Comparison of Linear and Non-Linear Equalizer using the Maltlab

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1 Comparison of Linear and Non-Linear using the Maltlab Seema Paliwal Assitant professor SDITS Khandwa Dilpreet Kaur Grov Und graduate student of engg. SDITS Khandwa Jyoti Krayla Und graduate student of engg. SDITS Khandwa ABSTRACT In this pap, we compare the BER pformance, burst ror pformance and the signal pow spectrum of diffent types of equaliz using the MATLAB simulation. The simulation and results shows the supiority of equalizs on one anoth. Genal Tms Int symbol intfence, signal to noise ratio. Keywords Bit ror rate, equaliz, burst ror. 1. INTRODUCTION In digital communication, the ultimate goal is the reliable transmission of information at the highest possible data rates. But int symbol intfence (ISI) occur when the high speed data is transmitted ov the communication channel. When the signal is transmitted from source, while reaching to destination, a delay spread is genated in all the multipath objects (IOs) which results in ISI and we get distorted signal at the receiv end. So, for the reliable communication we have to do some advancement at the receiv side which mitigates the effect of ISI. For credible communication, we have to use equalization techniques at the receiv side to combat ISI. An equalization technique is that which compensate ISI created by multipath tine dispsive or time varying channels. So, the main purpose of equaliz is to revse the effect that channel has on the transmitted signal, with the main aim of reproducing the original signal at the receiv end. Fig.1 System Model Fig.1 shows the system model whe a transmitt sends information through a dispsive channel due to which the channel output is corrupted by the additive white Gaussian noise. The task of the equaliz is to eliminate the effect of channel from the transmitted information and also to recov it and hence we get the original signal at the output of the receiv.. EQUALIZATION TECHNIQUES The are two types of equalization techniques: Linear ation- Suboptimal, but simple. Non-linear ation- for seve and noisy channels..1 Linear The most simple and common type of channel equaliz used in practice to reduce the ISI is a linear equaliz. The linear equaliz can be implemented as an FIR filt also known as transvsal filt. In this equaliz, the current and the past values of the received signal are linearly weighted by the adjustable filt coefficient and summed to produce the output as shown in Fig. Fig. Structure of a linear transvsal equaliz. The minimum mean squared ror that a linear equaliz can achieve is: E[ e( n) ] T / T / T F( e N jt N d. Non-linear Non-linear equalizs are used in applications whe the channel distortion is to seve for a linear equaliz to mitigate the effect of channel impairments. The reason for choosing non-linear equalizs ov linear equaliz is that the latt s pformance in channel that exhibit nulls is not effective. Noise enhancement in these regions and long impulse response are a problem. The basic reason for this problem is that in linear filting and noise are processed togeth, causing noise enhancement problem. Based upon the importance, the noise-linear are classified as: (1) 7

2 Decision Feedback (DFE). Maximum Likelihood Sequence Estimation (MLSE)...1 Decision feedback equaliz A decision feedback equaliz is a simple non-linear equaliz, particularly useful for channel with seve amplitude distortion. DFE consist of a feed forward filt (FFF) and feedback filt (FBF). The Fig3 shows the block diagram of decision feedback equaliz. The feed forward section is nothing but a linear equaliz whose output is given to the decision device. The feedback section is driven by the output of the decision device. Fig.3 Block diagram of decision feedback equaliz. The basic idea behind DFE is that once we have detected information symbol a decided upon, the ISI that induces on the future symbols can be estimated an subtracted out before detection of subsequent symbols. The minimum mean squared ror that a decision feedback equaliz can achieve is: E[ e( n) T ] exp / T / T ln F( e N jt N d The minimum mean squared ror of decision feedback equaliz is small than that of a linear equaliz... Maximum Likehood Sequence Estimation A DFE is not an optimum equaliz because it just outmatches the linear equaliz. MLSE gives optimum pformance as it tests all the possible data sequences and choose that data as output which has the maximum probability. MLSE as an equaliz was first proposed by Forney [For78] in which he setup a basic estimator structure and implement it with Vitbi algorithm. Howev, the computational complexity of an MLSE increases with large delay spread and signal constellation size. The numb of states of the Vitbi decod L is expressed as M, whe M is the numb of symbols in constellation, and L is the channel-speed length. The block diagram of MLSE receiv based on DFE is shown in Fig4. The MLSE is optimal in the sense that it minimized the probability of a sequence ror. () Fig.4 Block diagram of MLSE. The MLSE requires the knowledge of- The channel charactistics in ord to compute the metrics for making decisions. The statistical distribution of the noise corrupting the signal. 3. BIT ERROR RATE When the bits stream transmitted from the source ov the communication channel, then the numb of bits received that alted due to noise, intfence, distortion or bit synchronization rors is the numb of bit rors. Hence, BER is a pformance measurement that specifies the numb of bit corrupted or destroyed as they are transmitted from its source to its destination or BER is the numb of bit ror p unit time. BER can also be defined in tms of the probability of ror (POE). By the definition of bit ror rate we can define its simple formula: No.of Errors BER Totalno.of bits sent The are seval factors that affect BER include bandwidth, signal to noise ratio (SNR), transmission speed and transmission medium. 4. SIGNAL TO NOISE RATIO Signal to noise ratio (SNR) is a measure of the amount of signal divided by the amount of noise being received. SNR is mathematically expressed as: SNR 1log 1(Eb / N)dB whe, ( Eb / N) is the normalized SNR. Normalized SNR is the ratio of engy p bit to noise pow spectral density or it is also called SNR p bit. A high Signal to Noise ratio is good because it means that we are getting more signal and less noise. If SNR is high then the strength of the signal is also high but if it is low or vy poor then the signal is totally distorted and we can t recov the original signal from it. 5. BURST ERROR In telecommunication, a contiguous sequence of symbol is transmitted through the data transmission channel, and when they are opened at the receiv end the first and the last symbol are in ror and the exist no contiguous sequence of 8

