Neural Networks in Wireless Communications

Transcription

1 1 Neural Networks in Wireless Communications Keerthi Ram, MS 2006, IIIT Hyderabad Abstract Neural processing presents a different way to store and manipulate knowledge. It uses a connectionist approach, where connections emphasize the learning capability and discovery of representations. This work presents a study of the application areas for neural networks in wireless communication. Despite its capability to act as a black box and model systems using learning, domain knowledge is required to apply neural networks successfully in wireless communications. Considered in this work are neural network based adaptive equalization, field strength prediction in indoor networks and microstrip antenna design using neural networks. This provides non-linearity at a granular level to the neuron. The neural network is formed by such neurons arranged in layers as shown in fig. 2. Neurons of one layer fan out their output to the input of every other neuron in the next layer. All connections between neurons are weighted. The neural network thus can be viewed as having one input layer, where the input vector X is applied, one ore more hidden layers, and an output layer formed by m neurons. The output vector is thus of size m. Index Terms neural network applications, wireless communications, antennas, channel equalization A I.INTRODUCTION N artificial neural network (ANN) is a network of artificial neurons. Artificial neurons model the simple characteristics of neurons in the brain. Each neuron receives signals from other neurons through special connections called synapses. Some inputs excite the neuron, others inhibit it. When the cumulative effect of the inputs to a neuron exceeds a threshold, the neuron fires a signal to other neurons. Similarly an artificial neuron receives a set of inputs X=[x1,x2,...,xn], each coming through an in-bound connection. Connections have weights, and each input is multiplied by the weight of the connection it comes along. At the neuron, the weighted inputs are summed. If the weights are arranged in a vector W=[w1,w2,...,wn], then the computation of the neuron is precisely the dot-product p=x.w The neuron applies an activation function f on the dot-product to get its output y, given by y=f(p). The activation function is ideally shaped like the sgn function, but in reality the sigmoid function or tanh is used. Fig. 1. Structure of a neuron Manuscript received October 20, This work is part of the course requirements of EC 4321 Wireless Communications, Monsoon Fig layer neural network The learning aspect of the ANN is by virtue of the weighted connections. The neural network is trained using several training samples, and the error at the output, equal to the L2 norm of the expected and the observed output, is minimized by modifying the weights of each layer from the output layer proceeding backwards to the first hidden layer. A simple gradient descent approach is used, having the squared error (MSE) as minimization criterion. This weight correction is done by the neural network itself, and is hence self-organizing. An epoch in training consists of one cycle of all training samples sequentially applied to the ANN. Several epochs are applied until the squared error is minimized to a value below the desired MSE (typically 10-4 ) Once trained, ANNs have learned the mapping between the input and output, and can generalize to model the system whose behavior characterized the inputs and outputs. The capability of the ANN was proven by Kolmogorov [6] in his mapping-neural-network-existence theorem stating that any continuous function from the n-dimensional cube [0,1] n to the real numbers R can be implemented exactly by a three-layer neural network with n inputs, 2n+1 hidden neurons and m output neurons. Neural networks can in consequence be considered as universal function approximators.

2 2 A.Overview II.CHANNEL EQUALIZATION Wireless data transmission channels distort data signals in both the amplitude and phase, causing Inter-symbol Interference (ISI). This distortion causes the transmitted symbols to spread and overlap over successive time intervals, causing the information content also to spread among these symbols. Other factors like co-channel interference (CCI), multipath fading, cause further distortions to the received symbols. Signal processing techniques used at the receiver to overcome these interferences, so as to restore the transmitted symbols and recover their information are referred to as equalization methods. directed mode the tap gains are corrected based on a LMS gradient descent. The input to the decision device is a weighted sum of the delayed samples. Decision error is used in updating the tap coefficients. B.Methods Channel equalization algorithms are generally divided into two. The Most common one is performed by sending training sequences into the channel. The training sequences are known also at the receiver end. So by observing the changes at the receiver end, it is possible to extract the impulse response of the channel. Therefore at the receiver side, the inverse of the channel is applied, and the sources are recovered. The above described equalizer is called the zero-forcing (ZF) equalizer. ZF equalizers ignore additive noise, and may significantly amplify noise for channels with spectral nulls. The other method which does not use a training sequence is called blind channel equalization. Equalizers can be implemented as linear filters, or using non-linear methods - decision feedback. In training-based equalization, the viterbi algorithm is used after estimating the channel. Fig. 3. Block diagram showing noise and CCI, and the receiver structure for equalization The optimum linear equalizer was shown to be given by a filter matched to the channel and transmitter in cascade with a periodic filter that can be realized with a tapped delay line[1]. The viterbi detector is a non-linear recursive processor. It requires that ISI at the sampler output be limited to a finite number L of symbols (can be thought of as estimating the state sequence of a finite state markov process observed in memoryless noise) The adaptive LMS equalizer shown in fig. 4 is used in nonlinear operation. The processor consists of a tapped delay line in which the tap coefficients are modifiable. The equalizer operates in training mode to adjust using the preamble symbols and adapt to changing channel, and in decision Fig. 4. Adaptive LMS equalization The input to the decision device is the dot-product of the tap coefficients and the delayed samples. The weight correction is strikingly similar to the weight updation in a single neuron of a neural network. The maximal likelihood (ML) sequence receiver performs

