sequential pn acquisition scheme based on a

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Sequential PN Acquisition Scheme Based on a Fuzzy Logic Controller 1239

Fig. 1.Serial search strategy for spread spectrum acquistion

Fig. 2.AD-TLC acquisition scheme[4]

Firstly, the threshold level will be set to a constant value, without takinginto account the received signal power or the noise level. Despite it is not anoptimal solution when working with a fading channel, it is the most used inconventional systems due to its simplicity. The second approach was presentedin[4] with some approximations to Automatic Decision Threshold Level Control(AD-TLC) (see figure2).

There are some differences between both structures. The AD-TLC consists

on two branches of a serial search model, controlled by different versions of thesame PN sequence. The aim of the structure is to reach acquisition in the upperbranch and the lower branch is used as a noise power reference, preventing bothbranches from being acquired simultaneously. This brings us to the ConstantFalse Alarm Algorithm (CFAR)[4].

The goal of CFAR algorithm is to adapt the threshold value dynamicallyto keep a parameter called Pfa

1 in a constant value. In that algorithm [4] thedesired Pfa is set by the quotient

rR

where r and R are integer parameters setby the controller. So the algorithm operates in the following way:

The parameter y = min(ener1, ener2) is evaluated at each integration timed where ener1 and ener2 are the energies of both branches. This value isused as an estimation of the received noise level.

1 False Alarm Probability.


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1240 R.M. Alsina, J.A. Moran, and J.C. Socoro

After R integration times, y will resume the number of times that the noiselevel is being over the threshold. The quotient y

Ris an estimation of the Pfa,

which optimum value is rR

. The current threshold is increased if the estimated Pfa is greater than the

desired or decreased if its lower.

This algorithm has been tested over the ionospheric communication channelpresented in [11]. The results show that the acquisition scheme is too slow inmost situations. This can be overcome by the use of an adaptive step dependingon the difference of the instantaneous Pfa and the desired one. Another problemof this algorithm is that the control system waits R integration times to operate,so there is a compromise between the tracking speed and the robustness of theestimations.

Our proposal to improve the behaviour of the receiver is a dynamical estima-tion ofPfa using a low pass filter (LPF). This filter dynamically estimates themean value of y, so the computation time is then reduced. The knowledge of thedynamical response of the filter will help us in the controller design, choosing aclassical PI2 controller will be used for this purpose.

Some differences are shown between the features of the original CFAR con-troller and our improved system, because the problem of the original CFAR is itshigh dependence on the parameters R and r. The use of a low-pass filter providesa robust and dynamical estimation of the Pfa, improving the acquisition time.

Other possibilities have been investigated to improve the results achievedwith the PI controller. Fuzzy logic controllers offered better results but theyneeded higher computational load.

3 The Fuzzy Logic Controller

Up to this point we have to deal with the problem of setting the correct threshold.This can be achieved with a CFAR algorithm as we have seen in the previous

section. Nevertheless, the use of this serial search scheme does not offer theoptimum performance. Its response highly depends on the channel variabilityand this difficults the design of the parameters of the serial search acquisitionsystem.

A symbol time can be considered as a good choice for the integration time (d)as results show. On the other hand, it also simplifies the design of the receiverblocks. Nevertheless, depending on the transmission conditions (SNR) this timemay not be enough. At low signal to noise ratios a longer time must be used.The use of a sequential algorithm can overcome this problem using a variable

integration time depending on the measures reliability.It is known in [2] than the sequential method is optimum at known signalto noise ratios (SNR). This is not the case through a ionospheric channel asdeep fading cause high SNR fluctuations [11]. Nevertheless, the structure of the

2 Proportional integral.


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receiver provides a measure of the received noise level. This value can be usedto improve dynamically the system performance.

In a serial search method the decision is just taken depending on the measuredvalue against the threshold. If it is higher an acquisition state is set and the other

way round. A few amount of information is being used so the performance is farfrom the optimal. A logical reasoning system based on fuzzy logic theory [5,6]has been developed to improve the system results using the knowledge aboutthe channel. The reasoning system consists in a set of logical laws that generatea final decision [7]. Other examples of fuzzy logic applied to spread spectrumcommunications can be found, especially working in detection[9, 10].

