Optimum delay and mean square error using a mixed crosscorrelation and constant modulus algorithm

2000 ◽  
Vol 147 (1) ◽  
pp. 18 ◽  
Author(s):  
D.J. Brooks ◽  
S. Lambotharan ◽  
J.A. Chambers
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Constant Modulus ◽  
Constant Modulus Algorithm

New Dual-Mode FSE Suitable for High-Order QAM Signals

2013 ◽  
Vol 760-762 ◽  
pp. 478-482
Author(s):  
Hui Juan Gao ◽  
Yan Liu
Keyword(s):  
Steady State ◽  
Mean Square Error ◽  
Digital Transmission ◽  
High Order ◽  
Mean Square ◽  
Constant Modulus ◽  
Constant Modulus Algorithm ◽  
Dual Mode ◽  
Training Sequences ◽  
Second Mode

In the digital transmission system, constant modulus algorithm (CMA) is a famous blind equalization to overcome the inter-symbol interference without the aid of training sequences. But for the non-constant modulus signals such as higher-order QAM signals, the CMA just achieve moderate steady-state mean square error (MSE). So a new dual-mode fractionally-spaced equalization (FSE) suitable for high-order QAM signals is proposed, which makes full use of the character which is that the high-order QAM signals have the different modulus. This algorithm uses the FSE based on CMA as the basal mode and in the second mode it uses the FSE based on variable modulus algorithm. The simulation results show that compared with CMA the proposed algorithm has faster convergence rate and lower steady-state mean square error.

New Concurrent Fractionally-Spaced Blind Equalization

2010 ◽  
Vol 108-111 ◽  
pp. 363-368 ◽  
Author(s):  
Wei Rao ◽  
Ye Cai Guo ◽  
Min Chen ◽  
Wen Qun Tan ◽  
Jian Bing Liu ◽  
...  
Keyword(s):  
Steady State ◽  
Convergence Rate ◽  
Mean Square Error ◽  
Blind Equalization ◽  
Mean Square ◽  
Constant Modulus ◽  
Constant Modulus Algorithm ◽  
Underwater Acoustic ◽  
Underwater Acoustic Channels ◽  
Simulation Results

The paper proposes a concurrent constant modulus algorithm (CMA) and decision-directed (DD) scheme for fractionally-spaced blind equalization. The proposed algorithm makes full use of the advantages of CMA and DD algorithm. A novel rule to control the adjustment of DD’s tap weights vector is proposed which avoids the hard switch between CMA and DD in practice. Simulations with underwater acoustic channels are used to compare the proposed algorithm with the famous CMA. And the simulation results show that the proposed algorithm has faster convergence rate and lower steady state mean square error.

New FSE Based on MCMA and PLL

2013 ◽  
Vol 760-762 ◽  
pp. 467-471
Author(s):  
Yan Liu ◽  
Yuan Min Li
Keyword(s):  
Computer Simulation ◽  
Steady State ◽  
Convergence Rate ◽  
Mean Square Error ◽  
Carrier Phase ◽  
Digital Transmission ◽  
Mean Square ◽  
Constant Modulus ◽  
Constant Modulus Algorithm ◽  
Phase Rotation

In the digital transmission system, an efficient fractionally-spaced equalizer (FSE) for blind equalization based on modified constant modulus algorithm (MCMA) and phase locked loop (PLL) is proposed. Comparing with conventional FSE based on famous CMA, the proposed algorithm has not only lower steady-state mean square error and faster convergence rate but also the ability to recover carrier phase rotation. The efficiency of the method is proved by computer simulation.

An Optimized Combination of Frequency Domain Adaptive Equalizers

2014 ◽  
Vol 548-549 ◽  
pp. 766-770
Author(s):  
Ke Cheng Leng ◽  
Cheng Bie ◽  
Xi Gong ◽  
Ran Xu ◽  
Ye Cai Guo
Keyword(s):  
Frequency Domain ◽  
Mean Square Error ◽  
Time Domain ◽  
Blind Equalization ◽  
Mean Square ◽  
Constant Modulus ◽  
Equalization Algorithm ◽  
Adaptive Equalizers ◽  
Simulation Results ◽  
The Time Domain

