Up to now, the Mean Square Error (MSE) criteria, the residual Inter-Symbol Interference (ISI) and the Bit-Error-Rate (BER) were used to analyze the equalization performance of a blind adaptive equalizer in its converg...Up to now, the Mean Square Error (MSE) criteria, the residual Inter-Symbol Interference (ISI) and the Bit-Error-Rate (BER) were used to analyze the equalization performance of a blind adaptive equalizer in its convergence state. In this paper, we propose an additional tool (additional to the ISI, MSE and BER) for analyzing the equalization performance in the convergence region based on the Maximum Time Interval Error (MTIE) criterion that is used for the specification of clock stability requirements in telecommunications standards. This new tool preserves the short term statistical information unlike the already known tools (BER, ISI, MSE) that lack this information. Simulation results will show that the equalization performance of a blind adaptive equalizer obtained in the convergence region for two different channels is seen to be approximately the same from the residual ISI and MSE point of view while this is not the case with our new proposed tool. Thus, our new proposed tool might be considered as a more sensitive tool compared to the ISI and MSE method.展开更多
Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be ...Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. However, those expressions are not applicable for biased input signals. In this paper, a closed-form approximated expression is proposed for the residual ISI applicable for the noisy and biased input case. This new proposed expression is valid for blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. The new proposed expression depends on the equalizer’s tap length, input signal statistics, channel power, SNR, step-size parameter and on the input signal’s bias. Simulation results indicate a high correlation between the simulated results and those obtained from our new proposed expression.展开更多
A variable step-size parameter is usually used to accelerate the convergence speed of a blind adaptive equalizer with N1 + N2 -1 coefficients where N1 and N2 are odd values. In this paper we show that improved equaliz...A variable step-size parameter is usually used to accelerate the convergence speed of a blind adaptive equalizer with N1 + N2 -1 coefficients where N1 and N2 are odd values. In this paper we show that improved equalization performance is achieved when using two blind adaptive equalizers connected in series where the first and second blind adaptive equalizer have N1 and N2 coefficients respectively compared with the case where a single blind adaptive equalizer is applied with N1 + N2 -1 coefficients. It should be pointed out that the same algorithm (cost function) is used for updating the filter taps for the different equalizers and that a fixed step-size parameter is used. Simulation results show that for the low signal to noise ratio (SNR) environment and for the case where the convergence speed is slow due to the channel characteristics, the new method has a faster convergence speed with a factor of approximately two while leaving the system with approximately the same or lower residual intersymbol interference (ISI).展开更多
The National Institute of Standards and Technology (NIST) document is a list of fifteen tests for estimating the probability of signal randomness degree. <span style="font-family:Verdana;">Test number ...The National Institute of Standards and Technology (NIST) document is a list of fifteen tests for estimating the probability of signal randomness degree. <span style="font-family:Verdana;">Test number six in the NIST document is the Discrete Fourier Transform</span><span style="font-family:Verdana;"> (DFT) test suitable for stationary incoming sequences. But, for cases where the input sequence is not stationary, the DFT test provides inaccurate results. For these cases, test number seven and eight (the Non-overlapping Template Matching Test and the Overlapping Template Matching Test) of the NIST document were designed to classify those non-stationary sequences. But, even with test number seven and eight of the NIST document, the results are not always accurate. Thus, the NIST test does not give a proper answer for the non-stationary input sequence case. In this paper, we offer a new algorithm </span><span style="font-family:Verdana;">or test, which may replace the NIST tests number six, seven and eight. The</span> <span style="font-family:Verdana;">proposed test is applicable also for non-stationary sequences and supplies</span><span style="font-family:Verdana;"> more </span><span style="font-family:Verdana;">accurate results than the existing tests (NIST tests number six, seven and</span><span style="font-family:Verdana;"> eight), for non-stationary sequences. The new proposed test is based on the Wigner function and on the Generalized Gaussian Distribution (GGD). In addition, </span><span style="font-family:Verdana;">this new proposed algorithm alarms and indicates on suspicious places of</span><span style="font-family:Verdana;"> cyclic </span><span style="font-family:Verdana;">sections in the tested sequence. Thus, it gives us the option to repair or to</span><span style="font-family:Verdana;"> remove the suspicious places of cyclic sections</span><span><span><span><span></span><span></span><b><span style="font-family:;" "=""><span></span><span></span> </span></b></span></span></span><span><span><span><span></span><span></span><span style="font-family:;" "=""><span></span><span></span><span style="font-family:Verdana;">(this part is beyond the scope </span><span style="font-family:Verdana;">of this paper), so that after that, the repaired or the shortened sequence</span><span style="font-family:Verdana;"> (origi</span><span style="font-family:Verdana;">nal sequence with removed sections) will result as a sequence with high</span><span style="font-family:Verdana;"> probability of random degree.</span></span></span></span></span>展开更多
