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OFDM/OQAM
Another alternative to OFDM modulation is OFDM with Offset Quadrature Amplitude Modulation (QAM), or OFDM/OQAM in short. Unlike OFDM, which uses rectangular pulse shape in time domain, OFDM/OQAM has the flexibility of using various pulse shapes with different time-frequency localization properties. This makes OFDM/OQAM less sensitive to the frequency offset caused by the transmission channel and the receiver. Moreover, OFDM/OQAM does not use any CP, hence being more spectrally efficient than OFDM. The first studies related to OFDM/OQAM were presented in [23] and [24]. In [23], [24], their authors introduced a time-offset on each sub-carrier to transmit Pulse Amplitude Modulation (PAM) and QAM constellations, respectively. For the latter, a time shift between the real and imaginary parts is introduced. In [25], the authors highlighted the importance of time-frequency localization features of the prototype filters when transmitting over time-frequency dispersive channels. Some optimized prototype functions other than the rectangular function were also presented. From the signal processing perspective, the link to digital filter banks was first initiated in [32] and then carried out in [33],[18], [1] where the authors presented an implementation design in case of discrete-time prototypes. Hence, OFDM/OQAM is usually referred to as Filter Bank MultiCarrier (FBMC)/OQAM modulation.
Continuous OFDM/OQAM
OFDM modulation consists in transmitting a complex symbol cm,n = cℜm,n + jcℑm,n of duration T0 at time instance n, i.e., nT0 and frequency m, i.e., mF0, with F0 = 1 the T0 subcarrier spacing and j2 = −1. The particularity of OFDM/OQAM is to transmit either the real or the imaginary part of the complex symbol cm,n with a time offset equal to T20 . Moreover, a phase shift of π2 is introduced between two adjacent symbols in time and frequency. Assuming an even number of subcarriers M , the baseband continuous OFDM/OQAM signal is [34], [1]: +∞ N−1 T0 ∑ ∑ )ej2π(2m)F0t s(t) = (cℜ g(t nT ) + jcℑ g(t nT − − 2 − 2m,n 0 2m,n 0.
Time-frequency localization of prototype filters
As presented previously, the OFDM/OQAM modulation scheme relies on the principle of offsetting complex QAM while maintaining the perfect reconstruction constraint, i.e., meaning that for an OFDM/OQAM system as in Fig. 2.4, aˆm,n−α = am,n−α, ∨ m, n. Moreover, a good pulse shape with good time-frequency localization properties can be obtained. In this section, we discuss some well designed prototype filters for OFDM/O QAM modulation. First, we give the following definitions:
Ambiguity function
The orthogonality property of a pulse shape g(t) over a phase space can be analyzed by its ambiguity function Ag(τ, ν) defined as: Ag(τ, ν) = ∫−∞ g(t + 2 )g∗(t − 2 )e−j2πνtdt. (2.21) +∞ τ τ.
The ambiguity function of a given pulse shape also gives an insight of its energy leakage over time and frequency axes. The sampled version of the ambiguity function is defined as: Ag[l, k] = Ag(lT0, kF0), (2.22) and the orthogonality property (i.e. the perfect reconstruction) is satisfied if Ag[0, 0] = 1 and Ag[nT0, mF0] = 0 for (m, n) ≠ (0, 0).
Time-Frequency localization
Let g be a function of L2(R) with Gν its Fourier transform. We denote by ||.|| the norm associated with L2(R). The moments of order 1 and 2 in time and frequency are expressed as follows:
• moment of order 1 in time: ∫−∞ t|g(t)|2dt; m(1)(g) = ||g||2 (2.23) 1 +∞.