In order to overcome the defects of the high computational loads and selecting the threshold of mean square error (MSE) for time domain decision-directed constant modulus blind equalization algorithm (DD+CMA), a frequency domain parallel decision multi-modulus blind equalization algorithm based on frequency domain MMA(FMMA) and frequency domain LMS (FLMS) algorithm is proposed. The proposed algorithm is composed of the FMMA and FLMS, and the FMMA and FLMS run automatically in soft switching parallel manner. In running process, it is not necessary to selecting the threshold of the MSE. Moreover, the computational loads can be reduced by circular convolution in the frequency domain signals instead of linear one of the time domain signals. Simulation results show that performance of the proposed algorithm outperforms the FLMS and the FMMA algorithm.

scholarly journals CMA Channel Equalization Through An Adaptive MMSE Equalizer Based RLS Algorithm

2014 ◽  
pp. 129-134
Author(s):  
Tara Saikumar ◽  
B. Smitha ◽  
P. S. Murthy
Keyword(s):  
Mean Square Error ◽  
Minimum Mean Square Error ◽  
Channel Equalization ◽  
Residual Error ◽  
Optimization Approach ◽  
Mean Square ◽  
Constant Modulus Algorithm ◽  
Step Size ◽  
Error Level ◽  
Rls Algorithm

The adaptive algorithm has been widely used in the digital signal processing like channel estimation, channel equalization, echo cancellation, and so on. One of the most important adaptive algorithms is the RLS algorithm. We present in this paper n multiple objective optimization approach to fast blind channel equalization. By investigating first the performance (mean-square error) of the standard fractionally spaced CMA (constant modulus algorithm) equalizer in the presence of noise, we show that CMA local minima exist near the minimum mean-square error (MMSE) equalizers. Consequently, CMA may converge to a local minimum corresponding to a poorly designed MMSE receiver with considerable large mean-square error. The step size in the RLS algorithm decides both the convergence speed and the residual error level, the highest speed of convergence and residual error level.

scholarly journals Χρήση αυτορυθμιζόμενων ηλεκτρονικών εξισωτών σε οπτικά τηλεπικοινωνιακά συστήματα και δίκτυα με πυκνή πολυπλεξία μήκους κύματος και ρυθμό σηματοδοσίας 10 GB/S ανά οπτικό κανάλι

2010 ◽  
Author(s):  
Αθανάσιος Βγένης
Keyword(s):  
Mean Square ◽  
Least Mean Square ◽  
Constant Modulus ◽  
Constant Modulus Algorithm

Η παρούσα διατριβή εστιάζεται σε οπτικά τηλεπικοινωνιακά συστήματα με σύμφωνο δέκτη τετραδική διαμόρφωση φάσης και πολύπλεξη κατά πόλωση. Το κυριότερο πλεονέκτημα αυτών των συστημάτων σε σύγκριση με τα συμβατικά οπτικά τηλεπικοινωνιακά συστήματα με δέκτες άμεσης φώρασης είναι οι αυξημένες δυνατότητες ψηφιακής επεξεργασίας σήματος στο δέκτη που καθιστά εφικτή την εξίσωση των φαινομένων διάδοσης και την αποπολύπλεξη πόλωσης με ηλεκτρονικά μέσα. Μελετώνται διατάξεις ηλεκτρονικής επεξεργασίας σήματος. Η μελέτη διεξάγεται με χρήση προσομοίωσης με τη βοήθεια ηλεκτρονικού υπολογιστή. Προτείνεται η χρήση δύο πρωτότυπων μεθόδων αποπολύπλεξης σημάτων πολυπλεγμένων κατά πόλωση με πλεονεκτήματα ως προς την απόδοση, την αξιοπιστία και την ταχύτητα σύγκλισης σε σύγκριση με τις μεθόδους που έχουν προταθεί στη βιβλιογραφία. Στη συνέχεια μελετάται η απόδοση των ηλεκτρονικών εξισωτών ελαχίστου μέσου τετράγωνου (least-mean square) και σταθερής περιβάλλουσας (constant modulus algorithm) στην εξίσωση της χρωματικής διασποράς και της διασποράς τρόπων πόλωσης, τόσο μεμονωμένα, όσο και από κοινού. Στη μελέτη μας συμπεριλαμβάνουμε το θόρυβο φάσης και την ενδιάμεση συχνότητα, αίροντας αντίστοιχες απλοποιήσεις που συνήθως γίνονται στη βιβλιογραφία. Ακολούθως αναφερόμαστε στο πρόβλημα του εκφυλισμού του πίνακα συντελεστών των εξισωτών ελάχιστου μέσου τετραγώνου και σταθερής περιβάλλουσας παρουσία έντονης διεξασθένησης. Ο πίνακας συντελεστών στον οποίο έχει συγκλίνει ο εξισωτής ονομάζεται εκφυλισμένος όταν παράγεται η ίδια απεσταλμένη ακολουθία συμβόλων και στις δύο εξόδους του εξισωτή. Προτείνουμε τη χρήση του πολυχρηστικού εξισωτή σταθερής περιβάλλουσας (multiuser constant modulus algorithm equalizer). Η λύση που προτείνεται έχει πλεονεκτήματα αξιοπιστίας και απλότητας σε σχέση με αντίστοιχες προτάσεις στη βιβλιογραφία και αποδεικνύεται η άριστη απόδοσή της. Στη συνέχεια, γίνεται αναφορά στο φαινόμενο της ανισοσταθμίας ορθογωνιότητας που παρατηρείται στα οπτικά συστήματα με σύμφωνους δέκτες και αποτελεί ένα φαινόμενο το οποίο κατά κανόνα παραβλέπεται στις μελέτες της βιβλιογραφίας και αποδεικνύεται το ότι οι συμβατικοί ηλεκτρονικοί εξισωτές δεν μπορούν να το αντιμετωπίσουν. Τέλος, παραθέτουμε αποτελέσματα από την επεξεργασία πραγματικών πειραματικών δεδομένων για την επαλήθευση των συμπερασμάτων που προέκυψαν θεωρητικά.

