Kafes Kodlamalı-dik Kısmi Yanıtlı Sistemlerin (qpr-tcm) Hata Başarım Analizi

Abstract

There is a grovving need for reliable transmission of high quality voice and digital data in satellite-based land mobile communication systems, These systems which will be part of an emerging all-digital net\vork, are both power and bandwidth limitation, öne can employ bandwidth efficient mod¬ ulation tecniques such as those that have been developed över the past several years for terrestrial communication systems. in the past, coding and modulation were treated as separate operations with regard to overall system design. in particular, most earlier vvorks on coded digital communication systems independently optimized:l)conventional (block ör convolutionai) coding with maximized minimum Hamming dis¬ tance. and 2)conventional modulation \vith maximally separated signals. About a decade ago, Ungerboeck has introduced an effecrtve modu¬ lation technique for band-limited channels called "trellis coded modulation (TCM)". TCM schemes employ redundant nonbinary modulation in combi- nation with a ünite-state encoder which governs the selection of modulation signals to generate coded signal sequences. The detection errors caused by the channel noise can be lowered by increasing the distance between channel signals. The essential new concept of TCM is to use signal-set expansion to provide redundancy for coding, and to design coding and signal-mapping functions jointly so as to maximize directly the free distance (minimum Euclidean distance ) between coded signal sequences. At the receiver, the Viterbi decoder operates directly on the received channel signal instead of the corresponding binary sequences. Then, the code design problem turns out to be searching the encoders with good Euc¬ lidean distance properties instead of the encoders with good Hamming dis¬ tance properties. At the same information rate, important coding gains are obtained without bandwidth expansion. Signal set containing twice the necessary channel signals is used according to a finite-state encoder, thus, for M-AM, PSK and QAM systems, coding gains of 3-4 dB are obtained by means of simple trellis structure. vi in most transmission channels, bandwidth is at a premium, and an im- portant attribute of any good digital signalling scheme is its ability to make efficient use of the bandwidth. in high data rate communication systems, intersymbol interference (ISI) arises whenever the effects of öne transmit- ted are not allowed to die away completeîy before transmission of the next. Conventional Nyquist-type schemes are designed to eliminate intersymbol interference at the expense of a large number of signal levels. Lender showed that the ground rules iaid by Nyquist were unnecessarily restrictive. Öne of the key assumptions in Nyquist's work was that the transmitted pulse am- plitudes be selected independently. By introducing dependencies ör correla- tion betvveen the amplitudes and by changing detection procedure, Lender could achieve the symbol rate of 2lVsymbols/s in a bandwidth öf W Hz. Thus, the correlative schemes conceived by Lender, and later generalised by Kretzmer, could be regarded as a practical means of achieving the the- oretical maximum symbol rate packing of 2symbols/s/Hz postulated by Nyquist, using realizable and perturbation-tolerant filters. in many applications, correlative coding ör partial response signalling, which introduces intersymbol interference in a controlled way, is able achieve high data rates with fewer levels and hence \vith better error rate per- formance. in addition to higher data rates, correlative schemes achieve convenient spectral shapes and have error-detecting capabilities without in¬ troducing redundancy into the data stream. in partia] response signalling (PRS),intersymbol interference is controlled to achieve high data rate \vith fe\ver levels at the expence of error performance degradation caused by the expansion of signal space. Partial response signalling (PRS) schemes. also kno\vn as correlative coding techniques, are widely used in baseband sys¬ tems as well as in conjıınction with modulation techniques. Recently PRS schemes have been suggested for digital subscriber loops in order to irnprove timing recovery and to reduce crosstalk interference. Thus the effect of pa- rameters such as pulse shape, excess band\vidth, and system polynomial on performance measures related to timing and transmission rate variations is of interest. PRS system consists of a nonrecursive digital filter in cascade \vith ana- log filter. Duobinary and modified duobinary and dicode schemes are the most common used PRS systems. in duobinary signalling, two successive binary input pulses are added. Thus duobinary signalling introduces ISI, vii but it is controlled such a way that the interference comes only from the immediately preceeding symbol. Note that the operation of adding two successive symbols has provided an effective spectral shaping two the trans- mitted signal. in modified duobinary signalling, binary pulses spaced by two sample periods are subtracted. Modified duobinary signalling is suitable for sing!e-side band modulation. in dicode signalling, two successive binary input pulses are substracted. Duobinary and modified duobinary and di¬ code are cases of a \vider selection of partial response signalling metbods. The need for increases in data transmission rates in band-limited chan- nels leads to use a consideration of digital communication systems in \vhich both amplitude and phase modulation are used. vvith PSK the in-phase and quadrature components are not independent. Their values are constrained in order to produce a constant envelope signal, which is a fundamental characteristic of PSK. If this constraint is removed so that the quadrature channels may be independent. This general category of digital modulation is called quadrature amplitude modulation (QAM). For the special case of two levels on each quadrature channel, QAM is identical to 4-PSK. The sig¬ nal constellations for higher-level QAM systems are rectangular, however, and therefore distinctly different from the circular signal sets of higher-level PSK systems. QAM offers the advantage of less required po\ver than PSK for a given probability of error and alphabet size M, but at the cöst of in- creased equipment complexity and a sensitivity to possible non-linearities in the channel. in this thesis, to improve both the bandwidth efficiency and error per- formance, partial response signalling (PRS) and trellis coded modulation are examined together and named as Quadrature Partial Response Trellis Coded Modulation (QPR-TCM) for