DS-CDMA Blind Detection for Frequency-Selective Multipath Channels by Neural Networks

Majid Shakhsi Dastgahian*, Hossein Khoshbin**

majidshakhsi@gmail.com ,Ferdowsi University *

Saeed Shaerbaf*, Alireza Seyedin**

shaerbaf@yahoo.com ,Ferdowsi University *

** Ferdowsi University, khoshbin@um.ac.ir **Ferdowsi University, seyedein@um.ac.ir

Abstract—Up to now, various detection algorithms have been offered and investigated for DS-CDMA systems in multipath conditions. Here, We intend to implement sub-optimum receivers based on Maximum-Ratio-Combining (MRC) via neural network structures in Downlink systems. We will demonstrate that our design based on Radial Base function (RBF) and Multi Layer Perceptron (MLP) outperform in comparison of conventional detectors such as Match-Filter, Decorrelator Detector (DD) and MMSE manner. We also propose a new method when receiver doesn’t know sequence code in CDMA receiver system and illustrate that RBF is proper when number of users are low and MLP is prefer where the number of users increased.

Keywords-multipath channel; neural networks; DS-CDMA; Blind detection; RAKE receiver

I. Introduction

Increment of demands in cellular communication systems has provided verity of transreceive structures and so, such systems are volunteer for high data rate, high quality of services (Qos), low bit error rate, multimedia interaction and so on.

Nowadays, with such a noticeable growth in resource demands, it seems to be indispensable using of minimum of bandwidth. Therefore, one of practical methods looks to be utilizing of Code Division Multiple Access (CDMA).

In this method, there exist several users with a BS in a certain cell. Let's assume a downlink communication here. BS sends data to users with different orthogonal or pseudo orthogonal signatures. In side of receiver, every user multiply received data by own spread code and after preprocessing, detect desired symbols. If channel is modeled as a multipath Rayleigh then, received codes aren't orthogonal together anymore and so, cause to inter-symbol interference (ISI) and also multiuser interference (MUI). There are some ways to combat to ISI and multipath phenomena such as equalization or using RAKE receives. Also, some methods based on neural

networks are candidate for recognizing data inside of such receivers. At first, let in this paper assume codes to be available for all users. We propose to a blind detection based on neural networks by RBF and MLP under the assumption of lake of knowledge about spread code. Note that detection with such a structure can be used in military industrial and eavesdropping systems.

We organized this paper in following: in section II, we consider model of system of CDMA briefly. In Section III, we investigate conventional linear and non linear receivers for CDMA and weak/strong points of such systems. Pattern classifying problem for DS-CDMA is studied in section IV. RBF and MLP networks in DS-CDMA signal detection introduce in section V. eventually, we compare simulation results in section VI based on chip code information (CCI) for two cases: whether spread code knowledge exist or not.

II. Ds-CDMA Channel Model under assumption of synchronous transmission

In general, Multiuser downlink system has been showed in figure 2-1.

Universal transmitted signal model for every user is

( t − 1

Where is n bit in user k, is complex transmitted

Figure 2.1 Multiuser CDMA system

2010 5th International Symposium on Telecommunications (IST'2010)

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signal amplitude which can write as . and are energy and phase of each symbol, respectively. (t − ) denotes user k code during to sending of symbol n where s and s for i≠j are orthogonal and

1 (2)

Where, is received signal delay due to different distances from BS. In general, we can represent as follow:

∑ , m 3N

Where , shows mth chip for user k during a period of

time of symbol n, denotes processing gain and

(t) determines chip shape as gaussian or rectangular. Here we assume , 1,1 and choose PAM for modulation. Also, signal transmissions are done synchronously. That means, … K 0. Channel is modeled as a linear filter with impulse response and given to . If frequency selective channel is consist of discrete multipath components then, it writes as

∑ , . 4

Where, L is number of multipath components and , is complex gain for lth multipath component of user k, and . 0, shows delay of lth multipath component of user k in time period of symbol n. is spread channel delay (under assumption of Tm<T) and is Dirac function. Received CDMA signal in each user, is result of convolution of transmitted signal (1) with channel impulse response in addition to channel additive Gaussian noise and is given by:

∗ t tKN

, ,KNt 5

Where N is number of transmitted data packet, sign of ∗ denotes convolution operator and t is additive white noise with zero mean and power spectrum density of σ2.

