimation using fuzzy logic applied to direct sequence spread spectrum communication systems are classified into three types. The first group uses fuzzy logic to improve the detection stage of the DS-CDMA1 receiver, and they are presented by Bas et al and Jang et al (Bas, Pérez, & Lagunas, 2001)(Jang, Ha, Seo, Lee, & Lee, 1998). The second group uses fuzzy logic to improve interference rejection, with works presented by Bas et al and by Chia-Chang et al (Bas, & Neira, 2003) (Chia-Chang, Hsuan-Yu, Yu-Fan, & Jyh-Horng, 2005). Finally, fuzzy logic techniques are also improving estimation and control in the acquisition stage of the DSCDMA receiver, in works by Alsina et al (Alsina, Moran, & Socoró, 2005) (Alsina, Mateo, & Socoró, 2007).

ACQUISITION ESTIMATION IN DS-CDMA ENVIRONMENTS One of the most important problems to be solved in direct sequence spread spectrum systems is to achieve a robust acquisition of the pseudonoise sequence, that is to obtain an accurate estimation of its exact phase or timing position (Proakis, 1995). In timevarying environments this fact becomes even more important because acquisition and tracking performance can heavily degrade communication reliability. In this work a new multiresolutive acquisition system with a fuzzy logic estimator is proposed (Alsina, Mateo, & Socoró, 2007). The fuzzy logic estimation improves the accuracy of the acquisition stage compared to the results for the stability controller, through the estimation of the probability of being acquired, and the signal to noise ratio in the channel. Multiresolutive Acquisition Structure The aim of the multiresolutive scheme presented in (Moran, Socoró, Jové, Pijoan & Tarrés, 2001) is to find the correct acquisition point in a quick convergence. It gives a good trade-off between speed of convergence of the parallel systems and the low computational load of the serial search algorithms. An M order decimation is firstly applied to the input signal x[n]2 as acquisition stage can accept uncertainties under the chip period, and thus to decrease the computational load of the acquisition stage. Once 1

DS-CDMA stands for Direct Sequence Code Domain Multiple Access. The received signal x[n] is sampled at M samples per chip in order to give the necessary time resolution for the tracking stage. 2

the signal x[n] is decimated, the resulting signal r[n] is fed into the filters of a multiresolutive structure (see figure 1). Note that there are H different branches that work with decimated versions of the input signal, separated in H disjoint subspaces. Each  PG  (where PG is the length of branch has an adaptive FIR LMS filter of length N    H  the pseudonoise sequences, also called PN sequences), trained with a decimated version of the PN modulating sequence (PN-DEC).

Figure 1: Multiresolutive Adaptive Structure for Acquisition and Tracking Under ideal conditions, in a non-frequency selective channel with white Gaussian noise, just one of the filters should locally converge an impulse like  bi [k ]  [n   ] , where b[k] is the information bit,  represents the delay between the input signal PN sequence and the reference one and  is the fading coefficient for channel distorsion. The algorithm is reseted every new data symbol, and a modulus smoothing average algorithm is applied to each of the LMS solutions ( wi [n] ) to remove the data randomness component bi [k ] dependency, obtaining nonnegative averaged impulsional responses ( Wavi [n] ). A peak detection algorithm is used by the decisional system to find which of these filters has

detected the signal ( Wcon [n] ), and the position of the maximum (  ) in this filter will give the coarse estimation of the acquisition phase. Once restored the acquisition point by the decisional system, tracking is solved with another adaptive LMS filter ( wtr [n] ), which expands the search window around the acquisition point, using the full time resolution input signal x[n]. Thus, the estimation of the acquisition point (now called  ) is refined by the tracking and the signal can be correctly demodulated.