In our case the result of the fuzzy logic controller is a variable actresult [0, 2]and its value is proportional to the probability of being acquired: on low proba-bility of acquistion situations a value lower than the one is generated depending

on the input values and the other way round. Each integration time da sequencedec[n] =dec[n1] actresult is updated. Considering the case of boundary valuesfor the variable, some limits have been set using the channel behaviour knowl-edge. If the sequence value is higher than 1.8 an acquisition state is set. On theother hand, a non-acquisition state is reached if the sequence is lower than 0.2.For example, if the fuzzy logic controller gives a value equal to 1.9 an acquisi-tion will be set only in one step. Otherwise the system waits for another value.Depending if it is greater or lower than the one the sequence will increase ordecrease its final value. A positive slope will take us to an acquisition state and

a negative slope to a non-acquisition.

Fig. 3.Result computation for the fuzzy logic controller

Finally, we must design the rules to set an optimal reasoning control logic.In our case four rules have been used. More rules can be added if necessary onfuture implementations. However, the use of a great set of rules will increasethe computational cost, so we must take care about this fact. In figure3we can


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Fig. 4.actresult in function ofener1 and ener2

see the fuzzy logic controller implemented. Three different parameters controlthe acquisition algorithm as can be seen in figure 3. The variables used in thecontroller are the ratios ener1

threshold, ener2threshold

and ener1ener2

. The variables were selected

using the knowledge about the system performance.The input variables are used in the following way:

The first law uses the ratio ener1threshold

and ener2threshold

. If the first ratio is greaterthan one and the second one is lower there is a high probability of beingacquired.

The second law is active when ener1 is near the threshold. Then the ratioener1ener2

is compared to one. If it is bigger than one the system is probablyacquired, but maybe the threshold is not set on its optimum value, i.e. there

is a fading. If ener1 is lower than the threshold and

ener1ener2

is nearly one it shows thanboth measures of energy are nearly equal and lower than the threshold. Thesystem is in a non-acquisition situation.

Similar to the one above but now ener1ener2

is greater than one. The thresholdis not correct but we may be acquired, as there is a great difference betweenener1 and ener2.

The results will be obtained using a defuzzyfication method based on the

centroid [8]. The parameters have been used in order to generate a set of lawsthat control the acquistion system. The advantage of this system is that someimpossible situations in asingle dwellcan be evaluated. The use of three differentparameters gives us more information about the channel state and we can applya different criterion depending on the values of this parameters as figure 4shows.As a conclusion the reasoning capability of the receiver has been increased.


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4 Results

In this section the results obtained with the new acquisition approach will besummarized. One of the most severe problems found was that the variations on

the signal to noise ratio had a direct influence on the performance of the system.The results obtained with this new system offer better stability to the acqui-

sition system. In the ionospheric channel it is very important to keep acquireduntil there is an evidence of being lost. This needs to have a system evaluatingthe situation and taking the suitable decision. On the other hand, the reliabilityof the measures is not always the same, because it depends on the channel state.The sequential algorithm takes a variable time to conclude the acquisition statedepending on the channel conditions. If we have a good signal to noise ratio ashort time will be used. On the other hand we will wait until we are sure about

the decision.The final implementation of this new approach has increased the mean time

of the system remaining acquired. Simulations have been done up to -17dBsof signal to noise ratio and good results have been obtained through a whitegaussian channel. Obviously, the results are better than those of the CFARalgorithm. In the figure 5 we can see some results of the proposed algorithmcompared to the CFAR.

Fig. 5.Mean time of acquisition pdfs for CFAR and Fuzzy Logic Controller

As we can see, the mean time of acquisition is highly improved with the newapproach. Its also important to remark that the Pfa is even decreased with theuse of the new approach. Nevertheless, at low SNR the algorithm is a bit slowerin the initial synchronization due to the fuzzy logic controller.


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5 Conclusions

Up to this point we have seen the process to develop the new proposed acquisitionsystem and some results have been compared against other strategies. The main

advantage of a sequential fuzzy logic based algorithm is its robustness. When itis acquired it is really difficult to leave this state even with low signal to noiseratios. This is very important when working with the ionospheric channel as theSNR is variable with time.