Table of contents :
Acknowledgements
Abstract
Résumé
Contents
List of Figures
List of Tables
Abbreviations
Résumé Français
1 Introduction
2 State of the Art and Background
2.1 Introduction
2.2 OFDM
2.3 OFDM/OQAM
2.3.1 Continuous OFDM/OQAM
2.3.2 Discrete OFDM/OQAM
2.3.3 Time-frequency localization of prototype filters
2.3.3.1 Ambiguity function
2.3.3.2 Time-Frequency localization
2.3.3.3 The Square Root Raised Cosine Filter (SRRC)
2.3.3.4 The Extended Gaussian Function (EGF)
2.3.3.5 Time Frequency Localization (TFL) filter
2.3.3.6 Frequency Selective (FS) filter
2.4 Faster Than Nyquist Signaling
2.4.1 Nyquist criterion
2.4.2 FTN signaling
2.4.3 Related FTN research
2.5 Selected channel coding and precoding techniques
2.5.1 BCJR Algorithm
2.5.2 Turbo coding and turbo equalization
2.5.3 Turbo equalization
2.5.4 Convergence analysis using EXIT charts
2.5.5 Tomlinson Harashima Precoding
2.6 Conclusion
3 An FTN transceiver for OFDM/OQAM systems
3.1 Introduction
3.2 FTN-OQAM modem
3.2.1 FTN-OQAM modulator
3.2.1.1 The modulator structure for non-causal prototype filter .
3.2.1.2 The modulator structure for causal prototype filter
3.2.2 FTN-OQAM demodulator
3.3 Interference analysis for the FTN-OQAM transceiver
3.3.1 Interference analysis for continuous-time FTN-OQAM transceiver .
3.3.2 Interference analysis for discrete-time FTN/OQAM transceiver
3.4 The FTN-OQAM receiver
3.4.1 Time-domain MMSE turbo-equalization
3.4.2 Frequency-domain MMSE turbo-equalization
3.5 Simulation results
3.5.1 Effective minimum lossless packing factor investigation
3.5.2 Performance of the proposed FTN-OQAM transceiver
3.5.3 A word about complexity
3.6 Conclusion
4 Precoded FTN-OQAM
4.1 Introduction
4.2 Precoded FTN-OQAM transceiver: ISI and ICI cancellation
4.2.1 SIPC along time and frequency axes
4.2.2 The receiver structure
4.2.3 BCJR decoder modification
4.2.4 Simulation results
4.2.5 A word about complexity
4.3 Precoded FTN-OQAM transceiver: ISI cancellation
4.3.1 SIPC along time axis
4.3.2 The receiver structure
4.3.3 BCJR decoder modification
4.3.4 Simulation results
4.3.5 A word about complexity
4.4 Precoded FTN-OQAM transceiver: ICI cancellation
4.4.1 SIPC along frequency axis
4.4.2 The receiver structure
4.4.3 BCJR decoder modification
4.4.4 Simulation results
4.4.5 A word about complexity
4.5 Performance comparison between the proposed precoders
4.6 Conclusion
5 An enhanced design for FTN-OQAM transceiver
5.1 Introduction
5.2 Channel coding rate adaptation
5.3 Gray mapping enhancement
5.3.1 Non-precoded FTN-OQAM transceiver
5.3.2 Precoded FTN-OQAM transceiver
5.4 Symbols mapping enhancement
5.4.1 Precoded FTN-OQAM transceiver
5.4.1.1 SIPC-t precoding
5.4.1.2 SIPC-f precoding
5.4.2 Non-precoded FTN-OQAM transceiver
5.4.3 Simulation results
5.4.3.1 SIPC-t precoding
5.4.3.2 SIPC-f precoding
5.4.3.3 Non-precoded FTN-OQAM transceiver
5.5 Bits mapping Vs. Symbols mapping
5.6 Joint enhancement of channel coding and Gray mapping
5.7 Joint enhancement of channel coding and symbol mapping
5.8 Conclusion
6 Conclusion
6.1 Research contribution
6.2 Directions for future work
6.2.1 Channel coding
6.2.2 PAPR
6.2.3 Other equalization schemes
Bibliography