3 m symbols between them, this is the burst ror. The integ paramet m is refred to as guard band of the ror burst. 6. SIMULATION AND RESULT Using MATLAB simulation we get following results for diffent equaliz such as linear, decision feedback and MLSE in the tms of BER and Signal to Noise ratio and Burst ror occurrence. Fig.7: Comparison between Ideal BPSK and linear equaliz Fig.5: Unequalized BER pformance Fig.5 shows Unequalized BER pformance. When the signal is transmitted from source, then at the receiv side we haven t used the equaliz, i.e. the output which we get at the receiv end is unequalized output. In this figure as the SNR increases the BER decreases. Fig.8: Linear Signal Pow Spectrum Fig.8: Linear Signal Pow Spectrum. He we find that the amplitude of side lobes are increases but the deepness of nulls decreases. Fig.6: Unequalized Channel Frequency Response Fig.6 shows the unequalized signal pow spectrum. In this figure the are vy deep nulls which means that the channel is to seve and the signal can be strongly distorted by ISI. But in this the main lobe has vy high amplitude and side lobes have vy small amplitudes which means that 99.9% information is contained by main lobe. Fig.9: Comparison among BPSK, Linear and DFE equaliz Fig.9 shows Comparison among BPSK, Linear and DFE equaliz. On comparing the DFE output with the linear equaliz output we get improved BER pformance, i.e. as the SNR increases the BER of the DFE decreases more rapidly as compared to the linear equaliz. 9

4 Fig.1: DFE Signal Pow Spectrum Fig.1 shows DFE Signal Pow Spectrum. He the nulls are less deep and the magnitude of side lobes is also small Fig.11: Comparison among BPSK, Linear, DFE and Ideal MLSE equaliz. Fig.11 shows Comparison among BPSK, Linear, DFE and Ideal MLSE equaliz. On the analysis basis of BER vs SNR pformance we found that the BER pformance of ideal MLSE is bett than that of oths. Fig.1: Comparison among BPSK, Linear, DFE,Ideal MLSE and Impfect MLSE equaliz. Fig.1 shows Comparison among BPSK, Linear, DFE,Ideal MLSE and Impfect MLSE equaliz. He the BER pformance of the impfect MLSE is fairly closely to that of ideal MLSE. For ideal MLSE we assume that the channel is known and for impfect MLSE the channel is time varying. Fig.13: Impfect MLSE Channel Frequency Response Fig.13 shows Impfect MLSE Channel Frequency Response. He, the nulls are deep but the magnitude of the main lobe is vy high. So it 7. CONCLUSION This pap deals with the detailed pformance analysis of linear equaliz and non-linear equaliz. On the basis of theory we conclude the following - Linear equaliz is best suited for comparatively flat channel spectrum. When the channel distortion is too seve for the linear equaliz to mitigate the effects of channel impairments then we use decision feedback equaliz. DFE reach to pretty good steady-state pformance even with seve and noisy channels. But as DFE use decisions on data for removing the part of ISI; incorrect decisions can cause propagation ror in DFEs, since an incorrect decision may add ISI instead of removing it. The minimum mean square ror of DFE is always less than that of linear equaliz. Maximum likelihood sequence estimation (MLSE) is optimal in the sense of having the lowest probability of detecting the wrong sequence. Aft emging the above simulation and result we conclude the following: As the simulation progresses, the BER pformance updates for comparative analysis between the equalization techniques, i.e. the BER pformance of MLSE is bett than oths equalizs. The signal pow spectrum of DFE is much bett than that of linear equaliz. At the low BERs, both the MLSE algorithm and the DFE algorithm suff from ror bursts. Table 1. BER pformance of diffent E b / N (db) Unequali zed Linear DFE Outp ut Ideal MLSE Impf ect MLSE

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