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Efficient performance evaluation technique for digital satellite communication channels

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Efficient Performance Evaluation Technique for Digital Satellite Communication Channels

Jun-Myung Kim, Chang-Bong Jung, Hwi-Won Park, and In-Kwan Hwang Department

of

Radio Communication Engineering

Chung-buk National University, Republic of Korea ikhwang@trut.chungbuk.ac.kr

Abstract

-

In this paper, a new efficient performance evaluation method for digital satellite channel is suggested and its efficiency is verified in terms of computer run-time.

We adopt discrete probability mass functions in the suggested method for estimating statistical characteristics of received signal from the measured Nth order central moments to solve the existing difficulties of the Importance Sampling (IS) techniques. With the discrete probability mass function obtained from the less number of received signal samples than those required in IS, continuous cumulative probability function and its inverse function can be exactly estimated by using interpolation and extrapolation technique. With the simplified channel model, the overall channel performance evaluation can be done within a time drastically reduced. The simulation results applied to a nonlinear digital satellite channel showed a great efficiency in the sense of computer run-time, and demonstrated that the existing problems of IS for the nonlinear satellite channels with Mth-order memory can be completely solved.

I. INTRODUCTION

Communication technologies being newly suggested to cope with the exhaustion of frequency resources and to provide multimedia services are being rapidly changed into advanced complex ones which employ the variable frequency band allocation method and are mixed with signal processing techniques. The practical design of this kind of communication systems comes to depend on the computer simulation rather than analytic approaches and its importance is given much more weight day by day.

Due to the difficulties of analytic approach, the commercial simulators are required to adopt Monte Carlo (MC) method to get over the limits of analytic approach and to provide convenience and flexibility for users. However. those expensive commercial simulators having various functions cannot avoid the critical point of computation time. Therefore, those are not used for designing practical communication systems but only for evaluating link budgets.

Since the middle of 1970s: many researches to reduce computer simulation time that is the key to develop communication systems with competitiveness, have been progressed briskly. As a result, a number of papers have been published in the IEEE Transaction on Communication and published as special editions in Journal on Selected Areas in Communication in 1984, 1988, 1993, and 1997.

But most of the study results are restricted to simple system models and include many problems for practical use due to the complexity of the algorithms. In other words. all the approaches of these studies adopt Importance Sampling (IS) technique basically. Therefore it is very complicated to figure out the optimum biasing parameters for the practical

communication systems with nonlinear amplifiers and memories over 30-order. Even if we figure it out, it is unavoidable that the run-time saving effect of computer simulation for the memory systems falls down considerably.

Furthermore, it is impossible to estimate the exact performances for overall channel including encoder and decoder by IS technique. Therefore, in order to find the solutions for these existing difficulties, a completely different new approach is required.

This paper shows the potentiality of the perfect solution for the problems of IS techniques with a new approach that introduces discrete probability mass function using central moments of the received signals. With the computer simulation, the efficiency of this new approach for the digital satellite communication channels including all the difficulty factors of IS, such as non-linearity and memory, are demonstrated.

11. A NEW CHANNEL PERFORMANCE EVALUATION METHOD USING CENTRAL MOMENT

Figure I . shows the simplest BPSK channel model including all the basic difficulty factors which conventional studies couldn't work out, such as non-linearity and memory. And the system response, g(.) is the simple model to show that it is possible to be applied to even the practical complex systems if the suggested algorithm is efficient.

White Gaussian noise n(t) is added to a transmitted signal s(t) to produce a noisy signal x(t) at the receiver input.

Nonlinear

n

0 )

Memory

I

System

Figure 1 . Simple Equivalent base-band System Model

The transmitted signal may be written s ( t ) =

c

a , p ( t -

iT)

and the waveform x(t) is modeled by

where the information data 0, can take the value +A or -A

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with the equal probability, p(t) is a rectangular gating function having zero values everywhere except for unit value on [U, TI, and n(t) is a white Gaussian noise process of zero mean and the two-sided power spectral density of NoI2.

In order to get over the limit that the conventional studies couldn’t work out, as a new approach, the discrete Probability Mass Function (PMF) that has a lot of merit in many aspects. is introduced in this paper.

Figure 2. Continuous PDF and Discrete PMF

As like Figure 2, if the central moments of continuous Probability Distribution Function (PDF) and discrete Ph4F has same value for enough large order of N, both random variables are statistically equivalent as formula (4).

Therefore, the expectation for complex system function can be figured out as a simple summation as formula (5).

(3) .I

n = l - N for{ N = 2 ~ - 1

where, H(y) is defined -when Do is error region,

(4)

Expanding this concept, if we measure the Nth-order central moments from the samples of received signals and obtain the discrete Ph4F by using this, the channel error rate can be shown siniply as the summation of weighting, that is, the -summation of discrete probability.

