Blind Equlization For Next Generation Mobile Channels

MTECS-2008

Performance Assessment of Adaptive Equalizers for Indoor Mobile Channels Mohd Israil1 and M. Salim Beg2 1

2

AMU, Aligarh, Email:- [email protected] AMU, Aligarh, Email:- [email protected]

Abstract— The effect of inter symbol interference (ISI) in communication systems can be done through equalization. This paper deals with the performance of the linear and nonlinear equalizers for some fading channels such as those found in indoor mobile radio environments. A linear equalizer gives the good performance in case those channels, where the ISI is not too severe but it is not enough for severe ISI case. It can be seen that the nonlinear equalizer gives much better performance than linear equalizer. This paper also discusses the channel with different path and different amount of ISI present in the signal.

Index Terms: — Channel Impulse Response, Equalization, Multipath Fading,

I.

channel the time delay spread is generally inverse of the frequency. When the time delay spread is large, the adjacent signal may interfere with each other, causing intersymbol interference (ISI). And therefore the system gets degraded. The ISI becomes more when the delay spread is approximately 30% or more of the duration of the signal duration. The 4-QAM signaling is used in this work which is generated by inphase and quadrature phase suppressed carrier modulation. It is assumed here that the detectors know all about the channel i.e. perfect channel estimation is assumed. This assumption is made because the objective of this study is to assess the performance of detection processes in combating signal, fading and intersymbol interference.

INTRODUCTION

Pat h2

T

he multipath problem in the mobile communication system is caused by the reflection and scattering from buildings, hills and other obstacle along with the radio path. Radio waves arrive at the mobile radio receiver from the base station via many different paths, with different time delay as shown in the fig. 1. The path1, path2 and path3 are coming from the base station via LOS, reflection and refraction. These paths will combine vectorally at the receiver. Since these are with different phase so at the receiver side will get the constructive as well as destructive interference depending upon the phase relationship among the incoming signal [3-6]. In this work worst case scenario is considered. It is to be noted that when the receiver moves from one location to other, the phase relationship between the components of the various incoming signal changes. Along with this, it is to be noted that there will be Doppler shifts of the frequency component within the received signal due to the relative motion between the transmitter and receiver. The time difference of the first and last replica of the signal is known as multipath delay spread or time delay spread of the

230

Buildi ng

Direct Path

Pat h3

Base Station

Tall Buildings

Fig. 1. Multipath Radio wave Propagations

Mobile Terminal

MTECS-2008

II.

MODELING OF THE MOBILE FADING CHANNEL III.

Generally for generating the multipath fading channel Tapped Delay Line (TDL) channel model is used. A tapped delay line (TDL) is a delay line with at least one tap is illustrated in fig. 2.

EQUALIZATION

Equalization compensates the intersymbol interference (ISI) created by the multipath within time dispersive channel. Equalization must be adaptive in mobile environments, since the channel is generally unknown and time varying [6, 8]. A synchronous serial 4-QAM data transmission system is considered in this work. Signal at the input to the transmitter filter is

∑ s δ(t-iT), i

i

Where si = ±1±j represents the data symbol. If the impulse response of the linear baseband channel is y(t), sampled impulse response will become yh δ(t – hT). It can also be represented by the (g+1) component vector: V = [yi,0 yi,1 yi,2 yi,3 .........yi,g]

(1)

where yi= y(iT) and yi=0 for i<0 and i>g . In the form of ztransform, it is given as: Y(z) = yi,0 + yi,1 z -1 + ..........+ yi,g z –g

(2)

