Performance of Matched Filter System

International Journal of Engineering, Management & Sciences (IJEMS) ISSN-2348 –3733, Volume-2, Issue-2, February 2015

Performance of Matched Filter System Vibhuti Sharma , Monika Negi, Ira Joshi , Manju Mathur  Abstract— A basic problem that often arises in the study of communication system is that of detecting a pulse transmitted over a channel that is corrupted by channel noise. The information signal which has been sent from transmitted end is almost distorted at the receiving end. That’s why a filter known as “MATCHED FILTER” or “NORTH FILTER” is introduced to reduce these errors in transmission of signal A matched filter is a used in communication to “match” a particular transit waveform. It passes all the signal frequency components while suppressing any frequency components where there is only noise and allows to pass the maximum amount of signal power. The purpose of the matched filter is to provide maximum signal-to-noise power ratio & to minimize the probability of undetected errors received from a signal. Here in this paper we are going to conclude performance of a dual channel matched filter or performance under noisy environment. For better performance of dual channel matchedFilter system with minimum data input ,low cost & lower SINR under the assumptions of uncorrelated inputs &knownCorrelated matrices that the dual channel matched filter Is equivalent to a single channel matched filter designed to process both input signals.

Index Terms— North Filter, need of match filter, performance of dual channel matched filter.

II. NEED OF MATCHED FILTER A matched filter is a linear filter designed to give maximum Signal to noise ratio at its output.

X(t)= g(t)+w(t)

y(t)= go (t)+n(t)

I. INTRODUCTION While studying communication system one of the major problems arises regarding detection of pulse transmitted over a noisy channel. This disturbance is due to noise, which is an unwanted high amplitude short duration signals. This can be rectified by introducing a filter known as matched filter.[1] Matched filter is obtained by mutual relation of a known signal and an unknown signal. This is equivalent to convolution of one unknown signal with a conjugated time-reversed version of the signal (template).

To maximize the Signal to noise ratio (SNR) in presence of white Gaussian noise matched filter is optimal linear filter.

Basically Matched filters are used in RADAR in which a known signal is sent out and the reflected signals are examined for common elements of the outgoing signals. Pulse can be compressed by matched filter as impulse response is matched to input pulse signals. In image processing we use two dimensional matched filter to improve SNR for X-ray.[2]

Manuscript received December 09, 2014.

Vibhuti Sharma, M.Tech Scholar, Department of Electronics & Communication, RCEW Jaipur, Rajasthan ,India Monika Negi, M.Tech Scholar, Department of Electronics & Communication, RCEW Jaipur, Rajasthan ,India Ira Joshi, Asst. Prof. ,Department of Electronics & Communication, RCEW Jaipur, Rajasthan ,India Manju Mathur, Asst. Prof. , Department of Electronics & Communication, RCEW Jaipur, Rajasthan ,India

5

Fig 1 Matched filter

Let us consider x(t) as input consisting a pulse signal g(t) and is corrupted, disturbed and involved with additive noise w(t).

Let us assume that receiver have knowledge of the waveform of the pulse signal g(t). The source of uncertainties, doubts and errors lies in the noise w(t) . The receiver detects the pulse signal g(t) in an optimum manner.

III. MATCHED FILTER IN DIGITAL COMMUNICATIONS In communication system binary messages are transmitted to the receiver across the noise channel in which matched filter is used to detect the pulses in noisy received signalLetus take an example .consider we want to send a sequence "0101100100" coded in non-polarNon-return-to-zero (NRZ) through a certain channel.[3][4].

www.alliedjournals.com

Performance of Matched Filter System

We have reviewed in this paper that for the better performance of a dual channel matched filter system we have worked under the assumption of uncorrelated inputs and known correlated matrices. we have also assumed that SINRSignal for one channel is uncorrelated with the input signal for the other channel. After working on this the author of this paper developed exact expressions for the normalized SINR as a function of random variables with known distributions than using a Taylor series expansion.We have got the conclusion that dual channel matched filter is equivalent to a single channel matched filter designed to process both input signal.[11][13]

