Chapter 2 Channel Equalization

Chapter 2 Channel Equalization 2.1 Introduction In wireless communication systems signal experiences distortion due to fading [17]. As signal propagates, it follows multiple paths between transmitter and receiver. Every path introduces varying amount of phase shift, delay, attenuation and spreading in the signal components known as multipath induced fading. As a result, receiver receives multiple copies of the transmitted signal that gives either constructive or destructive interference. In constructive interference in phase signal components adds up and gives increased strength of received signal. In destructive interference out of phase signal components cancel each other and reduces strength of the signal. Fading channel models are used to test the communication systems under mobile environment [18, 19]. 2.2 Architecture of data transmission system In last couple of decades digital communication has experienced a massive growth. Communication equipments are becoming smaller, lighter and less energy consuming. It is expected that equipments should be more reliable, more robust and more economic in terms of spectrum use and operating at higher data rates [20]. The structure of the digital communication system is shown in the Fig. 2.1. Noise Input Transmitter Channel + Receiver Decision device Output Fig. 2.1 Structure of the digital communication system High speed data transmission over communication channels subject to interference and noise. The interference is usually the result of the restricted bandwidth of the channel and/or the presence of multipath distortion in the medium through which the information is transmitted. Equalization process reconstructs the transmitted data jointly removing interference and noise in the communication links. 9

Wireless channels are nonstationary, non predictable, nonlinear and time variant. When two or more copies of transmitted signal arrive at the receiver in slightly different times, they interfere and cause fading. The distortion is unknown so corrective system has to identify and continuously adapt to the time varying channel. Such a system is called an adaptive equalizer. The equalization problem has received great attention and different solutions to this problem may be found. 2.3 Structure of channel equalization system Adaptive equalizers may be supervised and unsupervised equalizers. In supervised equalizers it is necessary to excite the system periodically with a known training or pilot signal interrupting the transmission of useful information. A replica of this pilot signal is available at the receiver and the receiver compares the response of the system with input in order to update its parameters. Some communication systems like digital television or digital radios do not provide the scope for the use of a training signal. In this situation the equalizer needs some form of unsupervised or self recovery method to update its parameters are called blind equalizers. Recent advances in signal processing techniques have provided a wide variety of nonlinear equalizers [21]. In nonlinear channels with time varying characteristics, nonlinear equalizer provides better performance than linear equalizers because of their nonlinear decision boundaries [22]. Fig. 2.2 Channel equalization in a communication system Fig. 2.2 shows the use of adaptive equalizer for channel equalization in a communication system. An adaptive filtering algorithm requires the knowledge of the desired response so as to form the error signal needed for adaptive process to function. The transmitted sequence is the desired response for the adaptive equalization. In practice, an 10

adaptive equalizer is located at the receiver and is physically separated from the origin of its ideal desired response. One method to generate the desired response locally in the receiver is the use of training sequence in which a replica of the desired response is stored in the receiver. Naturally the generator of this stored reference has to be electronically synchronized with the known transmitted sequence. Second method is decision directed method in which a good facsimile of the transmitted sequence is being produced at the output of the decision device in the receiver. If this output is correct transmitted sequence then it is used as the desired response for the purpose of adaptive equalization. 2.4 Wireless fading channel modeling The field of mobile communication is changing the way of people interaction in their daily lives. The wireless industry has deployed an infrastructure for providing different services to the users. The design, production and deployment of such technological infrastructure require high cost therefore manufacturers search for different alternatives to avoid high cost. One of the alternatives is simulation of real wireless systems. Simulation allows less expensive testing of designs [23], [24]. The mathematical model of the channel is based on deployed transmission media and environmental conditions. Fading is the distortion added in modulated signal by channel influences. In wireless communication systems rapid fluctuations of the phase and amplitude of the signal that propagates through different paths causes fading. There has been significant research activity over past couple of decades on the performance of wireless channel models. In wireless transmission system the Rayleigh fading is a good approximation with no lineof-sight-path propagation [25, 26]. The Rayleigh fading channel considers multiplicative distortion h(t) in the transmitted signal s(t) in the form, y (t) = h(t) s(t) + n(t). Where, y(t) is channel output and n(t) is the noise. Many authors have proposed and developed wireless communication simulators that include gray coding modulation, different channel models, channel estimation, adaptive equalization and demodulation. They have tested different channel models for the data and image with constellations and BER plots under different modulations [23, 27, 28,]. We have developed, simulated and tested the performance of multipath fading channel model. 11