Fig. 2. Tapped Delay line model for generating Multipath channel

The received signal is A delay-line tap extracts a signal output from somewhere within the delay line, optionally scales it, and usually sums with other taps for form an output signal. Depending upon the variety of terrain including built-up urban and suburban/rural areas, the channel may have several significant resolvable paths with independent fading. The amplitude of these resolvable paths is Rayleigh distributed and the phase is uniformly distributed [6]. This paper addresses such ‘worst case’ models of mobile channels. The idea is that if a receiver can be designed to have a good tolerance to such a worst case design of a channel, then it is unlikely to have a poor performance over any practical channel that may be encountered in a mobile [6]. Fig. 2 shows channel model where input fed to the tapped delay line. The number of taps is equal to the number of the reflected signal reaching to the receiver via different fading paths. Output of the signal would be distorted, noisy and with intersymbol interference. Each of the Rayleigh fading paths is generated simply from two Gaussian noise sources q1(t) and q2(t). Each q1 (t) and q2 (t) are two statistically independent real-valued [3], Gaussian random waveforms, each with zero mean and the same power spectral density, q1 (t) and q2 (t) are generated independently by passing Gaussian noise source from two separate but identical filter. In this works five pole Bessel filter is used [9-10].

r(t) =

∑ s y(t-iT) + w(t) i

(3)

i

Where w(t) represents the additive white Gaussian noise waveform with zero mean and variance σw2. At the input the of the equalizer, r(t) is sampled at t=iT to give the received signal samples. g

ri =

∑

si-h yi,h + wi

(4)

h =0

These samples {ri} are fed to the equalizer whose output goes to the threshold detector.

A. Designing of Linear Equalizers The equalizer removes the ISI from the received samples {ri} such that the signal at the threshold detector input becomes xi ≈ si + ui

(5)

Where ui is a function of the noise samples, and si is the data symbol to be detected. The resultant signal at the output 231

MTECS-2008 of the equalizer xi is then easily detected by a threshold detector [8]. Linear equalization is a process of linear filtering of the distorted signal by a finite impulse response (FIR) filter, or transversal filter. In this work a 10 tap linear equalizer has implemented in the form of a feed forward transversal filter as shown in Fig. 3. The designing of an equalizer basically finding the coefficients C0, C1, C2,….,Cm-1. It can be seen that the sampled impulse response of the equalizer is given by an m-component row vector C = [C0 C1 C2 ........Cm-1]. Therefore, the z-transform of the sampled impulse response of equalizer is C(z)=C0+C1z–1+C2z-2+........+Cm-1 z –m+1

Fig.4. Nonlinear Equalizer

The corresponding sample value at the output of the multiplier is g

(6) ri/yi,0 = si +

∑

si-j (yi,j/yi,0) + (wi/yi,0)

j =1

g

ri/yi,0 = si+

∑

si-jvj + wi/yi,0

(9)

j =1

vj = y i, j/y i, 0 Si = symbol to be detected wi/y i,0 = noise component

Where:

g

∑

Si-jvj = intersymbol interference

j =1

Fig. 3. Model of linear feed forward transversal equalizer

The sampled impulse-response of the baseband channel, sampler and multiplier is 1/y i, 0 V = 1 v1 v2 …… vg

The equalizer essentially acts as the inverse of the channel Y(z) in order to cancel out the distortion (ISI). Thus, Y (z)*C (z) ≈ 1

(10)

Assuming that 1/yi, 0 V and the two possible initial values of si are known at the receiver, the output signal from the linear feed forward transversal filter in Fig. 6 is

(7)

g

∑

si-j' vj , where si-j' is the detected value of si-j.

j=1

This equation shows that channel and equalizer together produced no distortion in the channel.

Thus, the signal at the detector input at t=iT is g

xi = ri/yi,0 –

B. Nonlinear Equalizer

g

= si +

si-j yi,j + wi

∑ j=1

(11) g

si-j vj + wi/yi,0–

∑

si-j' vj

(12)

j=1

And with the correct detection of each si-j, such that si-j' = si-j for j=1,2,….g , then equation (13) becomes xi = si + wi/yi,0

g

∑

si-j' vj

j=1

Non-linear equalization is one in which the detector is used within the feedback path as shown in Fig. 4. Since the detector is a highly nonlinear device, therefore equalization becomes nonlinear. Non-linear equalizer uses decision directed cancellation of intersymbol interference (ISI). The received sample value at the input to the multiplier in Fig. 4, at time t=iT, is ri = si yi,0 +

∑

(13)

(8)

j=1

IV.