To fight against this problem the system uses a time varying integration.Depending on the conditions a variable is generated as an indicator of the prob-ability of being acquired. This variable is modified on a sequential way reachinga great value of confidence. Then the system makes the decision. Although itsgood response when the system is acquired we should take into account that the

first acquisition time is just a bit higher. This is not an important fact in ourchannel and in our application. The reason is that the first acquisition is goingto happen fewer times than the reacquisition so we have an improvement on thetotal mean value. On the other hand, when a non-acquisition happens there areoptimal strategies to search the correct position.

There are very important points that we must take care about. The computa-tional load of developing a fuzzy logic controller on a DSP is very important. Themean number of FLOPS needed to do all the process related to fuzzy controlleris greater compared to the conventional serial search system (including CFAR

algorithm). In our experiments, we have used the received samples of the iono-spheric transmission and we have processed them offline on a PC. Nevertheless,it is important to remark that some criterions can be used on the design of thecontroller to reduce the total number of operations. Some of them have alreadybeen used, and others will be implemented in future work, but the number ofFLOPS is still too high.

As a final conclusion a new proposal for acquisition system with very goodperformance on a highly varying channel has been proposed. We must remarkthat although the cost is high over a serial search method is far away from the

cost of a parallel strategy. On the other hand a new line of investigation hasbeen opened to motivate the use of logical reasoning systems on the acquisitionschemes. In our opinion the fuzzy logic theory is the best way to transfer theexpert knowledge about the channel to a set of logical rules.

References

[1] M.K.Simon, J.K.Omura, R.A.Scholtz, B.K.Levitt: Spread Spectrum Communica-tions Handbook, McGraw Hill, 1994.

[2] R.L.Peterson, R.E.Ziemer, D.E.Borth: Spread Spectrum Communications Hand-book, Prentice Hall, 1995.

[3] S.G.Glisic, B.Vucetic: Spread Spectrum CDMA Systems for Wireless Communi-cations, Artech House Publishers, 1997.


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[4] S.G.Glisic: Automatic Decision Threshold Level Control (ADTLC) in Direct Se-quence Spread Spectrum System based on Matched Filtering, IEEE Transactionson Communications, Vol. 36, No. 4, April 1991.

[5] L.A.Zadeh: Fuzzy Sets, Information and Control, Vol. 8, pages 338-353, 1965.

[6] L.A.Zadeh: Fuzzy Logic, Computer, p. 83-92, April 1988.[7] L.A.Zadeh: Outline of a new approach to the analysis of complex systems anddecision processes. IEEE Transactions Systems Man Cybernetics, 3, 28-44, 1973.

[8] Werner Van Leekwijck, Etienne E. Kerre: Defuzzification: Criteria and classifica-tion. Fuzzy Sets and Systems 108, 159-178, 1999.

[9] J.Jang, K.Ha, B.Seo, S.Lee, C.W.Lee: A Fuzzy Adaptive Multiuser Detector inCDMA Communication Systems, International Conference on CommunicationsICC1998.

[10] J.Bas, A.Perez, M.A.Lagunas: Fuzzy recursive Symbol-by-Symbol detector forsingle user CDMA receivers, ICASSP 2001, Salt Lake City (Utah-USA).

[11] J.Ll.Pijoan, C.Vilella, J.R.Regue, J.C.Socoro, J.A.Moran: DSP-based ionosphericradiolink using DS-SS, COST-262 fourth management comitee meeting, 22-23november 1999, Barcelona (Spain).

[12] J.A.Moran, J.C.Socoro, X.Jove, J.L. Pijoan, F. Tarres: Multiresolution AdaptiveStructure for acquisition in DS-SS receiver, ICASSP 2001, Salt Lake City (Utah-USA).

[13] C.Mateo, R.M.Alsina: Diseno de un sistema de control adaptativo a las condi-ciones del canal para un sistema de adquisicion de un receptor DS-SS, XIX Con-greso de la Union Cientfica Nacional de Radio, URSI2004, Barcelona (Spain).

sequential pn acquisition scheme based on a

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