Sayısal dik genlik modülasyonlu işaretlerin çoklu kafes yapıda tasarımı ve hata başarımlarının incelenmesi - Ersöz, Ufuk (Fen Bilimleri Enstitüsü, 1991)
Bu tez çalışmasında çoklu kafes kodlamalı modülasyon tekniğinin dik genlik modülasyonlu (QAM) işaretlere uygulanması problemi ele alınmıştır. Tasarlanan iki durumlu çoklu kafes kodlamalı QAM sistemin, klasik kafes kodlamalı QAM sisteme göre üstünlükleri araştırılmış, her iki sistemin hata başarım sınırları analitik yöntemlerle hesaplanmıştır. Ayrıca bir bilgisayar benzetim modeli oluşturularak elde edilen sonuçlarla yukarda adı geçen sistemlerin hata başarım değerleri işaret - gürültü oranına göre çizilmiştir. Sonuç olarak çoklu kafes kodlamalı tekniğe göre tasarlanan 16-QAM sistemin hata başarımının kafes kodlamalı tekniğe göre daha iyi olduğu görülmüş ve elde edilen sonuçlar verilmiştir.

In this thesis, multiple trellis coded modulation technique is applied to quadrature amplitude modulation (QAM) signals. The limits of error performance is computed for multiple trellis coded QAM signals with an analytical method. In addition, a computer simulation model is given to determine how much improvement of error performance is provided by multiple trellis coding technique with respect to classical trellis coding technique. In digital communication system design the main purpose is to increase the error performance in transmitting binary data sequences and the function of modulation and error-correction coding are separated. Conventional encoders and decoders for error correction operate on binary, code symbols transmitted over a discrete channel. With a code of rate k/n, n-k redundant check symbols are appended to every k information symbols. Since the decoder receives only discrete code symbols, Hamming distance is the appropriate measure of distance for decoding. The rate loss is occured by sending redundant check symbols. Generally, there exist two posibilities to compensate for the rate loss: increasing the modulation rate if the channel permits bandwidth expansion, or enlarging the signal set of the modulation system if the channel is band limited. However, when modulation and error- correction coding are performed in the clasical independent manner, dissappointing results are obtained. Trellis coded modulation (TCM) is envolved by Ungerboeck [1], [2], [3] as a combined coding and modulation technique for digital transmission over band limited channels. Its main attraction is the achievement of significant coding gains over conventional uncoded VI multilevel modulation without compromising bandwidth efficiency. TCM schemes employ redundant nonbinary modulation in combination with a finite state encoder which governs the selection of modulation signals to generate coded signal sequences. In the receiver, the noisy signals are decoded by a soft-decision maximum-likelihood sequence decoder. Simple TCM schemes can improve the robustness of digital transmission against additive noise by 3 dB compared to conventional uncoded modulation. With more complex TCM schemes, the coding gain can reach 6 dB or more. These gains are obtained without bandwidth expansion or reduction of the effective information rate as required by traditional error-correction schemes. Signal waveforms representing information sequences are most impervious to noise-induced detection errors if the are very different from each other. Mathematically, this translates into the requirement that signal sequences should have large distance in Euclidean signal space. The essential new concept of TCM that led to the above mentioned gains was 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 sequences. This allowed the construction of modulation codes whose free distance significantly exceeded the minimum distance between uncoded modulation signals at the same information rate, bandwidth and signal power. In TCM schemes, the trellis branches are labeled with redundant nonbinary modulation signals rather than with binary code symbols. Divsalar, Simon and Yuen [4], [5], [6] envolved trellis coding with asymmetric modulation technique by designing the signal constellations to be asymmetric. This technique provides a performance gain over the traditional symmetric constellations combined with trellis coding. Divsalar and Simon [7], demonstrated trellis coded modulation technique referred to as multiple trellis coded modulation (MTCM) which is capable of achieving asymptotic performance gains without resorting to modulation asymmetry. In addition this technique circumvents the problem of code catastrope. The principle is to design a rate nk/(n + l)k (k=2,3,4,...) encoder and combine it a suitable mapping function with a 2n+1 point VII - signal constellation outputting k of these signal points in each transmission interval. Since, in each transmission interval, kn bits enter the encoder and k symbols leave the modulator, thre exist a unity bandwidth expansion relative to an uncoded 2n-point uncoded systems. It is important that values of k greater than 1 (k = 1 corresponds to the conventional TCM systems) for certain cases produce increased values of dfree with symmetric modulations. Trellis coded modulation (TCM) refers to the technique wherein a rate n/(n + l) trellis code is combined with an 2n+ point signal constellation to produce