DATA TRANSMISSION OVER FADING CHANNEL

This paper is considering three cases of the fading channel with various power delay profiles and number of paths introduced in the channel. In this paper single path, two paths 232

MTECS-2008 with equal as well as unequal power distribution and three paths with equal power and unequal power distribution is considered. In indoor mobile radio communication system the relative motion between transmitter and receiver is small and therefore the values of Doppler spread would also be less. In this work the carrier frequency 900 MHz while the mobility is 2 m/s for worst case channel while using Doppler frequency spread are 6 Hz. CH10 is the flat fading (single path) fading channel, CH11 is a two path fading channel with equal power distribution, CH12 is two path fading channel with power distribution [80% 20%] CH13 is a three path fading channel with power distribution [70% 20% 10%] carrier frequency 900 MHz. Channel CH11 and CH13 are the worst case situation of the channel where the ISI present in the signal will be equal to the signal power. In the single path fading there is no need of equalizer so the received signal sample can be directly given to the threshold detector. The parameters like mean variances of the channel CH10 are given in table 1. Performance of CH10 is given in fig. 5 and fig 6.. The theoretical and simulated parameters of CH11, CH12 and CH13 are given in the table 2, table 3 and table 4 respectively, whereas their BER performance curve of the above channels given in the fig. 5 for linear equalization and in fig. 6 for nonlinear equalization .

Parameter

Table 1 Simulation Results of Single-Path Rayleigh Channel (CH 10) Theoretical Value Practical value

Mean of Rayleigh Path

0.8862

0.8787

Variance of Rayleigh Path Mean of q1

0.2146

0.2132

0

-0.0344

Variance of q2

0.5

0.4882

Mean of q2

0

0.0368

Variance of q2

0.5

0.4646

Rayleigh Channel (CH 12) Theoretical Value

Parameter

Mean of Rayleigh Path 1

0.7927

Practical value 0.8043

Mean of Rayleigh Path 2

0.3965

0.3912

Variance of Rayleigh Path1 Variance of Rayleigh Path2 Mean of q1

0.1717

0.1954

0.0429

0.0472

0

0.0860

Mean of q2

0

0.0073

Mean of q3

0

Mean of q4

0

0.0160

Variance of q1

0.4

0.4000

0.0062

Variance of q2

0.4

0.4352

Variance of q3

0.1

0.1000

Variance of q4

0.1

0.1000

Parameter

Table 4 Simulation Results of Three-Path Rayleigh Channel (CH 13) Theoretical Value Practical value

Mean of Rayleigh Path 1

0.7415

0.7252

Mean of Rayleigh Path 2

0.3963

0.3941

Mean of Rayleigh Path 3

0.2802

0.2782

Variance of Rayleigh Path1 Variance of Rayleigh Path2 Variance of Rayleigh Path3 Mean of q1

0.1502

0.1939

0.0429

0.0457

0.0212

0.0232

0

-0.1314

Mean of q2

0

-0.0243

Mean of q3

0

-0.0265

Mean of q4

0

0.0178

Mean of q5

0

0.0238

Mean of q6

0

0.0057

Variance of q1

0.35

0.3500

Variance of q2

0.35

0.3500

Variance of q3

0.10

0.1000

Variance of q4

0.10

0.1000

Variance of q5

0.05

0.0500

Variance q6

0.05

0.0500

Table 2 Simulation Results of Two-Path Rayleigh Channel (CH 11) Parameter Theoretical Value Practical value Mean of Rayleigh Path 1 0.6267 0.6230 Mean of Rayleigh Path 2 0.6267 0.6230 Variance of Rayleigh 0.1073 0.1127 Path1 Variance of Rayleigh 0.1073 0.1127 Path2 Mean of q1 0 -0.0014 Mean of q2 0 0.0023 Mean of q3 0 0.0014 Mean of q4 0 0.0023 Variance of q1 0.25 0.25 Variance of q2 0.25 0.25 Variance of q3 0.25 0.25 Variance of q4 0.25 0.25

Table 3 Simulation Results of Two-Path

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MTECS-2008 V. CONCLUSION

Fig. 5 BER Vs SNR curve for linear equalizer

Figure 6 shows the performance curve for the CH10, CH11, CH12 and CH13 of Nonlinear Equalizer, while the figure 7 gives the comparison in the performance of the linear and non linear equalizer for the channel CH12.