3 ML detection on the entire data sequence. It is simpler than non-linear processors, but its complexity grows at O(L M ) where L is the number of interfering symbols. (For rather small values of L and M the implementation becomes impractical) A suboptimal modification to the ML sequence detector can be drawn from a reduced state viterbi algorithm instead of considering at each recursive step all possible sequences, eliminate all but the few likely ones. The Decision feedback equalizer (DFE) is such a pre-filter to reduce the complexity of the viterbi detector. The action of the DFE is to feedback a weighted sum of past decision to cancel the ISI they cause to the present signaling interval. The Least mean-square DFE is structured as shown in fig. 5. It consists of a T/2-spaced feedforward FIR filter, and a T- spaced feedback filter. The feedforward and feedback tapped delay lines contain Nf and Nb tap coefficients respectively. This equalizer is denoted as LMSDFE (Nf, Nb). If there is no feedback Nb, then the structure reduces to a linear equalizer is made negligible, SIR=100 db. And if system is studied in CCI, then AWGN is made negligible, SNR=100 db. Training length in symbol periods is 200 for LMSDFE and 1000 for MLPDFE. Data frame length, including the training period is 2000 symbol periods. Simulation experiments were run over ensembles of upto 5000 independent trials. Convergence performance of LMSDFE and MLPDFE for the case of SNR=15 db is shown in fig Fig. 5. LMS decision feedback equalizer A neural network based equalizer can be built on the same principle. It would consist of a three-layer MLP(multilayer perceptron) whose input signal samples are identical to that of the conventional equalizer. The input signal to the MLP equalizer consists of the Nf and Nb data samples in the feedforward and feedback tapped delay lines of the equalizer, respectively. This equalizer is denoted as MLPDFE((Nf,Nb), N1, N2) where N1 and N2 are the number of neurons in hidden layers 1 and 2 respectively. Fig. 7. Bit Error Rate (BER) vs. output Signal-to-interference ratio (SIR) Fig. 7 shows that when the parameters of the neural network are suitably configured, then performance converges with that of the LMS DFE. The modifiable parameters for the MLP are learning rate (also referred to as step size), number of neurons in the hidden layers. In high noise or interference situations the MLPDFE performance matches or surpasses the LMSDFE. W.K.Lo et al conclude that size of neural network impacts greatly the performance of the equalizer. D.Linear time series prediction Another way to look at the DFE is as a one step linear predictor. Consider the system shown in fig. 8. Fig. 6. Neural Network DFE The input layer has Nf + Nb nodes. The MLP equalizer generates at the symbol rate a single output which is the input to the decision device. C.Performance The effects of CCI and AWGN were considered separately by W.K.Lo et al[3]. If system is studied in AWGN, then CCI Fig. 8. Feedback Filter of DFE In Fig. 8, the following quantities are at play dk = sk xk dk^ = sk xk^ = dk + xk xk^ bk = gk * dk^ zk = sk - bk

