Orthogonal Signals and the Orthogonalization Procedure

2021 ◽  
pp. 18-55
Author(s):  
Stevan Berber
Keyword(s):  
Spread Spectrum ◽  
Communication Systems ◽  
Orthogonal Frequency Division Multiplexing ◽  
Theory And Practice ◽  
Schmidt Orthogonalization ◽  
Code Division Multiple ◽  
Digital Communication Systems ◽  
Spreading Sequences ◽  
Multiplexing Systems ◽  
Orthogonalization Procedure

Chapter 2 is dedicated to the principle of signal orthogonalization, because orthogonal signals are widely used in telecommunication theory and practice, like the carriers of baseband signals, subcarriers in orthogonal frequency division multiplexing systems, and the spreading sequences in spread-spectrum and code division multiple access (CDMA) systems. The orthonormal basis functions are defined and the procedure of the vector representation of signals is demonstrated. The Gram–Schmidt orthogonalization procedure and construction of the space diagram are presented in detail. Using orthonormal signals, signal synthesizers and analysers that can be used to form discrete-time transmitters and receivers are theoretically founded. Understanding of this chapter is a prerequisite for understanding Chapters 4–10, because the orthonormal signals defined in this chapter will be used throughout the book. The basis harmonic orthonormal functions will define the carriers in the discrete and digital communication systems.

scholarly journals Suitable Spreading Sequences for Asynchronous MC-CDMA Systems

2018 ◽  
Vol 3 ◽  
pp. 9-13 ◽  
Author(s):  
Mouad Addad ◽  
Ali Djebbari
Keyword(s):  
Communication Systems ◽  
Multiple Access ◽  
Signal To Noise Ratio ◽  
Multiple Access Interference ◽  
High Data ◽  
Research Areas ◽  
Rate Transmission ◽  
Cdma Systems ◽  
Code Division Multiple ◽  
Spreading Sequences

In order to meet the demand of high data rate transmission with good quality maintained, the multi-carrier code division multiple access (MC-CDMA) technology is considered for the next generation wireless communication systems. However, their high crest factor (CF) is one of the major drawbacks of multi-carrier transmission systems. Thus, CF reduction is one of the most important research areas in MC-CDMA systems. In addition, asynchronous MC-CDMA suffers from the effect of multiple access interference (MAI), caused by all users active in the system. Degradation of the system’s bit error rate (BER) caused by MAI must be taken into consideration as well. The aim of this paper is to provide a comparative study on the enhancement of performance of an MC-CDMA system. The spreading sequences used in CDMA play an important role in CF and interference reduction. Hence, spreading sequences should be selected to simultaneously ensure low CF and low BER values. Therefore, the effect that correlation properties of sequences exert on CF values is investigated in this study. Furthermore, a numerical BER evaluation, as a function of the signal-to-noise ratio (SNR) and the number of users, is provided. The results obtained indicate that a trade-off between the two criteria is necessary to ensure good performance. It was concluded that zero correlation zone (ZCZ) sequences are the most suitable spreading sequences as far as the satisfaction of the above criteria is concerned.

scholarly journals Αρχιτεκτονικές και αλγόριθμοι εκτίμησης ραδιοδιαύλου για σύγχρονα ευρυζωνικά ασύρματα συστήματα επικοινωνιών

2010 ◽  
Author(s):  
Αθανάσιος Μαρούσης
Keyword(s):  
Spread Spectrum ◽  
Code Division Multiple Access ◽  
Orthogonal Frequency Division Multiplexing ◽  
Multiple Access ◽  
Multiple Input Multiple Output ◽  
Frequency Division Multiplexing ◽  
Frequency Division ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Code Division Multiple