The fuzzy logic acquisition estimation The fuzzy logic acquisition estimator has been designed using data of the impulsional response of all the LMS filters from the structure. Their values variations give information about the probability of being correctly acquired, and also about SNR ratio variations in the channel. In the conducted experiments, the subspace has been divided into four subspaces (H=4), so four LMS filters compose the acquisition stage. The length  PG  of the PN sequences is PG=127, so each filter has N    32 taps to converge.  H 

Input Variables Four different parameters have been defined as inputs in the fuzzy estimator; three of them referred to the values of the four modulus averaged acquisition LMS filters ( Wavi [n] ), especially the LMS filter adapted to the decimated sequence PN-DEC (called Wcon [n] ), and one about the tracking filter ( wtr [n] ) that refines the search: 





Ratio1: it is computed as the quotient of the peak value of the LMS filter Wcon [n] divided into the mean value of this filter but the maximum. Wcon [ ] Ratio1  1 N Wcon [n] N n1; n Ratio2: it is evaluated as the quotient of the peak value of the LMS filter Wcon [ ] divided into the average of the value of the same position in the other three filters Wavi [n] . Wcon [ ] Ratio2  H 1 Wavi [ ] H  1 i1; Wavi Wcon Ratio3: it is obtained as the quotient of the peak value of the LMS filter Wcon [ ] divided into the mean value of the three other filters Wavi [n] .

Ratio3  

Wcon [ ] 1 1 N  Wavi [n] H  1 i 1; Wavi Wcon N n1 H

Ratio1 track: it is computed as the quotient of the peak value of the LMS tracking filter wtr [ ] , being  the most precise estimation of the correct acquisition point, divided into the mean value of the same filter but the maximum. wtr [ ] Ratio1 _ track  1 N  wtr [n] N n1; n

These parameters have been chosen due to the information they contain about the probability of being acquired, and also about the SNR level in the channel and its variations. They value variations give good estimations about acquisition quality and a good measure for SNR. Output Variables The results will be obtained using a defuzzyfication method based on the centroid (Leekwijck & Kerre, 1999). Two output variables will be computed:  Acquisition: gives a value in the range of [0,1], being zero when it is Not Acquired and one if it is Acquired. Three more fuzzy sets have been defined between the extreme values; Probably Not Acquired, Not Determined and Probably Acquired.  SNR Estimation: gives a value (in the range of [-30,0] dBs in our experiment) of the estimated SNR value in the channel. Acquisition will show a value of reliability for the correct demodulation of the detector. The multiresolutive structure only gives an estimation of the acquisition point, and Acquisition value evaluates the probability of being acquired, and so, the consistency of the bit demodulation. SNR Estimation will give us information about channel conditions; this will help not only in acquisition and tracking, but also in detection as in (Verdú, 1998) or (Alsina, Morán & Socoró, 2005).

Figure 2: Acquisition for Ratio1 and Ratio3

Figure 3: Gradient plot for SNR Estimation for Ratio2 and Ratio3

If-Then Rules A total of sixty-five rules have been used to define the two outputs in function of the input values. In figure 2 the surface for Acquisition for inputs Ratio1 and Ratio3 is shown, and figure 3 shows the gradient plot for SNR Estimation for inputs Ratio2 and Ratio3. Rules have been defined to take into account the best performance, in its range, of each

input parameter value to design the two outputs of the fuzzy estimator. This means the value range is only considered where their estimations are more reliable for both outputs. The most critical estimation for the output Acquisition is the correspondence to Not Determined; this means that the input parameters have no coherent values of Acquisition or Not Acquisition. To obtain a precise output value, the fuzzy estimator evaluates the degree of implication of each input parameter to the membership functions and projects this implication to the fuzzy sets of the output variable Acquisition, in order to obtain its value through defuzzyfication. Ratio1 and Ratio1 track are the best input parameters to estimate Acquisition when channel conditions are good; these two parameters are supported by Ratio2 and Ratio3 when SNR worsen. On the other hand, SNR Estimation most robust evaluations are made by Ratio2 and Ratio3; they are improved by Ratio1 track when SNR is high, and by Ratio1 when SNR is very low.