It has been showed that match filter outputs are sampled for data detection in every symbol period [4],[5]. Match filter sample for lth path and kth user is

, , 6 T ,T ,

We define output samples of MF as a vector is given by , , , , … , , T €L 7

And rewrite it as a matrix for all of user in form of

T , T , … , KT T €KL (8)

Also we can concatenate them in a total data packet for K users and define as

T T … T N T €N KL (9)

Since the real channel is non ideal, thus chip codes are not orthogonal to each other and so, in receiver side we will have correlation matrix as 1,1 .

Matrix form of received signal in MS is modeled as y = S H A b +w while channel consider synchronous. S is matrix of pseudo noise chip codes of all users and H denotes channel matrix. Also, A and b represent amplitude of transmitted symbols and PAM symbol vector, respectively. w is additive noise vector in entrance of receivers. If channel is frequency selective, we can rewrite this model as y = RCAb + w.

III. Linear and non linear detection for CDMA system

It is easy to estimate impulse response For slow fading channels and it can be assumed to know. In this case, optimum receiver (based on minimum symbol error probability) for user k includes a match filter as ii is convolution of a wave signature, , to impulse

response of channel, . In multipath channels, such a match filter, called coherent RAKE [5],[6].

Output of RAKE receiver for user k in CDMA system achieves by maximum ratio combining (MRC) of MF outputs for different propagation paths which weights for this combination are channel components and they should multiply by spread codes. That is,

∑ ,∗ , 10

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If ISI assumed to be zero, this receiver is optimum. Otherwise, we have to perform data detection by MLSD method. MLSD method is implemented by Viterbi algorithm [7]. We can overcome to ISI by channel equalization methods such as DFE. In fast fading channel, it's not easy to estimate channel response. Therefore, receiver structure might be different in comparison to previous case. In fact, receiver minimize symbol error rate (SER) which is complicated operation [8]. Receiver, in this way, called correlator/estimator, since MLSD is consist of a estimator which estimate received signal free of noise. For performing of computations, we multiply correlation by received signal. This estimator is a linear filter and called Minimum Mean Square Error detector (MMSE).

Verdu [1] discussed over multi user detection (MUD) for such system when channel is known. Minimum error probability in receiver must compute maximum probability of transmitted signal for both, all users and all symbol periods. MLSD multiuser receiver minimizes wrong decision probability for vector b include of all of users. Because of complexity of nonlinear operation, this receiver can't be a simple correlator/estimator anymore. Then in place of it, we propose a multiuser detector which works close to optimum. Linear equalizer multiuser receiver, process match filter output vector, y ( MRC by one linear operator as MRC . One selection for T is and called decorrelator or zero forcing (ZF). This method is stable toward far-near phenomenon in a cell but has high computational complexity especial when number of users in a cell is increased. If we choose another T as MMSE receiver, where σ , in addition to having a decorrelator, we have advantage of removing of multiuser interference, however, under condition of channel and noise power knowledge. In practical application, this receiver designs as adaptive.

Recently, neural networks introduce for nonlinear receivers. Neural networks use simple parallel weighted processors. Due to such a parallel structure, neural network trains under a decision boundary formula readily and so, learning property becomes compatible and resistant. Receivers based on neural networks works as adaptive and might outperform rather than some linear and nonlinear conventional receivers. For instance, MLP networks propose to data detection under AWGN channel restriction in [9]. Also, SOM in [10] and RBF in [11] have been studied in this field.