This may be written

/=I ( 7 )

In order to find the exact error rate using discrete PMF, enough orders of central moments should be measured. And the increased numbers of samples are required to predict higher order central moment exactly. In other words, unless enough numbers of samples are not taken, it may not be possible to predict errorless

BER.

This may make the suggested approach be inconsistent in the aspect of sample saving factor improvement.

But this problem can be solved easily if the properties of the central moment approach are carefully analyzed.

For the estimation of exact

BER

and maximization of sample saving effect, we can:

*

increase the weighting point number of discrete PMF,

*

introduce the biasing PMF,

*

take the interpolation and extrapolation technique using discrete CPD.

Especially, for the satellite communication channel with nonlinear amplifier, Gaussian noise in the uplink is transformed into non-Gaussian noise in the downlink. The sample saving factor can be maximized by applying both interpolation and extrapolation methods using Discrete CPD, in order to estimate enough exact channel error rate with a few samples and the lower-order central moments.

Figure 3. shows that Discrete CPD and the estimated CPD obtained by measuring and using the central moment of Gaussian noise with lo4 samples are compared with the theoretical CPD. It shows that the exact estimation of

lo-*

BER

is possible with only lo4 samples when we interpret the threshold value equal to -1. This illustrates the performance evaluation speed is improved by about 1 O7 times.

The conventional IS techtuque is the method that has an interest in a small error region and increases the error occurrence and then compensates the effect in the receiver.

But it makes a trouble in calculating the optimal biasing parameter. Also, it cannot help avoiding the drastic decrease of sample saving factors in the system with Mth-order memories.

However, it is easy to figure out the errors below the bounded value, if we adopt the central moment technique and statistical characteristics can be extracted by just observing the status of signal and noise of a receiver in the overall region. Semi- Analytic method that seeks the ch<annel error rate by using error function that simply measures the convergent variance with the considerably small number of samples is the one of similar example using this concept.

True CPD

1 - -

Estimated 10000 sarnules of Noise CPD with

-1 -0.5 0 0.5 1

16

Figure 3. CPD of Gaussian Noise

HI. PERFORMANCE ESTIMATION FOR SATELLITE COMMUNICATION CHANNEL WITH THE SUGGESTED METHOD

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Random ' Y ( t TWTA

<

Sequence -b

Generator

Figure 4. Simple Digital Satellite Communication Channel Model

BPF + Demodulator-, cpD Function / Error Estimator

' " 3 4 5 6 7 8 9 1 0 1 1

mb

1 g :

(a) TWTA Input Back-Off-14dB

*BO= -14dB (min.)

**MC

1

***CMT MC

1

CMT

(dR\ (dB)

(b) TWTA Input Back-Off-IdB

10 11

Figure 5 . Digital Satellite Communication Channel Performance BER Curves

47.1 44.4 540 10

56.1 51.1 2200 10

Figure 4. is a model of the simple digital satellite communicat- ion channel. The channel performance i s evaluated as follows.

(dB) 3

*

Measure the central moments of received signals

*

Obtain discrete PDF from the algorithm.l'l

*

Obtain discrete CPD by using discrete PDF.

~, J

**MC ***CMT MC CMT

(dB) (dB)

4.3 3.6 2 10

I

I Estimation ofPe I Run-time

1

Table 1. Computer Run-time Comparison between MC and CMT (TWTA BO=-14dB, CMT=30000 Samples,

MC=I 0 0 0 P e Samples)

I Estimation of Pe 1 Run-time

I Eb/No I *BO=-14dB I (min.)

I

1 V 1 V

11 I -54.1 I -53.3 I 2000 I 10 Table 2. Computer Run-time Comparison

between MC and CMT (TWTA BO=- 1 dB, CMT=30000 Samples,

MC= I000/Pe Samples)

*

BO :

* * *

CMT :

TWTA Input Back-Off

**

MC : Monte Carlo

Central Moment Technique

*

Produce continuous CPD with discrete CPD by applying interpolation, and extrapolation technique. At this time, the performance of channel can be obtained by applying the error detection threshold value of the received signals.

The characteristics of TWTA, TWT275H of Hughes Company, operating in the linear region where input Back-off is -14dB and in the nonlinear region where input Back-off is -1dB are assumed. Figure 5 illustrates that Gaussian PDF converted

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(4)

into non-Gaussian noise can be easily estimated by using CMT, and this can be the basis which can estimate qualitatively and quantitatively the difference of channel performance occurred in the case of interpreting the nonlinear operation is a simplified linear operation.

When TWTA operates in the linear region where the input back-off is -14dB and in the nonlinear region where the input back-off is -IdB, Figure 5. shows the BER performance of the channel.