the quadrature amplitude modulation (QAM). The error performance spectral efficiency and simplicity can make QPR-TCM a popular choise in mobile digital radio systems. Calderbank-Mazo has defined an important performance measurement, asymptotic coding gain (ACG) that is effective at high signal to noise ratios. Asymptotic coding gain js a function of minimum distance error events in the trellis, and averages squared signal power. Then Zehavi-Wolf has de- veloped an analytical approach that will be used in deriving error-event probability and bit-error rate of trellis codes that is not limited to only high signal to noise ratios. The method is based on the generating function viii approach, usually denoted by T(w. I, /). The generating fuction is derived from the state diagram of the code and contains in a closed form ali of the weight distribution properties of the code. When the code is linear, the all-zeros code\vord is assumed, without loss of generality. to be the correct codevvord. The generating function enumerates the distance, length, and the number of errors on any incorrect path (as compared with the correct path) at any step of the Viterbi aîgorithm. in the third chapter, a new receiver for data transmission systems emp- loying combined partial response-trellis coded modulation (QPR-TCM) is introduced and named as 6QPR-TCM for two-state TCM encoder. it is shown that the two-state TCM encoder followed by the partial-response step decreases the number of the allovved signals from 9, which is the un- coded 4QAM case to 6. Combined QPR-TCM trellis structure reduces the number of states from 8 to 4, since ali the combinations of memory digits are not allo\ved. 6QPR-TCM output is analytically written by input data using Calderbank-Mazo approach. For ali the possible input data at the output of the combined scheme there occurs only six different signals. in this chapter, a new combined scheme 9QPR-TCM is also introduced. The encoder has three memory element and t\vo of them tarry the same value with the PRS memory. Therefore combined QPR-TCM scheme has reduced trellis state number from 32 to only S. 9QPR-TCM output is also analytically expressed by means of input, using Calderbank-Mazo approach. For ali possible input data, at the output nine different signal is detected. in the forth chapter, analytical error event upper bounds of QPR-TCM schemes are derived using Zehavi-Wolf approach and compared to 4QAM- TCM in AWGN environment. Asymptotic coding gain of 6QPR-TCM is found as 3 dB. compared to the uncoded PRS-BPSK. 6QPR-TCM scheme is upper bounded and compared to the two-state 4QAM-TCM. it is shown that 4QAM-TCM performs better than 6QPR-TCM at ali SNR values in AWGN environment. Asymptotic coding gain of 9QPR-TCM is 4.77 dB compared to the un¬ coded PRS-BPSK. This scheme is upper bounded and compared to the four-state 4QAM-TCM. 4QAM-TCM has better error performance than the considered scheme for ali SNR values. ix Trellis coding with expanded signal set is known to provide several deci bels of coding gain without requiring more bandwidth compared to its coun terpart in an affitive white Gaussian noise (AWGN) channel. This is usually achieved by combining a modulator with a redundant alphabet of channel symbols at the transmitter and maximum-likelihood sequence estimation (MLSE) decoding at the receiver. While the performance of a trellis coded communication system is well known, it is still not clear how such a system would pertform when corrupted by colored noise. In many partical trellis coded systems where noise is not white, the error performance degradates due to the correlation between noise samples. In this case minimum distan ce paths have different contributions to the error performance and the one which is the most seriously affected by noise correlation is chosen. In the fifth chapter, error event probability lower bounds of 6QPR-TCM and 9QPR-TCM schemes are derived and compared to the related schemes in colored noise case. It s shown that 4QAM-TCM scheme performs better than the proposed schemes at all SNR values. Thus far in this thesis the design and performance of QPR-TCM is dis cussed for the idealized additive white Gaussian and colored noise environ ments. It is seen that the primary advantage of QPR-TCM over modulation schemes employing traditional error correction coding is its ability to achieve increased power efficiency without the customary expansion of bandwidth introduced by the coding process. Thus any channel that is both power- limited and bandwidth-limited would be ideally suited to QPR-TCM. One such application is the mobile satellite channel, where bandwidth is constrained by the desire to accommodate a large number of users in a given transmission bandwidth, and power is constrained by the flux density limitation of the satellite's radiated transmission and the physical size of the mobile's antenna. In addition to the usual additive thermal noise back ground, the mobile satellite channel is impaired by Doppler frequency shift due to vehicle motion, multipath fading and shadowing. Perhaps the most serious of these impairements is the latter, where for reliable performance the system must be able to combat short fades and recover quickly from long fades. For mobile satellite communication, multipath fading produces a re ceived signal with an amplitude which can be modelled by Rician statistics with parameter K representing the ratio of the power in the direct (line of sight) and specular component to that in the diffuse component. If shadow ing is severe, than a Rayleigh statistical model becomes appropriate which can be looked upon as the limiting case of a Rician channel when K ap proaches zero. Of course, the case of no fading corresponds to a Rician channel with K approaches infinity. In this study, it is assumed that the phase-shift due to the fading is per fectly removed in the detection process and only the effects of the amplitude fading is considered. It is also considered that the channel state information (i.e., information derived from the channel that can be used to design the decoding metric to give improved performance) is available at the receiver. These assumptions considerably simplify the performance analysis and per mits the use of the transfer function upper bound techniques. In the sixth chapter, using the Zehavi-Wolf modified method, the bit error probability of 6QPR-TCM and 9QPR-TCM are upper bounded for different fading parameter K values and compared to 4QAM-TCM schemes. At high signal to noise ratios, the proposed schemes have better error per formance than the related schemes for small values of K.