Due to non-ideal coefficients of the adaptive equalizer used in the system, a convolutional noise arises at the output of the deconvolutional process in addition to the source input. A higher convolutional noise may m...Due to non-ideal coefficients of the adaptive equalizer used in the system, a convolutional noise arises at the output of the deconvolutional process in addition to the source input. A higher convolutional noise may make the recovering process of the source signal more difficult or in other cases even impossible. In this paper we deal with the fluctuations of the arithmetic average (sample mean) of the real part of consecutive convolutional noises which deviate from the mean of order higher than the typical fluctuations. Typical fluctuations are those fluctuations that fluctuate near the mean, while the other fluctuations that deviate from the mean of order higher than the typical ones are considered as rare events. Via the large deviation theory, we obtain a closed-form approximated expression for the amount of deviation from the mean of those fluctuations considered as rare events as a function of the system’s parameters (step-size parameter, equalizer’s tap length, SNR, input signal statistics, characteristics of the chosen equalizer and channel power), for a pre-given probability that these events may occur.展开更多
Recently, closed-form approximated expressions were obtained for the residual Inter Symbol Interference (ISI) obtained by blind adaptive equalizers for the biased as well as for the non-biased input case in a noisy en...Recently, closed-form approximated expressions were obtained for the residual Inter Symbol Interference (ISI) obtained by blind adaptive equalizers for the biased as well as for the non-biased input case in a noisy environment. But, up to now it is unclear under what condition improved equalization performance is obtained in the residual ISI point of view with the non-biased case compared with the biased version. In this paper, we present for the real and two independent quadrature carrier case a closed-form approximated expression for the difference in the residual ISI obtained by blind adaptive equalizers with biased input signals compared with the non-biased case. Based on this expression, we show under what condition improved equalization performance is obtained from the residual ISI point of view for the non-biased case compared with the biased version.展开更多
In the communication field, during transmission, a source signal undergoes a convolutive distortion between its symbols and the channel impulse response. This distortion is referred to as Intersymbol Interference (ISI...In the communication field, during transmission, a source signal undergoes a convolutive distortion between its symbols and the channel impulse response. This distortion is referred to as Intersymbol Interference (ISI) and can be reduced significantly by applying a blind adaptive deconvolution process (blind adaptive equalizer) on the distorted received symbols. But, since the entire blind deconvolution process is carried out with no training symbols and the channel’s coefficients are obviously unknown to the receiver, no actual indication can be given (via the mean square error (MSE) or ISI expression) during the deconvolution process whether the blind adaptive equalizer succeeded to remove the heavy ISI from the transmitted symbols or not. Up to now, the output of a convolution and deconvolution process was mainly investigated from the ISI point of view. In this paper, the output of a convolution and deconvolution process is inspected from the leading digit point of view. Simulation results indicate that for the 4PAM (Pulse Amplitude Modulation) and 16QAM (Quadrature Amplitude Modulation) input case, the number “1” is the leading digit at the output of a convolution and deconvolution process respectively as long as heavy ISI exists. However, this leading digit does not follow exactly Benford’s Law but follows approximately the leading digit (digit 1) of a Gaussian process for independent identically distributed input symbols and a channel with many coefficients.展开更多