IV. Pattern classification problem for DS-CDMA

If interpret received vector geometrically, then we can say it as a classification problem. Signals can be denoted as orthogonal basis. So, we can write y(t) = ∑ x Φ t where Φ t orthogonal basis and x desired vector component. For resemblance testing of signals we can use Euclidean metric and inner product. So, more resemble signals usually classify in the same class. Euclidean distance between two vectors, , is denoted by d(x,y) = ∑ . We can also define inner product in another way as < x,y > = ∑ . Relationship between these methods is that when maximize inner product then it means minimize Euclidean distance and vice versa. If two classes Ω1 ,Ω2 represent +1,-1 classes respectively, it obtains a linear separator as wTΦ x 0 Ω1 (11) , wTΦ x 0 Ω

Let b is nth detected bit in CDMA system as followed b A b s t σn t , sK 12

Then, for user 1 and user 2 we have b b A b A b ρ n′ t 13

V. RBF and MLP structures A. Neural networks based on radial basis

RBF and MLP networks use to categorize of discrete pattern, function approximation, signal processing and any application which maps input to output and its structure is consist of input layer, radial basis hidden layer and output layer. ith neuron in first layer test distance between input vector, x, and weight vector, v, and by stimulus function, φ x where is usually gausian, detect output. Spread factor in this network, σ, shows norm of difference between weight vector and input vector and it determines experimentally. Output layer operate linearly and map result of hidden layer into output layer. Therefore, y ∑ w φ x j1, … , n , where φ x exp T i1, … , c denotes activation function and w is ith weight from ith hidden neuron to jth output neuron and n is total number of output neurons. The adjustable parameters

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Figure 6.1) performance for 10 users with 2 multipath channel and chip code 16

Figure 5.1. An RBF network with one output.

include mean square error (MSE), spread factor, and number of neurons which can be added to hidden layer for satisfying of error condition in every step.

Figure 5.1 illustrates an RBF network with inputs x , … . , xK and output y. The arrows in the figure symbolize parameters in the network. The RBF network consists of one hidden layer of basis functions, or neurons. At the input of each neuron, the distance between the neuron center and the input vector is calculated. The output of the neuron is then formed by applying the basis function to this distance. The RBF network output is formed by a weighted sum of the neuron outputs and the unity bias shown.

B. Neural networks based on back propagation error

Such a network is one of the most applicable tools for pattern classification and resolving of nonlinear problem. Back propagation networks are necessarily multilayer perceptrons (usually with one input, one hidden, and one output layer). In order for the hidden layer to serve any useful function, multilayer networks must have non-linear activation functions for the multiple layers: a multilayer network using only linear activation functions is equivalent to some single layer, linear network. When a learning pattern is clamped, the activation values are propagated to the output units, and the actual network output is compared with the desired output values, we usually end up with an error in each of the output units.

Figure 5.2 shows a typical MLP structure with different layers. It has some benefits such as high training speed, and don't fall to local minimum. Initial weights of Different layers usually select randomly in interval of [-1,1].

VI. Simulation result

In this paper, we find number of error bits for Match filter, decorrelator and MMSE receivers when we send 20000 data bit. signal in entrance of MF is modeled in

matrix form as y = S H A b + w(t) where, y is received vector, S is spread code matrix for users, H is channel matrix and A , w are amplitude of transmitted signal in form of a diagonal matrix and additive Gaussian noise vector, respectively. Also b is modulated data vector for all users. Dimension of mentioned parameters are respectively as follow. , K, K K, K , K , K where K is number of total users and m is pseudo noise spread code. For simplicity, we consider PAM for modulation. Here, we perform simulation for K=4,6,,8,10,12 and m=7,15. After receiving of data vector, we combine received signals from different path with special weights and make a RAKE receiver. Thus, we assume that receiver know about channel coefficients. Channel components for frequency selective conditions choose as [1 0.5 0.25]. that means, we have three path for propagate of transmitted signal. Also, here we suppose don't have delay for different path and so, all of them reach together. We consider Matrix P as P= for obtaining maximum ratio combining. Then received signals multiply by specified CDMA codes and finally they applied to a comparator for recognizing sign of bits. Since transmitted signals reach to receiver from multi path simultaneously and they can combine together, thus, there exists correlation between received signals and so, MF is not a proper way to remove correlation anymore. Also, decorrelator and MMSE methods don't have

Figure 5.2 a typical MLP structure

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Suitable performances while number of users increased. In comparison to such a conventional structure, neural networks such as RBF and MLP are suitable because they learn by training how determine weights for specifying threshold level and so can recognize better, the sign of transmitted bits. For training of RBF we use of toolbox of MATLAB.

The Simulation results are showing that proper Spread factor for RBF is 0.85. Initial number of neurons equal to 10 and it can be increased dynamically if it doesn’t satisfy MSE restriction.