a coded modulation which has no bandwith expansion relative to an uncoded 2n point modulation of the same type yet gives significant performance improvement. Traditionnally, TCM systems have employed symmetric signal constellations, uniformly spaced signal points. Although symmetric signal constellations are optimum for uncoded systems, the same is not necessarily true for TCM. In fact, it has been shown [4], [5], [6] that by designing the signal constellations to be asymmetric, in many instances, obtain a performance gain over the traditional symmetric TCM designs. The measure of performance gain and the amount of it achieved is, in general, a function of many factors, namely, signals to noise ratio (SNR), complexity of the trellis encoder (number of trellis code states), and the number of modulation levels. For TCM systems, an asymptotic measure of performance gain is the comparison of the minimum free Euclidean distance d of the trellis code relative to the minimum distance d. of the uncoded modulation. In certain cases of asymmetry, the asymptotic improvement as measured d can only be achieved in free the limit as points in the signal constellation merge together. Trellis code becomes catastrophic. Multiple trellis coding, wherein more than one channel symbol per trellis branch is transmitted, has been shown to yield a performance gain with symmetric signal sets, comparable to that previously achieved only with signal constellation asymmetry. The advantage of multiple trellis coding over the conventional trellis coded asymmetric modulation technique is that the potential for code catastrophe associated with the latter has been eliminated. VIII Biglieri [9] presented a generating function method which enumarates all possible incorrect paths for all possible correct paths, for trellis codes. The generalized generating function can be obtained as the transfer function of a state diagram regarded as a signal flow graph. The state diagram is defined over an expanded set of states, namely 2 v, where 2V is the number of states in the trellis and v is the memory of the code. Since the number of the states grows exponentially with 2v rather than v, this method is only useful for very simple codes. Zehavi and Wolf [10] designed a generating function method which can be applied to a special class of trellis codes. For this class of codes the error weight distribution, the error event probability, and the bit-error event probability can be bounded by a generating function of a state diagram containing 2V states. The generating function usually denoted by T(W,L,I), is derived from the state diagram of the code and contains in a closed form all of the weight distribution properties of the code. This method can be applied to many important codes, including Ungerboeck codes and Calderbank-Mazo codes. The basic principles of TCM were published in 1982. Further descriptions followed in 1984 and coincided with a rapid transition of TCM from the research stage to practical use. In 1984, a TCM scheme with a coding gain of 4 dB was adapted by the International Telegraph and Telephone Consultative Committee (CCITT) for use in new high speed voiceband modems. Prior to TCM, uncoded transmission at 9.6 kbit/s over voiceband channels was often considered as a practical limit for data modems. Since 1984, data modems have appeared on the market which employ TCM along with other improvements in equalization, synchronization, and so forth, to transmit reliably over voiceband channels at rates of 14.4 kbit/s and higher. Similar advances are being achieved in transmission over other bandwith - constrained channels. The common use of TCM techniques in such applications, as satellite, terrestrial microwave and mobile communications, in order to increase throughput rate or to permit satisfactory operation at lower signal to noise ratios, can be safely predicted for the near future. In section 2 the trellis coded modulation technique is presented and the basic principles are determined. The IX differences of this technique from the classical error correction coding are explained. The design of PSK and QAM signals based on TCM technique are shown. In section 3 the multiple trellis coded modulation technique and the improvement with respect to the classical trellis coded modulation are explained. In section 4 the design of 16-QAM system based on the multiple trellis method is given and compared to the classical trellis coded 16-QAM system. In section 5 upper bounds on the error event and the bit error probabilities for multiple and classical trellis coded 16-QAM systems are obtained with an analytical method and a comparision is given. For the same error probability a reduction of 1.25 dB in the signal to noise ratio (SNR) is provided by the MTCM method. In section 6 a computer simulation model is given for systems mentioned in section 5. The error performance obtained in the simulation study show that the multiple TCM technique provides an improvement for the 16-QAM signals with respect to the classical TCM.
Design and performance analysis of quadrature amplitude modulated signals based on multiple trellis coded modulation technique
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1991
Keywords: Kafes kodlama; Modülasyon yöntemleri; Trellis coding; Modulation methods