Η παρούσα διδακτορική διατριβή πραγματεύεται την ανάπτυξη και αξιολόγηση νέων αρχιτεκτονικών και αλγορίθμων εκτίμησης του ραδιοδιαύλου σε σύγχρονα ευρυζωνικά ασύρματα συστήματα επικοινωνιών. Η αναγκαιότητα του θέματος συνδέεται άμεσα με το γεγονός ότι η βαθμίδα εκτίμησης του ραδιοδιαύλου σε πραγματικό χρόνο αποτελεί κομβική συνιστώσα στην αποδοτική λειτουργία μιας ασύρματης ζεύξης και κατ' επέκταση ενός ασύρματου συστήματος. Επιπλέον, η ενσωμάτωση νέων τεχνικών εκπομπής και λήψης για τη βελτίωση του ρυθμού μετάδοσης τόσο των υπαρχόντων, όσο και των μελλοντικών ευρυζωνικών ασύρματων συστημάτων αυξάνει τις απαιτήσεις ενός εκτιμητή του ασύρματου διαύλου. Στοχεύοντας σε μια ολοκληρωμένη προσέγγιση, αρχικά, αναπτύσσονται συστήματα όπου η πληροφορία μεταδίδεται χρησιμοποιώντας τα πεδία του χώρου, του χρόνου, της συχνότητας και του κώδικα. Τέτοια συστήματα είναι τα Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (ΜΙΜΟ-OFDM), τα MIMO Multicarrier Code Division Multiple Access (MIMO MCCDMA) και τα MIMO Spread Spectrum MC Multiple Access (MIMO SS-MC-MA). Στη συνέχεια, προτείνονται καινοτόμες βαθμίδες εκτίμησης διαύλου και αναπτύσσονται αλγόριθμοι που επιτρέπουν τη συνεχή εκτίμηση του σε περιβάλλοντα διάδοσης με μεταβαλλόμενα χαρακτηριστικά και μικρές τιμές συνοχής στα πεδία του χώρου του χρόνου και της συχνότητας. Σκοπεύοντας στην καλύτερη δυνατή αξιοποίηση των διαθέσιμων ραδιοπόρων του συστήματος, οι προτεινόμενες μέθοδοι είναι προσαρμοστικές και επιτρέπουν τη δυναμική επιλογή των παραμέτρων τους ανά περίπτωση. Ανάλογα με τα γενικά χαρακτηριστικά του περιβάλλοντος διάδοσης είναι δυνατή η ρύθμιση των επιμέρους παραμέτρων ώστε η χρήση τους να είναι βέλτιστη. Η παραμετροποίηση των αρχιτεκτονικών και των μεθόδων που εξετάζονται επιτρέπει α) την ασφαλή και ενημερωμένη εκτίμηση του διαύλου και β) την προσαρμοστική επιλογή του κατάλληλου σχήματος εκπομπής για τη μεγιστοποίηση είτε του ρυθμού μετάδοσης δεδομένων, είτε της αξιοπιστίας της ζεύξης. Οι προτεινόμενες μέθοδοι είναι επαναληπτικές και παρουσιάζουν εξαιρετικά χαρακτηριστικά επίδοσης με μικρό αριθμό επαναλήψεων. Το γεγονός αυτό επιτρέπει την αποδοτική εκτίμηση του ραδιοδιαύλου αλλά και τη βελτίωση της συνολικής επίδοσης του συστήματος. Επιπλέον, ιδιαίτερο βάρος δίνεται στην ελαχιστοποίηση της εκπαίδευσης που απαιτούν οι επαναληπτικές μέθοδοι. Σε κάθε επανάληψη, τα εκτιμηθέντα δεδομένα που προκύπτουν χρησιμοποιούνται ανά περίσταση με δύο πιθανούς τρόπους ως επιπλέον είσοδοι του εκτιμητή, είτε α) για την εξάλειψη της ενδογενούς παρεμβολής, είτε β) ως εικονικοί πιλότοι. Επίσης, εξετάζεται η χρήση μη-ορθογώνιων τεχνικών πλήρους ρυθμού όπου το σφάλμα ορθογωνιότητας είναι γνωστό στο δέκτη. Τέλος, υπό το πρίσμα της ρεαλιστικής αξιολόγησης των προτεινόμενων μεθόδων και αρχιτεκτονικών, πραγματοποιούνται μελέτες επίδοσης όπου μοντελοποιούνται και λαμβάνονται υπόψη οι ατέλειες των RF τμημάτων των πομποδεκτών. Αυτό γιατί, σε πρακτικά ασύρματα συστήματα ο εκτιμητής διαύλου καλείται να εκτιμήσει συνολικά την επίδραση του ασύρματου μέσου διάδοσης και των βαθμίδων του πομπού και του δέκτη που παρεμβάλλονται μέχρι τον ανιχνευτή πληροφορίας στο δέκτη και οι οποίες συντελούν στην αλλοίωση των χαρακτηριστικών του σήματος πληροφορίας.

scholarly journals Quaternary DS-SSMA Communications Employing Generalized Detector over Rayleigh Fading Channels

2020 ◽  
Vol 16 ◽  
Keyword(s):  
Signal Processing ◽  
Fading Channels ◽  
Spread Spectrum ◽  
Communication Systems ◽  
Rayleigh Fading ◽  
Gaussian Approximation ◽  
Direct Sequence Spread Spectrum ◽  
Asynchronous Communication ◽  
Signature Sequences ◽  
Spreading Sequences

This paper deals with an employment of the complex modulators and generalized receivers constructed based on the generalized approach to signal processing (GASP) in noise in quaternary direct-sequence spread-spectrum multiple-access (DS-SSMA) communication systems with complex signature sequences in flat Rayleigh fading. Owing to availability of large sets of complex spreading sequences possessing perfect correlation characteristics, the interest to use the complex spreading sequences in DS-SSMA communication systems has increased. The complex spreading sequences investigated in the present paper are based on the recently introduced orthogonal unified complex Hadamard transform (UCHN) sequences. In the present paper, the complex processing in modulators and generalized receivers is also employed with the purpose to take advantage of the correlation properties of complex signature sequences. We derive the average bit error rate (BER) for quarternary synchronous communications system based on the generalized approach to signal processing in noise first, and then the BER for quaternary asynchronous ones is evaluated using the characteristic function approach. We presented some results based on the Gaussian approximation method for asynchronous communication systems constructed on the basis of the generalized approach to signal processing in noise Computer modeling results demonstrate that the communication systems using UCHT spreading sequences perform generally better than the GOLD sequences and the 4-phase family A sequences. Comparative analysis between the asynchronous communication systems constructed on the basis of the generalized approach to signal processing in noise demonstrates superiority over the asynchronous communication systems employing the correlation receiver.