scholarly journals A Simple and Robust Equalization Algorithm for Variable Modulation Systems

Electronics ◽  
2021 ◽  
Vol 10 (20) ◽  
pp. 2496
Author(s):  
Wanru Hu ◽  
Zhugang Wang ◽  
Ruru Mei ◽  
Meiyan Lin
Keyword(s):  
Adaptive Equalization ◽  
Mean Square ◽  
Least Mean Square ◽  
Constant Modulus ◽  
Phase Shift Keying ◽  
Constant Modulus Algorithm ◽  
Training Sequences ◽  
Shift Keying ◽  
The Stability ◽  
Variable Modulation

This paper proposes a simple and robust variable modulation-decision-directed least mean square (VM-DDLMS) algorithm for reducing the complexity of conventional equalization algorithms and improving the stability of variable modulation (VM) systems. Compared to conventional adaptive equalization algorithms, known information was used as training sequences to reduce the bandwidth consumption caused by inserting training sequences; compared with conventional blind equalization algorithms, the parameters and decisions of the equalizer were determinate, which was conducive to a stable equalization performance. The simulation and implementation results show that the proposed algorithm has a better bit error rate (BER) performance than that of the constant modulus algorithm (CMA) and modified constant modulus algorithm (MCMA) while maintaining the same level of consumption of hardware resources. Compared to the conventional decision-directed least mean square (DDLMS) algorithm, the proposed algorithm only needs to make quadrature phase shift keying (QPSK) symbol decisions, which reduces the computational complexity. In parallel 11th-order equalization algorithms, the operating frequency of VM-DDLMS can reach up to 333.33 MHz.

scholarly journals A Novel Adaptive Algorithm Addresses Potential Problems of Blind Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Yasin ◽  
Muhammad Junaid Hussain
Keyword(s):  
Hybrid Algorithm ◽  
Smart Antenna ◽  
Additive White Gaussian Noise ◽  
Lms Algorithm ◽  
Mean Square ◽  
Least Mean Square ◽  
Constant Modulus ◽  
Constant Modulus Algorithm ◽  
Proposed Model ◽  
Potential Problems

A hybrid algorithm called constant modulus least mean square (CMLMS) algorithm is proposed in order to address the potential problems existing with constant modulus algorithm (CMA) about its convergence. It is a two-stage adaptive filtering algorithm and based on least mean square (LMS) algorithm followed by CMA. A hybrid algorithm is theoretically developed and the same is verified through MatLab Software. Theoretical model is verified through simulation and its performance is evaluated in smart antenna in presence of a cochannel interfering signal and additive white Gaussian noise (AWGN) of zero mean. This is also tested in Rayleigh fading channel using digital modulation technique for Bit Error Rate (BER). Finally, a few computer simulations are presented in order to substantiate the theoretical findings with respect to proposed model. Corresponding results obtained with the use of only CMA and LMS algorithms are also presented for further comparison.

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