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Generalized Error Probability Analysis of Arbitrary Two-Dimensional Modulation Systems;tǬ$ܭ2008-02\ՑYPxhttps://repository.hanyang.ac.kr/handle/20.500.11754/147377;
http://hanyang.dcollection.net/common/orgView/200000408959;A two-dimensional (2-D) modulation scheme is a prospective technique to improve high-rate transmission over wireless links without increasing the bandwidth. The symbol-error rate (SER) or bit-error rate (BER) of the system with the modulation scheme depends on the parameters related to the generation of a baseband signal, such as constellation, bits-to-symbol mapping and a priori probability. The error probabilities are also subject to the various factors, such as an additive white Gaussian noise (AWGN), nonlinearity of high power amplifiers (HPA), I/Q imbalances, fading, phase error. In order to accurately analyze the effect by the parameters or factors on SER and BER, a numerical expression for the error probabilities is necessarily required. However, the closed-form expressions of the SER and BER over AWGN channel, the background channel of the digital communication system, have not yet been derived. Consequently, it is very difficult to evaluate SER and BER of the system with the parameters or factors.
This dissertation focuses on a new analysis method for the probability of the phase angle between two vectors perturbed by Gaussian noise using two rotations of coordinates. The method is utilized to simplify the accurate analyses of the error probabilities of some two-dimensional modulation schemes. In chapter 2, the new analysis method is presented, and from the analysis method, closed-form expressions are derived for SER and BER of MPSK with I/Q balance observing the regular patterns. Then, I/Q imbalances, the main sources of the performance degradation generated in receiver, are investigated and exact expressions for SER and BER of I/Q imbalanced M-ary phase shift keying (MPSK) are developed. In chapter 3, a general expression is provided to obtain the exact error probabilities for arbitrary 2-D signaling with unequal a priori probabilities over nonlinear AWGN channels. To this end, a decision boundary between two signal vectors with different a priori probabilities is found. A basic shape that acts as a component to form an arbitrary decision region is also provided. In addition, as an extension of the provided general expression, a closed-form expression is presented for the error probability of arbitrary 2-D signaling over Nakagami-m fading channels and analyze the effect of the impediments on the error performances for various two-dimensional modulation schemes.
The presented new method deals with any constellation, bits-to-symbol mapping, and unequiprobable signaling and considers the performance degradation factors generated in practical system. It is a useful tool to solve all the problems addressed up to now in the literature for evaluation of the SER and BER.; 2( (2-D) p )@ X t X pt0 ȡD XՌ X0 L8 ֬ ι@ 8 Ƿ4 ¤\ . t\ 2( p )t ȩ ¤\X $X U` (symbol error rate : SER) D $X U` (bit error rate : BER) @ 0<\ 0 8 (X 8 1ĳ, D Q, U` (a priori probability) 0| XՌ . \, SER/BER 1@ ¤\ x H L (additive white Gaussian noise : AWGN), ଜ% 0 (high power amplifier : HPA) X D 1, 0X I/Q (I/Q imbalances), \ (multipath) X\ t) (fading) , $X (phase error) X x Xt . 0| t\ 1 X x \ ƥD XՌ X0 t SER/BER \ U\ 1 )t l. 췘 8 ¤\X $X 1 \ l XՌ ɉ ǔ ֬Lĳ 8 ¤\X 0 D x AWGN D X p( U\ $X 1 )t X .
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