The paper has presented modeling and simulation of indoor mobile radio fading channels with frequency 900 MHz. Various Parameters of the channel such as mean, variance and fading rate have been checked and verified through computer simulation in order to enhance the validity of the results. Data has been transmitted over the fading channels using 4-QAM. Performance of the communication system using 10 tap linear equalizer as well as nonlinear equalizer has been assessed in terms of the BER Vs SNR curves obtained for various cases. For the worst case model of the channel, such as what is considered in this work, it is found that the performance of the linear equalizer is not very satisfactory. Thus for the worst case type of channels used in this work, it is suggested that some other error mitigation techniques such as channel coding should be used in conjunction with linear equalizers. However, it has been shown that the linear equalizer shows improved performance when the channel intersymbol interference is relatively smaller. In order to get a better performance for data transmission over channels with worst case ISI channels, nonlinear equalizers have been found to give relatively better results.

VI. [1] [2] [3]

[4]

Fig. 6: BER Vs SNR Curve for Nonlinear equalizer for CH10, CH11, CH12 and CH13

Fig. 7: Comparison of linear and nonlinear equalizer for channel CH12

REFERENCE

A.P. Clark, Adaptive detectors for digital modems, Pentech Press, 1989. A.P. Clark, S.G. Jayasinghe Channel estimation of land mobile radio systems, IEE Proc. Vol. 134, July 1987, pp. 383-393. T.A. Sexton and K. Pahlavan, “Channel modeling and adaptive equalization of indoor radio channels”, IEEE Journal Selected Areas in Communications, vol. 7, January 1989, pp. 114-121.

K. Pahlavan S.J. Howard and T.A. Sexton, “Decision feedback equalization of the indoor radio channel” IEEE Trans. on Communication., vol. COM-41, 1993, pp. 164-170. [5] M. Bhat and M. Salim Beg, “Computer simulation and modeling of high speed data transmission over mobile radio links”, Journal of Institution of Engineers (I), vol. 77, Sept. 1996, pp. 20-23. [6] T. S. Rappaport, Wireless Communications, Principles and Practice, Prentice Hall, New Jersey, 1996. [7] M. Salim Beg and Mohd Nazri Muhayiddin, “Receiver Signal Processing For Next Generation Wideband Digital Cellular System,” Proceeding Of International Wireless And Telecommunication Symposium (IWTS 98), Shah Alam, Malaysia, pp.400-403, May 11-15, 1998. [8] M. Salim Beg, S. C. Tan and Hazemi Hamidi, “Performance Assessment of Some Adaptive Equalizers in Mobile Radio Environments”, Proc. Int. Symposium. on Wireless Personal Multimedia Communications, pp. 761-766, Bangkok, Thailand, Nov. 2000. [9] Tau Wang, Vimel K. Dubey and Teong Ong, “Genearation of scattering function for mobile communication channel: A computer simulation approach”, International Journal of wireless information Networks, vol. 3 No. 3,1997 [10] Fabio A. Schreiber and Marcello L. Falleni, “Analysis of DataTransmission Performance over a GSM Cellular Network” IEEE ,Proceedings of The Thirtieth Annual Hawwaii International on System Sciences 1997. [11] M. Salim Beg and Mohd. Israil, “Adaptive Equalization for Indoor Fading Channel”, Proceeding of National Conference on Emerging Trends in Communication and Computing (ETCC-07), 27-28 July 2007, NIT Hamirpur, pp. 382-385.

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