Fig 2 Digital signal in Communication System

A sequence in NRZ code mathematically and can be described as a sequence of unit pulses or shifted rect functions, each pulse being weighted by +1 if the bit is "1" and by 0 if the bit is "0". Formally, the scaling factor for the kthbit is, ak= We can represent our message, M(t), as the sum of shifted unit pulses: Fig 5 Dual channel matched filter system

WhereTis the time length of one bit. Thus, the signal to be sent by the transmitter is

Size, reduced data and low cost. When estimated correlation matrices are used in place of true correlation matrices the dual channel matched filter system Achieves Nearly the same Normalized SINR as the single Channel With The Half The secondary data. Here we can say that the single channel matched filter can be replaced by a Dual channel matched filter of small

Fig 3 Binary bits

If we model our noisy channel as an AWGN channel, white Gaussian noise is added to the signal. At the receiver end, for a Signal-to-noise ratio of 3dB[5][6]. .

III. PERFORMANCE OF A DUAL CHANNEL MATCHED FILTERSYSTEM

Fig 6 Single channel matched filter system

A key element in replacing a single channel system with a dual channel system thedecor relation preprocessing, which basically requires the introduction of a transformation that Block diagonalizes the correlation matrix. This requirement for preprocessing introduces a new challenge: finding a fixed transformation that block diagonalizes the family of correlation matrices of interest and that has an efficient implementation. Depending on the family of correlation matrices, such a transformation may or may not exist. A family of matrices that can be efficiently blocked [7]-[10].

Fig 4Cumulative probability distribution ofnormalizedSINR forsingle channel and dual channel systems.

6

www.alliedjournals.com

ACKNOWLEDGEMENT

International Journal of Engineering, Management & Sciences (IJEMS) ISSN-2348 –3733, Volume-2, Issue-2, February 2015

We authors acknowledged Mrs. ShwetaSharda H.O.D ECE RCEW for her Support and Encouragement.

REFERENCES [1]S.Haykin,”CommunicationsSystems”,Willey [2]Scott d. berger”Performance of a Dual Channel Matched Filter System”IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 35, NO. 4 OCTOBER 1999 [3]Reed, I. S., Mallett, J., and Brennan, L. “Rapid convergence rate in adaptive arrays”. IEEE Transactions on Aerospace and Electronic Systems, AES-10 (Nov. 1974), pp.853—863.

[4]Khatri, C., and Rao, C. R. “Effects of estimated noise correlation matrix in optimal signal detection”.IEEE Transactions on Acoustics, Speech, and SignaProcessing, ASSP-35 (May 1987), 671—679.

[5]Muirhead, R. J. (1982) “Aspects of Multivariate Statistical Theory”. New York: Wiley, 1982.

[6]Papoulis, A. (1991) “Probability, Random Variables, and Stochastic Processes “. New York: McGraw-Hill, 1991.

[7]Hogg, R. V., and Craig, A. T. “Introduction to Mathematical Statistics “.Englewood Cliffs, NJ: Prentice-Hall, 1995.

[8]Good, I. “The inverse of a centrosymmetric matrix.Technimetrics”, 12 (Nov. 1970), 925—928.

[9]Cantoni, A., and Butler, P.”Eigenvalues and eigenvectors of symmetric centrosymmetric matrices. Linear Algebra and Its Applications”, 13 (1976), 275—288.

[10] Therrien, C. W.”Discrete Random Signals and Statistical Signal Processing “Englewood Cliff, NJ: Prentice-Hall, 1992.

[11] Shapiro, H. “Simultaneous block triangularization and block diagonalization of sets of matrices”.”Linear Algebra and Its Applications”, 25 (1979), 129—137.

[12] Barker, G., Eilfer, L., and Kezlan, T.” A non-commutative spectral theorem”.”Linear Algebra and Its Applications”, 20 (1978), 95—100.

[13] Ramstad, T., Aase, S., and Husøy, J. “SubbandCompression of Images: Principles and Examples. Msterdam": Elsevier, 1995

7

www.alliedjournals.com