In this paper a closed-form approximated expression is proposed for the Intersymbol Interference (ISI) as a function of time valid during the entire stages of the non-blind adaptive deconvolution process and is suitab...In this paper a closed-form approximated expression is proposed for the Intersymbol Interference (ISI) as a function of time valid during the entire stages of the non-blind adaptive deconvolution process and is suitable for the noisy, real and two independent quadrature carrier input case. The obtained expression is applicable for type of channels where the resulting ISI as a function of time can be described with an exponential model having a single time constant. Based on this new expression for the ISI as a function of time, the convergence time (or number of iteration number required for convergence) of the non-blind adaptive equalizer can be calculated. Up to now, the equalizer’s performance (convergence time and ISI as a function of time) could be obtained only via simulation when the channel coefficients were known. The new proposed expression for the ISI as a function of time is based on the knowledge of the initial ISI and channel power (which is measurable) and eliminates the need to carry out any more the above mentioned simulation. Simulation results indicate a high correlation between the simulated and calculated ISI (based on our proposed expression for the ISI as a function of time) during the whole deconvolution process for the high as well as for the low signal to noise ratio (SNR) condition.展开更多
文摘Up to now, the Mean Square Error (MSE) criteria, the residual Inter-Symbol Interference (ISI) and the Bit-Error-Rate (BER) were used to analyze the equalization performance of a blind adaptive equalizer in its convergence state. In this paper, we propose an additional tool (additional to the ISI, MSE and BER) for analyzing the equalization performance in the convergence region based on the Maximum Time Interval Error (MTIE) criterion that is used for the specification of clock stability requirements in telecommunications standards. This new tool preserves the short term statistical information unlike the already known tools (BER, ISI, MSE) that lack this information. Simulation results will show that the equalization performance of a blind adaptive equalizer obtained in the convergence region for two different channels is seen to be approximately the same from the residual ISI and MSE point of view while this is not the case with our new proposed tool. Thus, our new proposed tool might be considered as a more sensitive tool compared to the ISI and MSE method.
文摘Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. However, those expressions are not applicable for biased input signals. In this paper, a closed-form approximated expression is proposed for the residual ISI applicable for the noisy and biased input case. This new proposed expression is valid for blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. The new proposed expression depends on the equalizer’s tap length, input signal statistics, channel power, SNR, step-size parameter and on the input signal’s bias. Simulation results indicate a high correlation between the simulated results and those obtained from our new proposed expression.
文摘A variable step-size parameter is usually used to accelerate the convergence speed of a blind adaptive equalizer with N1 + N2 -1 coefficients where N1 and N2 are odd values. In this paper we show that improved equalization performance is achieved when using two blind adaptive equalizers connected in series where the first and second blind adaptive equalizer have N1 and N2 coefficients respectively compared with the case where a single blind adaptive equalizer is applied with N1 + N2 -1 coefficients. It should be pointed out that the same algorithm (cost function) is used for updating the filter taps for the different equalizers and that a fixed step-size parameter is used. Simulation results show that for the low signal to noise ratio (SNR) environment and for the case where the convergence speed is slow due to the channel characteristics, the new method has a faster convergence speed with a factor of approximately two while leaving the system with approximately the same or lower residual intersymbol interference (ISI).
文摘The National Institute of Standards and Technology (NIST) document is a list of fifteen tests for estimating the probability of signal randomness degree. <span style="font-family:Verdana;">Test number six in the NIST document is the Discrete Fourier Transform</span><span style="font-family:Verdana;"> (DFT) test suitable for stationary incoming sequences. But, for cases where the input sequence is not stationary, the DFT test provides inaccurate results. For these cases, test number seven and eight (the Non-overlapping Template Matching Test and the Overlapping Template Matching Test) of the NIST document were designed to classify those non-stationary sequences. But, even with test number seven and eight of the NIST document, the results are not always accurate. Thus, the NIST test does not give a proper answer for the non-stationary input sequence case. In this paper, we offer a new algorithm </span><span style="font-family:Verdana;">or test, which may replace the NIST tests number six, seven and eight. The</span> <span style="font-family:Verdana;">proposed test is applicable also for non-stationary sequences and supplies</span><span style="font-family:Verdana;"> more </span><span style="font-family:Verdana;">accurate results than the existing tests (NIST tests number six, seven and</span><span style="font-family:Verdana;"> eight), for non-stationary sequences. The new proposed test is based on the Wigner function and on the Generalized Gaussian Distribution (GGD). In addition, </span><span style="font-family:Verdana;">this new proposed algorithm alarms and indicates on suspicious places of</span><span style="font-family:Verdana;"> cyclic </span><span style="font-family:Verdana;">sections in the tested sequence. Thus, it gives us the option to repair or to</span><span style="font-family:Verdana;"> remove the suspicious places of cyclic sections</span><span><span><span><span></span><span></span><b><span style="font-family:;" "=""><span></span><span></span> </span></b></span></span></span><span><span><span><span></span><span></span><span style="font-family:;" "=""><span></span><span></span><span style="font-family:Verdana;">(this part is beyond the scope </span><span style="font-family:Verdana;">of this paper), so that after that, the repaired or the shortened sequence</span><span style="font-family:Verdana;"> (origi</span><span style="font-family:Verdana;">nal sequence with removed sections) will result as a sequence with high</span><span style="font-family:Verdana;"> probability of random degree.</span></span></span></span></span>