Table 1. shows the results of measured running time required to estimate performance by means of both Monte-Carlo method and the method we have proposed. In Figure 5., as the value of Eb/No is large, the efficiency of the proposed method radically increases. The proposed algorithm can be efficiently used for estimating the low error rate of the digital TV and the satellite ATM channels.

IV. CONCLUSIONS

This paper analyzes a simple system to explain the suggested algorithm but also shows the possibility that it can be applied to all general systems. As shown in the results comparing the running time of MC and CMT, Table 1 and Table 2, the suggested method can make the debugging and development of simulation program considered impossible due to extremely long run-time, possible through the radical improvement effects in computation time.

Specially, the improvement effect is clear for low error rate region. And it makes possible the performance evaluation in all SNR, for only about 5-15 minutes. The suggested method is expected to be fully used to design practical communication systems with competitiveness.

ACKNOWLEDGEMENT

This study is supported as a project No.CI-98-0894, by Ministry of Information and Communication Republic of Korea.

And we would like to acknowledge contributions from Cadence Company who supported Signal Processing Worksystem (SPW).

REFERENCES

[ I ] In-kwan Hwang and Ludwik Kurz. "Digital data Transmission over Nonlinear Satellite Channel", IEEE Transactions on Communications, vol. 41. no. 11, pp. 1694- 1702, Nov 1993.

[2] P J Smith. M Shafi. and H Ciao, "Quick Simulation A Review of Importance Sampling rechniques in

Communication Systems", "On Importance Sampling i n

Digital Communications Part I Fundamentals. " IEEE Journal on Selected Areas in Communications, Vol 15. No 4. pp 597- 6 13, May 1997

[3] Dingqing Lu and Kung Yao, "Improved lmpotance Sampling Technique for Efficient Simulation of Digital Communication Systems", IEEE Journal on Selected Areas in Communications, V01.6. No. 1, pp. 67-75, January 1988.

[4] Michel C. Ieruchim, "Techniques for Estimating the Bit Error Rate in the Simulation of Digital Communication

Systems", IEEE Journal on Selected Areas in Communications, Vol. SAC-2, No. I , pp. 153-1 70, January 1984.

[5] Nevio Benvenuto, Antonio Salloum, and Lucian0 Tomba,

"Performance of digital radio links based on semianalytic method", IEEE Journal on Selected Areas in Communications, vol. 15, no. 4, pp. 667-676, May 1997.

[6] J. C. Chen, D. Lu, J. S. Sadowsky, and Yao, "On importsance sampling in digital communication

-

Part I:

Fundamentals", IEEE Journal on Selected Areas in Communications, vol. 1 I , no. 3, pp. 289-299, September 1993.

[7] M. C. Jeruchim, K. Sam Shanmugan, E. Biglieri, and P.

Balaban, "Computer-aided modeling, analysis, and design of communication links: Introduction and issue overview", IEEE Journal on Selected Areas in Communications, vol. 6, no. I , pp.

1-4, May 1988.

[SI Wael A. AI-Qaq, and J. Keith Townsend, "A stochastic inportance sampling methodology for the efficient simulation of adaptive system in frequency nonselective Rayleigh fading channels", IEEE Journal on Selected Areas in Communications, vol. 15, no. 4, pp. 614-625, May 1997.

[9] Narayan B. Mandayam, and Behnaam Aazhang, "Gradient estimation for stochastic optimization of optical CDMA system", IEEE Journal on Selected Areas in Communications, vol. 15, no. 4, pp. 735-750, May 1997.

[IO] J. S. Sadowsky, "A new method for Viterbi decoder simulation using importance sampling", IEEE Transactions on Communications, vol. 38. pp. 1341-1345, Sept 1990.

[ I l l A. C. M. Hopmans and J. P. C. Kleijnen, '-Importance sampling in systems simulation: A practical failure", Math.

And Comput. In Sirnulation, Vol. 31, pp. 209-220, 1979.

[12] M. Pent, L. L. Presti, G. D'aria, G . De Luca,

"Semianalytic BER evaluation by simulation for noisy nonlinear bandpass channels", IEEE Journal on Selected Areas in Communications, vol. 6 , no. 1, pp. 34-4 I , Jan 1988.

[I31 Michel C. Jeruchim, "On the application of importance sampling to the simulation of digital satellite and multihop links", IEEE Transactions on Communications, com-32. no. I O , pp. 1087-1092, oct 1984

[I41 E. L. Pinto and Joao C. Brandao, "On the efficient use of computer simulated digital signals to evaluate performance parameters", IEEE Journal on Selected Areas in Communications, vol. 6, no. I , pp. 52-56, Jan 1988.

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