2.5 Fading and channel models Multipath propagation causes rapid variations in the phase, dispersion and amplitude of the signal. The Fig. 2.3 shows direct and reflected paths between moving receiver and stationary transmitter. Transmitter A (Direct) (Reflected) Receiver (Reflected) B Fig. 2.3 Fading concept The types of fading are shown in Fig. 2.4. Fading A, B: Obstacles Large Scale Fading Small Scale Fading (Depending on multipath time delay spread) Flat fading Bandwidth of the signal < Bandwidth of the channel Delay Spread < symbol period Frequency selective fading Bandwidth of the signal > Bandwidth of the channel Delay Spread > symbol period Small Scale Fading (Depending on Doppler spread) Fast Fading High Doppler Spread. Coherence time < Symbol period. Channel variations faster than baseband signal variation. Slow Fading Low Doppler Spread Coherence time > Symbol period Channel variations slower than baseband signal variation. Fig. 2.4 Types of fading 12

Fading may be large scale fading or small scale fading [29]. Based on multipath delay spread, small scale fading is classified as flat fading and frequency selective fading. For bandwidth of the signal smaller than bandwidth of the channel and delay spread smaller than relative symbol period leads to flat fading whereas if bandwidth of the signal is greater than bandwidth of the channel and delay spread is greater than symbol period then frequency selective fading occurs. Based on Doppler spread, small scale fading may be fast or slow fading. If coherence time of the channel is larger than delay constraint of the channel then slow fading occurs. Slow fading is due to shadowing effect of hill or large building in the main signal path. If delay constraint of the channel is greater the coherence time of the channel then fast fading occurs. The use of time diversity technique reduces the effects of variations in the channel conditions and increases robustness of the communication system along a fast fading channel. Rayleigh fading channel model assumes that the magnitude of a signal passed through the channel varies according to a Rayleigh distribution. Rayleigh fading is applicable for non-dominant line-of-sight propagation path between the transmitter and receiver. Rician channel model considers the dominant wave as phasor sum of line-of-sight and ground reflected signals. Along with dominant component, the mobile antenna receives a large number of reflected and scattered waves. The channel fading rate is determined by speed of the mobile unit. The selection of algorithm and its rate of convergence depend on the channel data and coherence time. Nakagami fading channel model considers the instance for multipath scattering with relatively large time delay spreads and different reflected wave clusters. The delays time of individual reflected waves are nearly equal and phases of are random. Envelope of each cluster signal is Rayleigh distributed within any cluster. Between clusters, the average time delay is different. If the delay time is more than bit duration of a digital signal then different clusters produce intersymbol interference [30]. 2.6 Proposed multipath fading channel model Fig. 2.5 shows the basic structure of the proposed multipath fading channel model. The developed wireless multipath fading channel model considers effect of a propagation environment on a radio signal as signal strength variations, phase variations and additive noise. 13

The model is expressed as, y(t) = g 1 s(t) + a[τ g 2 s(t)] + b[τ g 2 s(t)] + n(t) (2.1) Where, y(t) is output signal of the channel, s(t) is input signal, τ is delay or phase shift, g 1 is fixed gain, g 2 is variable gain, n(t) is noise, a and b are terrain dependent variables. Signal input s(t) Fixed Gain Delay (Phase shift) + Signal Output y(t) Variable Gain or Attenuation Fig. 2.5 Multipath fading channel structure The channel model was tested for sine wave and complex inputs. The effect of noise and scattering property of the channel were tested. The model has been tested, analyzed and compared with the BER performance of Rayleigh channel model and AWGN channel models. It has been observed that more accurate model is Rayleigh channel model as its BER curves have steepness and values more closely to theoretical analysis. The proposed multipath fading channel simulation model provides similar performance. The channel model can be used to test the performance of wireless communication system in a mobile environment. 2.7 Effect of noise on fading Noise is considered as any measurement that is not part of the phenomena of interest. The noise is generated by using matlab function, y = AWGN (x, SNR, measured ). This function is used to add the white Gaussian noise to the vector signal x. AWGN adds complex noise for x is complex. Signal-to-noise ratio (SNR) per sample, ratio of symbol energy to noise power spectral density (Es/N 0 ) etc. describes relative power of noise in a channel. A bit error ratio is the ratio of the number of bits in error to the total number of bits transmitted during a specified time interval. Signal-to-noise ratio compares the level of information signal to the level of noise. SNR = (P signal / P noise ) = (A signal / A noise ) 2. 14