Here, we consider maximum training error equal to 0.001. Initial weights are selected randomly and we have three layers for neural networks. SNR is chosen to be 0dB to 30dB.

Figure 6.1, 6.2 compare two different non linear receivers based on RBF and MLP as compared to conventional receivers when receivers know the sequence code or they don't have any knowledge about sequence code. Number of users supposed to be 4,6,8,10 and 12 and SNR vary from 0 to 25dB,30dB for them. For every user, one 16 chip code multiplies by symbols and then transmitted over channel. Such a code is selected as a semi orthogonal. Here we use a pseudo noise sequence (PN-S) for spread code. As we can see in figure 6.2, RBF method outperforms MLP and even MMSE for K=4. One of the interesting result in this figure is that MLP blind has a lower BER than MLP. It means that we can design a simple receiver without knowing the chip code information (CCI). Figure 6.1 plotted for K=10 and we understand that method of MLP has a good training when number of users increased. Also, MLP Blind outperforms nonlinear and even linear receivers such as MMSE considerably.

Figure 6.3 shows diagram of error probability variations in terms of user increment in a eight PN chip code when channel is frequency selective with two path

in every link. One can infer that RBF network is optimum when numbers of users are low, while MLP will be dominant network as number of users increased. Totally, MLP and RBF outperform MF and DD and are near to MMSE detection. Eventually, figure 6.4 represents diagram of error probability in terms of user growth when channel has no multipath and number of chip of PN is 16. As we can observe, MLP and Blind MLP have a behavior close to MMSE.

VII. Conclusion

We investigate nonlinear receiving in DS-CDMA systems based on RBF and MLP and compare their performances to conventional receivers such as MF, DD and MMSE. Results showed that proposed methods outperform when number of users are increased and they can be acceptable methods when we have blind detection. That means these systems can implement in eavesdropping applications.

Figure 6.2) performance for 4 users with 2 multipath channel and chip code 16 Figure 6.3) Total performance for different users with 2 multipath

channel and number of chip codes 8

Figure 6.4) Total performance for different users with 1 multipath channel and number of chip codes 16

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References: [1] Verdu S (1984) Optimum multiuser signal detection. Ph.D.

thesis,Department of Electrical and computer Engineering,University of Illinois at Urbana-Champain, Illinios,USA.

[2] Stojanovic M,Prokis JG & Catipovic JA (1995) Analysis of impact of channel estimation errors on the performance of a decision feedback equalizer in fading multipath channels. IEEE Transactions on Communications 43(2/3/6) :p 877-886.

[3] Khuram. V, Fathi M. (2005) Blind Information-Theoretic MultiUser Detection Algorithms for DS-CDMA and WCDMA Downlink Systems. IEEE Transaction on neural network.Michigan Uni, USA

[4] Verdu S (1986) Minimum probability of error for asynchronous Gausian multiple-access channels. IEEE Transaction on Information Theory 32(1): p 85-96.

[5] Mahendra.C, Puthusserypady.S (2006) Multiuser Receiver for DS-CDMA Signals in Multipath Channels: An Enhanced Multisurface Method. IEEE Transaction on neural network. National University of Singapore.

[6] Forney GD (1972) Maximum-likelihood sequence estimation of digital sequence in the presence of intersymbol interference. IEEE Transaction on Information Theory 18(3)

[7] Forny GD (1973) The Viterbi algorithem. Proceedings of IEEE 61(3): p 268-278

[8] Prokis JG (2008) Digital communications. McGraw-Hill, New York City, New York, USA, 3rd edn

[9] Ibnkahla M (2007) Neural Network Modeling and Identification of Nonlinear MIMO Channels. Electrical and Computer Engineering Department Queen's niversity Kingston Ontario K7L3N6 Canada

[10] Hottinen A (1994) Self Organization multiuser detection. Proc.IEEE International Symposiem on Spread Spectrum Techniques and Application (ISSSTA), Oulu, Finland, 1: p 152-156

[11] Bhanja. I (2006)Performance evalution of Phase Optimized Spreading codes in Non-linear DS-CDMA Receivers. Thesis. National Institue of Technology,Rourkela.

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