Results In this section the results obtained with the new acquisition and SNR fuzzy logic estimator will be summarized. Several simulations using an Additive White Gaussian Noise channel (AWGN), with very fast SNR changes, have been done to show the performance of the fuzzy estimator in terms of reliability, stability and convergence time. Acquisition Reliability vs. Stability Control A previous acquisition estimation was obtained using a stability control (Moran, Socoró, Jové, Pijoan & Tarrés, 2001), that took into account preservation of the acquisition point for evaluation and comparison purposes. It considered that the system was acquired due to continuous repetitions of the acquisition point given by the multiresolutive scheme. This stability control gave a binary response about the performance of the system: either the information demodulated was reliable (then the receiver was acquired), or the information was not reliable (and then the receiver was not acquired). Despite its good performance, shown in figure 4, the new fuzzy approach improves the results for wider SNR range. The quality of the fuzzy acquisition estimation is much better for very low SNR compared to the stability control, and its global performance for the whole range of SNR in our tests is improved. The stability control is not a good estimator for critical SNR (considered around -15dBs), and it decreases its reliability when SNR decreases. Despite showing similar performance around critical SNR, the fuzzy logic estimation of Acquisition improves its performance for worse SNR ratios.

Figure 4: % of Correct Estimation of Acquisition using the Fuzzy Estimator and the Stability Control

SNR Estimation in Time Varying Channels In figure 5.a the acquisition system has been simulated in an AWGN channel, forcing severe and very fast SNR changes. SNR Estimation mean value, obtained through an exponential smoothing average filter, is compared to the SNR in the AWGN channel. The SNR in the channel is estimated quite precisely until very low SNR (near -20dBs) by the fuzzy block, as the input parameters are not stable enough to make a good prediction for lower values. To observe the recovery of the fuzzy estimator in case of fast SNR changes in the channel, a detail of SNR Estimation is shown in figure 5.b. This information shows the channel state to the receiver, and allows further improvements of reliability of the demodulation by means of different approaches (Verdú, 1998).

FUTURE TRENDS Future work will be focused on increasing the stability against channel changes using previous detected symbols. The fuzzy estimator outputs will be used to design a controller for the acquisition and tracking structure. Its aim will be to improve the stability of estimation of the correct acquisition point (  ) through an effective and robust control of its variations for sudden channel changes, so memory will be added to the fuzzy logic estimator. Further research will also take into account multipath channel conditions and possible variations, including rake receiver features, in order to reach a good acquisition and tracking performance in high frequency selective channels, like ionospheric channel. Furthermore, the reliability of the results encourages us to use the acquisition estimation to minimize the computational load of the acquisition system for proper channel

conditions. A more efficient fuzzy logic control can be designed in order to achieve a better trade-off between computational load (referred to the LMS filters adaptation) and acquisition point estimation accuracy (  ).

Figure 5: a) SNR Estimation in a Varying SNR Channel; b) Detail of SNR Estimation when adapting to an instantaneous SNR variation

CONCLUSION Up to this point the new proposed acquisition system estimator has been exposed and some results have been compared against a stability control strategy. The main advantage of a multiresolutive fuzzy estimator is its reliability when evaluating the probability of acquisition, its stability and the fact that converges very quickly when there are fast channel SNR changes. As a final conclusion, a new proposal for multiresolutive acquisition system with a very good performance in highly time varying channels has been proposed. The computational load of a fuzzy estimator is higher than the same cost in a stability control. The mean number of FLOPS in a DSP needed to do all the process is greater compared to the conventional stability control. This has to be taken into account because the multiresolutive structure should make its computational cost minimum to work on-line with the received data. Further work will be done to compare the computational load added to the structure to the global improvements of the multiresolutive receiver, to decide whether this cost increase is affordable for the acquisition system.