While considering effect of BER on SNR, the results show that BER is more at low SNR since in low SNR, white Gaussian noise dominates the signal. The BER error can be improved by improving SNR. For high SNR, phase estimation error is more and BER cannot be improved by simply enhancing SNR. Thus, BER performance is worse in flat fading channels as well as frequency selective fading channels and it is best in AWGN channel. A channel is to be modeled physically by trying to calculate the physical processes that modify the transmitted signal. In wireless communication the channel can be modeled by calculating the reflection from every object in the environment. 2.8 Simulation results and discussion 2.8.1 Multipath fading channel model with sine and complex input Simulations results of proposed multipath fading channel model with sinusoidal and complex input signals have been presented below. Fig. 2.6 Flowchart for obtaining faded signal 15

Received signal power (db) Amplitude (Volts) Channel Equalization As shown in Fig. 2.6, input signal is passed through fixed gain mechanism for zero attenuation signal components. Variable gain mechanism through delay is used for getting variable attenuation and phase shifted signal components. 2 1.5 1 0.5 0-0.5-1 -1.5-2 0 1 2 3 4 5 6 7 8 9 10 Time (ms) Fig. 2.7 Multipath fading channel output for sine wave input Multipath fading channel output for sine wave input (1 khz) is shown in Fig. 2.7. The blue coloured signal represents input sine wave. The faded signal output has been denoted by the number of red signals. Received signal power varies with variation in phase shift and attenuation in different signal components. More the phase shift, lower is the received signal power at the channel output. A typical variation in received signal power with time in multipath fading channel model is shown in Fig. 2.8. 50 0-50 -100-150 -200-250 0 1 2 3 4 5 6 7 8 9 10 Time (ms) Fig. 2.8 Simulated fading signal 16

Amplitude (Volts) Amplitude (Volts) Channel Equalization For evaluating the performane of the channel with complex input, we have used square wave as it contains multiple harmonic components. Multipath fading channel output for complex wave (square wave) input is presented in Fig. 2.9 2 1.5 1 0.5 0-0.5-1 -1.5 Fig. 2.9 Multipath fading channel output for square wave input The blue colored signal represents input square wave (1 khz). It is observed that when signal passes through the channel, signal gets phase shifted due to reflections from the objects and obstacles along the path. The faded signal outputs have been denoted by the number of red signals. -2 0 1 2 3 4 5 6 7 8 9 10 Time (ms) 2.8.2 Multipath fading channel in presence of noise 2 1.5 1 0.5 0-0.5-1 -1.5-2 0 1 2 3 4 5 6 7 8 9 10 Time (ms) Fig. 2.10 Multipath fading channel output for sine wave input with noise 17

Amplitude (Volts) Channel Equalization 2.5 2 1.5 1 0.5 0-0.5-1 -1.5 Fig. 2.11 Multipath fading channel output for square wave input with noise We have generated white Gaussian noise that represents channel noise. The noise is mixed with resultant signal and results are presented in the Fig. 2.10 and Fig. 2.11. The noise is generated by using matlab function y=awgn(x,snr, measured ). This function adds white Gaussian noise to the signal. 2.8.3 BER Vs SNR The flowchart for obtaining the BER Vs SNR performance of multipath fading channel is shown in the Fig. 2.12. -2 0 1 2 3 4 5 6 7 8 9 10 Time (ms) Start BPSK modulation Channel Compute values of SNR + Noise Demodulation Compute the BER for fading channel Compare BER and SNR End Fig. 2.12 Flowchart for obtaining BER Vs SNR plot 18