Two Conversion Formulas of Known Optimal Sequences

2015 ◽  
Vol 713-715 ◽  
pp. 2012-2015
Author(s):  
Fan Xin Zeng ◽  
Zhen Yu Zhang
Keyword(s):  
Spread Spectrum ◽  
Code Division Multiple Access ◽  
Communication Systems ◽  
Multiple Access ◽  
Spread Spectrum Communication ◽  
Autocorrelation Functions ◽  
Construction Methods ◽  
Code Division Multiple

This paper investigates the construction methods of sequences with optimal autocorrelation functions. The approaches proposed by us are to convert the known optimal sequences into the required sequences. In order to arrive at our goal, we establish two conversion formulas, and summarize their performance. The proposed methods can provide lots of candidates of spread sequences for the applications of code-division multiple-access (CDMA) spread spectrum communication systems.

scholarly journals Pseudorandom Sequences in Spread-Spectrum Communications Generated by Cellular Automata

2012 ◽  
Vol 10 (5) ◽  
Author(s):  
F.C. Ordaz-Salazar ◽  
J.S. González-Salas ◽  
E. Campos-Cantón ◽  
H.C. Rosu
Keyword(s):  
Cellular Automata ◽  
Spread Spectrum ◽  
Communication Systems ◽  
Signal To Noise Ratio ◽  
Pseudorandom Sequence ◽  
Pseudorandom Sequences ◽  
Information Signal ◽  
Shift Keying ◽  
Golden Code ◽  
Digital Communication Systems

Dynamical systems methods have been recently used in spread-spectrum digital communication systems. Theexpansion of the spectrum using a pseudorandom sequence with a higher frequency than the information signal is thekey feature for its robustness against the signal traveling interference through the channel. In this work, we propose togenerate pseudorandom sequences by employing cellular automata and we check these sequences have thenecessary properties which are required in modern communication systems. The computed sequences obtained bythe cellular automata are tested in a quadrature phase shift keying (QPSK) spread-spectrum communication system.The efficiency of the system is analyzed by computing the bit error rate under different signal to noise ratio conditions.These results are compared with systems that employ Golden code and other typical pseudorandom sequences.

DRIVING SYNCHRONIZATION OF SPATIOTEMPORAL CHAOS AND ITS APPLICATIONS IN CDMA COMMUNICATIONS

2001 ◽  
Vol 11 (12) ◽  
pp. 3117-3124
Author(s):  
REN YONG ◽  
YONGXIANG XIA ◽  
XIUMING SHAN ◽  
YUAN JIAN
Keyword(s):  
Communication Systems ◽  
Original System ◽  
Spatiotemporal Chaos ◽  
Sequence Generation ◽  
Chaotic Sequences ◽  
Spatial Periodicity ◽  
Pseudo Noise ◽  
Code Division Multiple ◽  
User Interference ◽  
Spreading Sequences

This paper investigates the driving synchronization of spatiotemporal chaos. Using this method, synchronization could be achieved efficiently. By improving the driving sequence generation method, the spatial periodicity in the original system is overcome. Large quantities of chaotic sequences are available, which possess the excellent properties expected in Code Division Multiple Access (CDMA) communications. These chaotic sequences can be used as the spreading sequences in place of the traditional pseudo-noise sequences. We also evaluate the performance of the chaotic CDMA communication systems and compute the average bit error rate caused by the multi-user interference and the noise in the channel. The theoretical and simulation results show the excellent performance of the scheme.

scholarly journals Statistical Analysis of Multiple Access Interference in Chaotic Spreading Sequence Based DS-CDMA Systems

2017 ◽  
Vol 21 (1) ◽  
pp. 34
Author(s):  
A. Litvinenko ◽  
E. Bekeris
Keyword(s):  
Statistical Analysis ◽  
Communication Systems ◽  
Multiple Access ◽  
Multiple Access Interference ◽  
Matlab Simulation ◽  
Spreading Sequence ◽  
Sequence Generation ◽  
Code Division Multiple ◽  
Correlation Properties ◽  
Spreading Sequences

This paper presents a statistical analysis of multiple access interference (MAI) in Direct Sequence Code Division Multiple Access (DS-CDMA) communication systems based on different types of chaotic spreading sequences. The probability distribution of the interference in a system with K users causing the MAI is studied using MATLAB simulation. For chaotic spreading sequence generation six different 1-D chaotic maps are used: modified Bernoulli, modified Tent, Gauss, Sine-Circle, Cubic and Pinchers map. A brief statistical analysis of the cross-correlation properties of the chaotic sequences generated by the aforementioned maps is also presented.

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