文摘Due to non-ideal coefficients of the adaptive equalizer used in the system, a convolutional noise arises at the output of the deconvolutional process in addition to the source input. A higher convolutional noise may make the recovering process of the source signal more difficult or in other cases even impossible. In this paper we deal with the fluctuations of the arithmetic average (sample mean) of the real part of consecutive convolutional noises which deviate from the mean of order higher than the typical fluctuations. Typical fluctuations are those fluctuations that fluctuate near the mean, while the other fluctuations that deviate from the mean of order higher than the typical ones are considered as rare events. Via the large deviation theory, we obtain a closed-form approximated expression for the amount of deviation from the mean of those fluctuations considered as rare events as a function of the system’s parameters (step-size parameter, equalizer’s tap length, SNR, input signal statistics, characteristics of the chosen equalizer and channel power), for a pre-given probability that these events may occur.
文摘Recently, closed-form approximated expressions were obtained for the residual Inter Symbol Interference (ISI) obtained by blind adaptive equalizers for the biased as well as for the non-biased input case in a noisy environment. But, up to now it is unclear under what condition improved equalization performance is obtained in the residual ISI point of view with the non-biased case compared with the biased version. In this paper, we present for the real and two independent quadrature carrier case a closed-form approximated expression for the difference in the residual ISI obtained by blind adaptive equalizers with biased input signals compared with the non-biased case. Based on this expression, we show under what condition improved equalization performance is obtained from the residual ISI point of view for the non-biased case compared with the biased version.
文摘In the communication field, during transmission, a source signal undergoes a convolutive distortion between its symbols and the channel impulse response. This distortion is referred to as Intersymbol Interference (ISI) and can be reduced significantly by applying a blind adaptive deconvolution process (blind adaptive equalizer) on the distorted received symbols. But, since the entire blind deconvolution process is carried out with no training symbols and the channel’s coefficients are obviously unknown to the receiver, no actual indication can be given (via the mean square error (MSE) or ISI expression) during the deconvolution process whether the blind adaptive equalizer succeeded to remove the heavy ISI from the transmitted symbols or not. Up to now, the output of a convolution and deconvolution process was mainly investigated from the ISI point of view. In this paper, the output of a convolution and deconvolution process is inspected from the leading digit point of view. Simulation results indicate that for the 4PAM (Pulse Amplitude Modulation) and 16QAM (Quadrature Amplitude Modulation) input case, the number “1” is the leading digit at the output of a convolution and deconvolution process respectively as long as heavy ISI exists. However, this leading digit does not follow exactly Benford’s Law but follows approximately the leading digit (digit 1) of a Gaussian process for independent identically distributed input symbols and a channel with many coefficients.
文摘In this paper a closed-form approximated expression is proposed for the Intersymbol Interference (ISI) as a function of time valid during the entire stages of the non-blind adaptive deconvolution process and is suitable for the noisy, real and two independent quadrature carrier input case. The obtained expression is applicable for type of channels where the resulting ISI as a function of time can be described with an exponential model having a single time constant. Based on this new expression for the ISI as a function of time, the convergence time (or number of iteration number required for convergence) of the non-blind adaptive equalizer can be calculated. Up to now, the equalizer’s performance (convergence time and ISI as a function of time) could be obtained only via simulation when the channel coefficients were known. The new proposed expression for the ISI as a function of time is based on the knowledge of the initial ISI and channel power (which is measurable) and eliminates the need to carry out any more the above mentioned simulation. Simulation results indicate a high correlation between the simulated and calculated ISI (based on our proposed expression for the ISI as a function of time) during the whole deconvolution process for the high as well as for the low signal to noise ratio (SNR) condition.