Quadrature component of x Channel Equalization Fig. 2.13 BER Vs SNR plot for Multipath fading channel The BER is calculated from the number of bits received in error divided by the number of bits transmitted. BER= (Bits in Error) / (Total bits transmitted). SNR is the ratio of the received signal strength over the noise strength in the frequency range of the operation. SNR= 10 log 10 (Signal Power/Noise Power). The result in Fig. 2.13 shows that BER is inversely related to SNR. High BER causes low SNR and vice versa. The number of bit errors in the received bit stream has been altered due to noise, interference and distortion. 2.8.4 Scattering property of the channel 2 Scatter plot 1.5 1 0.5 Irregular object 0-0.5-1 -1.5-2 -2-1 0 1 2 In-Phase component of x Fig. 2.14 Scattering property of the channel 19

The function scatterplot(x) is used to generate a scatter plot of the signal x. Shape and complexity of x decides its interpretation. For x is a real two-column matrix, the function interprets first and second columns as in-phase and quadrature components respectively. The function denotes in-phase components for real parts and quadrature components for imaginary part of complex vector x. If x is a real vector then function interprets it as a real signal. 2.9 Performance of channel models When multipath fading occurs, the BER will increase for a given channel SNR. The techniques such as diversity, equalization, data interleaving are used to combat multipath fading. 2.9.1 Rayleigh model The Rayleigh fading channel considers a multiplicative distortion h(t), transmitted signal s(t) and the noise n(t). The channel model is written as, y(t) = h(t){s(t) + n(t)} (2.2) Rayleigh fading is the specialized model for no line-of-sight propagated signal and it is considered as a special case of the Rician fading channel model. In Rayleigh fading, the amplitude of the signal is characterized by Rayleigh distribution. The performance analysis on the basis of BER and SNR is shown in the Fig. 2.15. Fig. 2.15 BER Vs SNR in Rayleigh channel model 20

When direct line-of-sight path does not exist between transmitter and receiver, the resultant signal at the receiver will be the sum of all the reflected signal components through indirect paths and scattered waves. This increases BER at low SNR. 2.9.2 AWGN Channel Model AWGN channel model is very straightforward in which we have to only add a white Gaussian noise into input signal at given SNR and bandwidth. The Gaussian channel is important for providing an upper bound on system performance. The AWGN channel model is shown in Fig. 2.16. White Noise at given SNR and bandwidth Transmitted signal Received signal Fig. 2.16 Block diagram of AWGN channel model Fig. 2.17 BER Vs SNR in AWGN channel model BER Vs SNR performance of the AWGN channel model is presented in Fig. 2.17. In this model the channel has only stochastic influence. The stochastic influence is actually an interference simply called noise. The Central Limit Theorem advocates that the total interference has a Gaussian distribution. Moreover, we assume that this distribution is the same at every time and does not depend on its past. 21

Table 2.1 Performance comparison of Rayleigh, AWGN and Multipath Fading Channel model for BER= 10-3 Modulation Rayleigh Channel AWGN Channel Multipath Fading Technique (SNR in db) (SNR in db) Channel (SNR in db) BPSK 24.00 6.50 29.00 2.10 Validation of the Multipath fading channel model We have used correlation test method for verifying adequacy of a multipath fading channel model. Rayleigh fading channel model assumes that the magnitude of a signal passed through the channel varies according to a Rayleigh distribution. Rayleigh fading is applicable for non-dominant line-of-sight propagation path between the transmitter and receiver. We have compared the Multipath fading channel model with Rayleigh channel model and AWGN channel model by considering BER Vs SNR performance. From the comparison Table 2.1, it is clear that Rayleigh channel model supports high SNR than AWGN channel model. The multipath fading channel model gives still better SNR. 2.11 Conclusion Simulations results show that Rayleigh channel model supports high SNR than AWGN channel model. The developed multipath fading channel model gives still better performance. This model can be used to test the performance of wireless communication systems under different terrain conditions. The radio channels are extremely random and time-variant. The wireless multipath channel adds dispersion, attenuation, and phase shift in the input signal known as fading. Adaptive equalization methods are needed, since the channel response is usually not known beforehand and it is often time varying. Adaptive equalization is used to recover the original information by compensating the channel effects. Chapter 3 describes adaptive filters based on neural networks for channel equalization, comparison and testing of the systems for quality. 22