REFERENCES Alsina, R.M., Morán, J.A., & Socoró, J.C. (2003). Multiresolution Adaptive Structure for Acquisition and Detection in DS-SS Digital Receiver in a Multiuser Environment. IEEE International Symposium on Signal Processing and its Applications. Alsina, R.M., Morán, J.A., & Socoró, J.C. (2005). Sequential PN Acquisition Based on a Fuzzy Logic Controller. 8th International Workshop on Artificial Neural Networks, Lecture Notes in Computer Science. (3512) 1238-1245. Alsina, R.M., Mateo, C., & Socoró, J.C. (2007). Multiresolutive Adaptive PN Acquisition Scheme with a Fuzzy Logic Estimator in Non Selective Fast SNR Variation Environments. 9th International Workshop on Artificial Neural Networks, Lecture Notes in Computer Science. (4507) 367-374. Bas, J., Pérez, A., & Lagunas, M.A. (2001). Fuzzy Recursive Symbol-by-Symbol Detector for Single User CDMA Receivers. International Conference on Acoustics, Speech and Signal Processing. Bas, J., & Neira, A.P. (2003). A fuzzy logic system for interference rejection in code division multiple access. The 12th IEEE International Conference on Fuzzy Systems, (2), 996-1001. Chia-Chang, H., Hsuan-Yu, L., Yu-Fan, C., & Jyh-Horng, W. (2005). Adaptive interference supression using fuzzy-logic-based space-time filtering techniques in multipath DS-CDMA. The 6th IEEE International Workshop on Signal Processing Advances in Wireless Communications, p. 22-26. Glisic, S.G., & Vucetic, B. (1997). Spread Spectrum CDMA Systems for Wireless Communications. Artech House Publishers. Jang, J., Ha, K., Seo, B., Lee, S., & Lee, C.W. (1998). A Fuzzy Adaptive Multiuser Detector in CDMA Communication Systems. International Conference on Communications. Leekwijck, W.V., & Kerre, E.E. (1999). Defuzzification: Criteria and Classification. Fuzzy Sets and Systems. (108) 159-178. Mateo, C., & Alsina, R.M. (2004). Diseno de un Sistema de Control Adaptativo a las Condiciones del Canal para un Sistema de Adquisición de un Receptor DS-SS. XIX Congreso de la Unión Científica Nacional de Radio. Morán, J.A., Socoró, J.C., Jové, X., Pijoan, J.L., & Tarrés, F. (2001). Multiresolution Adaptive Structure for Acquisition in DS-SS Receiver. International Conference on Acoustics, Speech and Signal Processing.

Peterson, R.L., Ziemer, R.E., & Borth, D.E. (1995). Spread Spectrum Communications Handbook. Prentice Hall. Proakis, J.G. (1995). Digital Communications. McGraw-Hill. Verdú, S. (1998). Multiuser Detection. Cambridge University Press. Zadeh, L.A. (1965). Fuzzy Sets. Information and Control. (8), 338-353. Zadeh, L.A. (1973). Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Transactions Systems Man Cybernetics. (3), 28-44. Zadeh, L.A. (1988). Fuzzy Logic. Computer, 83-92.

TERMS AND DEFINITIONS Defuzzyfication: After computing the fuzzy rules, and evaluating the fuzzy variables, this is the process the system follows to obtain a new membership function for each output variable. Degree of Truth: It denotes the extent to which a preposition is true. It is important to not be confused with the concept of probability. Fuzzy Logic: Fuzzy logic was derived from Fuzzy Set theory, working with a reason that it is approximate rather than precise, deducted from the typical predicate logic. Fuzzy Sets: Fuzzy sets are sets whose members have a degree of membership. They were introduced to be an extension of the classical sets, whose elements’ membership was assessed by binary numbers. Fuzzyfication: It is the process of defining the degree of membership of a crisp value for each fuzzy set. IF-THEN Rules: They are the typical rules used by expert fuzzy systems. The IF part is the antecedent, also named premise, and the THEN part is the conclusion. Linguistic Variables: They take on linguistic values, which are words, with associated degrees of membership in each set. Linguistic Term: It is a subjective category for a linguistic variable. Each linguistic term is associated with a fuzzy set. Membership Function: It is the function that gives the subjective measures for the linguistic terms.