4 4 Define ek = zk xk ek = sk bk xk = sk xk bk = dk bk = dk (gk*dk^) Assume that the previous n estimations are correct, then x k-n = x^k-n for 1<=n <= N and d k-n = d^ k-n thus, ek = dk (gk * dk^) = dk * (δk gk) Then the feedback filter is precisely the one step linear predictor of of dk based on exact knowledge of dk-n for n = 1 to N. Neural networks are well suited to the problem of linear prediction, and the role of neural networks in the DFE can be viewed from this perspective also. b) Local shielding effects 4) Influence of the location of the receiver site a) Loal reflectors b) Local shielding effects c) Shape of the room of the receiver d) size of the room of the receiver Measurement and quantization of all these parameters is discussed in [5]. Training samples consisted of about 5000 patterns including measurements in different transmitter and receiver environments. The statistical distribution of each input parameter should be homogeneous, so measurements in a lot of environments is necessary. III.FIELD STRENGTH PREDICTION A.Introduction Indoor wave propagation depends on several parameters such as structure of the building, material of the walls, location of the transmitter, carrier frequency, and several more. A number of empirical and deterministic (ray-optical) models have been developed for field value prediction in indoor environments. G.Wolfle and F.M.Landstorfer present an artificial neural network based model for the prediction of electric field strength. Their work reports a higher accuracy, owing to the possibility to consider parameters which are difficult to include in analytic equations. The neural network model is independent of time variation effects, and the generalization capability is well served in this problem. In the model constructed by G.Wolfle et al[5], each point in an area is predicted as a single point, and independent of neighbouring opints. This leads to smaller computation time. The input to the neural network include several parameters about the point at which the field is to be predicted. The output of the neural network represents the field strength at that point. The neural network is trained with measured field strength values inside buildings. B. Parameters of the model The parameters of the prediction model can be subdivided into four groups: 1) General parameters a) free space attenuation (distance, frequency) b) Visibility (LOS, OLOS, NLOS) 2) Influence of the walls between transmitter and receiver a) Transmission loss of the direct ray b) waveguiding effect of the walls 3) Local arrangement of the walls at the transmitter site a) Local reflectors Fig. 9. Structure of neural network for field strength prediction Using a network structured as in Fig. 9, G.Wolfle et al were able to obtain a mean error of 0.2 db and standard deviation of 3.5 db IV.ANTENNA DESIGN Most wireless phenomena like the design or analysis of antennas, estimation of direction of arrival, adaptive beamforming techniques, have quite a nonlinear relationship with their corresponding input variables. Neural networks can be used in these areas - microstrip antenna analysis and design, wideband mobile antenna design. A.Low Profile Antennas When antenna occupies appreciable volume a compact wireless device, and as transceivers are integrated into other devices, accurate characterization of antenna becomes necessary for the device's high performance. Analysis of parameters such as input resistance, bandwidth, resonant frequency of different regular shaped microstrip antennas have been modeled using neural networks [7]. Accuracy and simplicity were the key features of these networks, making ANN candidate for use in CAD algorithms.

5 5 a(mn) h(mn) є m n Fmn [6] K. Homik, M. Stichcombe, and H. While, "Multilayer Feedforward Networks are Universal Approximators," Neural Networks,2, 1989, pp [7] A.Patnaik, D.E.Anagnostou,R.K.Mishra, Applications of Neural Networks in wireless communications, IEEE Antennas and Propagation Magazine, Vol. 46, No. 3, June 2004 [8] H.Jaeger, H.Haas., Harnessing nonlinearity: predicting chaotic systems and saving energy in wireless communication, Science magazine,vol. 304, No. 5667,pp 7880, April 2004 [9] LiMin Fu, Neural Networks in Computer Intelligence, ISBN , 2003 Fig. 10. Microstrip Antenna design using Neural Networks - parameters are the side length, substrate height, dielectric constant, and mode numbers B.Arrays and Smart Antennas Arrays use multiple antenna elements to achieve enhanced performance, including high gain. They can also support electrical beam steering to improve transmission and reception. Neural networks have been successfully applied to direction-of-arrival estimation and beamforming for antenna arrays [7]. Radial basis function (RBF) neural networks are used in this case. RBF's differ from MLP in that the activation function at a neuron can be considered as the vector gaussian having the in-bound weights as mean, and the input vector as the random variable. The activation function is the vector gaussian distribution function. The weights are self-adjusted by using the k-means clustering technique. V.CONCLUSION Neural networks are mathematical models for a selforganizing and learning black box, which is a universal function approximator and time series predictor. Neural networks are built based on domain knowledge and can be used for causal modeling of systems in uncertainty and noise. Wireless communication systems present ample scope for neural networks to be applied, but performance of the neural network depends on fine tuning the parameters to the network, and proper quantization of inputs. REFERENCES [1] C.A.Belfiore, J.H.Park.Jr, Decision Feedback Equalization in Proc. August [2] D.Jianping, N.Sundararajan, Communication channel equalization using complex-valued minimal radial basis function neural networks, IEEE trans. on Neural networks, Vol 13, No. 2, May 2002 [3] W.K. Lo, H.M.Hafez, Neural network channel equalization, Intl. Joint Conference on Neural Networks, 1992 [4] S.U.H. Qureshi, "Adaptive Equalization", Proc of IEEE, vol. 73, no. 9, Sept 1985 [5] G.Wolfle, F.M.Landstorfer, "Field strength prediction in indoor environments with neural networks", in IEEE 47th Vehicular Technology Conference (VTC) 1997, Phoenix, AZ, pp , May 1997