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Coherent Detection of the CPM Signal
Although the bandwidth of the CPM signal in (1.1) is infinite, strictly speaking, we assume hereafter that it can be limited to Ns=2T, Ns being a positive integer chosen such that the approximation is fair. Thus, a sampling rate yielding Ns samples per symbol produces an approximated set of sufficient statistics [14] provided that the received signal has been pre-filtered through an analog low-pass filter having a vestigal symmetry around Ns=2T. An oversampling factor Ns = 10 is considered in the whole document.
Optimal Maximum Likelihood Sequence Estimation (MLSE) Detector for CPM
We assume that the signal is transmitted over a Gaussian channel. The equivalent baseband received signal, denoted by r(t), reads as: r(t) = s(t; h; a) + n(t); (1.9).
where n(t) is a realization of a zero-mean wide sense stationary complex circularly symmetric Gaussian noise, independent of the signal, and with double-sided power spectral density 2N0 over the bandwidth of s(t; h; a). The MLSE-detector aims to find the sequence ^a minimizing the Euclidean distance between s(t; h; ^a) and the received signal r(t) defined by ^a = arg min ~a k r(t) s(t; h; ~a) k2.
MAP symbol coherent detection of CPM signals
While the Viterbi algorithm enables to estimate the most probable sequence, the maximum a posteriori (MAP) symbol detection provides the most likely symbol. It aims to maximize the a posteriori probability (APP) p(anjr) [15]: ^an = arg max a2M p(an = ajr) (1.16).
The BCJR algorithm [16] performs a symbol by symbol MAP detection and uses the trellis representation of the CPM. Using the definition of n given in (1.3.1), we can express the conditional probability of (1.16) as p(an = ajr) = X n+1jan=a p(n+1jr).
Performance of the CPM Modulation
The performances of a waveform modulation format are often described by two criteria which are its spectral efficiency and its power-efficiency. The existence of a compromise between these two criteria often makes it difficult to choose a waveform rather than another. In order to select the proper CPM formats, it’s necessary to make a detailed study of the effect of each CPM parameter (h,L,g(t)). In this study, other aspects such as complexity will be considered to satisfy technical specifications.
Power spectral density (PSD)
This paragraph deals with the spectral properties of CPM signals. Despite the fact that the constant envelope is an interesting property, it is often detrimental at the expense of the PSD.It induces an occupied bandwidth much higher than the bandwidth of signals with envelope fluctuation. In the case of CPM modulations, this handicap can be compensated thanks to the high correlation of partial response CPM signals. The adoption of a frequency response length higher than one (L > 1) introduces a correlation in the signal, and thus reduces the spectral occupancy of the CPM signals. The higher parameter L the higher the reduction is. The spectrum of CPM signals also strongly depends on the frequency response, the modulation order and the modulation index.
Some estimation techniques of the CPM spectra have been proposed in [10], [17]. These semi-analytical methods are based on the computation of the signal correlation nd thus allow to deduce an estimate of the spectrum [18]. The advantage of these techniques is that they require little numerical resources compared to other conventional methods. We opted for the periodogram method to estimate the spectra of CPM signals. In this calculation, we consider the Fourier transform averaged over several observation windows of the signal. Let x be a sampled signal of length Nx. x = (x1; x2; :::; xNx1; xNx).
Table of contents :
List of Tables
1 Introduction
1.1 Machine-to-machine communications
1.2 Scope of the Thesis
1.3 Continuous Phase Modulation
1.3.1 CPM Signal Model
1.3.2 Coherent Detection of the CPM Signal
1.3.3 Performance of the CPM Modulation
1.3.4 Limitations of the CPM Modulation
1.4 Outline of Thesis
2 Precoded Ternary CPM with Improved SE
2.1 Introduction
2.2 Information rate and Spectral Efficiency
2.2.1 Information Rate
2.2.2 Spectral Efficiency
2.3 Precoder Design
2.4 Corresponding Detector
2.5 Simulation Results
2.5.1 Spectral Efficiency
2.5.2 Asymptotic Bit Error probability
2.5.3 Serial Concatenation with an outer encoder
2.5.4 Performance Analysis through EXIT Chart
2.6 Conclusions
3 Reduced Complexity Receiver for CPM signals
3.1 Introduction
3.2 Previous Works on Reduced Complexity Detectors for CPM
3.3 Reduced-State Trellis-Based CPM Receivers
3.3.1 Design of a Trellis with a Reduced State Number
3.3.2 Simulations
3.4 Iterative Reduced-Complexity detection for bit interleaved coded CPM
3.5 On the optimization of a PSP-based CPM detection
3.5.1 Uncoded CPM Case: Minimum Distance Analysis
3.5.2 Coded CPM: EXIT Charts Analysis
3.6 Conclusions
2 Contents
4 Robustness to Modulation Index Mismatch and Phase Noise for a binary CPM
4.1 Introduction
4.2 A Brief Review of Previous Studies
4.3 CPM Signals and Laurent Decomposition
4.4 Robust Precoded CPM Schemes
4.4.1 AMI precoder
4.4.2 Proposed precoder
4.4.3 Corresponding detector
4.4.4 Spectrum and Spectral Efficiency
4.4.5 Uncoded Performance
4.4.6 Simulation Results
4.5 Robust CPM Detection
4.5.1 Factor Graph and Sum Product Algorithm
4.5.2 Proposed Receiver
4.6 Simulation Results
4.7 Conclusions
5 Robust CPM-based Multi-user Systems
5.1 Introduction
5.2 Literature Review on Multi-user CPM systems
5.3 Robust multiple-access technique based on synchronous AMI precoded ternary CPM
5.3.1 Multiuser System based on phase-shifted AMI precoded ternary CPM
5.3.2 Corresponding Multi-user Joint Detector
5.3.3 Simulations Results
5.3.4 Summary
5.4 Robust FG-based detection for FDM-CPM systems
5.4.1 System Model
5.4.2 FG-Multiuser Detection Based on Laurent decomposition
5.4.3 Presence of Modulation Index Mismatch and Phase Noise
5.4.4 Simulation Results
5.5 Conclusions
6 Conclusions & Perspectives
Bibliography
