Generalized discrete Fourier transform with non-linear phase : theory and design

Constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold codes have been successfully used over several decades in various engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communications systems. Among these popular transforms, DFT is a linear phase transform and widely used in multicarrier communications due to its performance and fast algorithms. In this thesis, a theoretical framework for Generalized DFT (GDFT) with nonlinear phase exploiting the phase space is developed. It is shown that GDFT offers sizable correlation improvements over DFT, Walsh, and Gold codes. Brute force search algorithm is employed to obtain orthogonal GDFT code sets with improved correlations. Design examples and simulation results on several channel types presented in the thesis show that the proposed GDFT codes, with better auto and cross-correlation properties than DFT, lead to better bit-error-rate performance in all multi-carrier and multi-user communications scenarios investigated. It is also highlighted how known constant modulus code families such as Walsh, Walsh-like and other codes are special solutions of the GDFT framework. In addition to theoretical framework, practical design methods with computationally efficient implementations of GDFT as enhancements to DFT are presented in the thesis. The main advantage of the proposed method is its ability to design a wide selection of constant modulus orthogonal code sets based on the desired performance metrics mimicking the engineering .specs of interest. Orthogonal Frequency Division Multiplexing (OFDM) is a leading candidate to be adopted for high speed 4G wireless communications standards due to its high spectral efficiency, strong resistance to multipath fading and ease of implementation with Fast Fourier Transform (FFT) algorithms. However, the main disadvantage of an OFDM based communications technique is of its high PAPR at the RF stage of a transmitter. PAPR dominates the power (battery) efficiency of the radio transceiver. Among the PAPR reduction methods proposed in the literature, Selected Mapping (SLM) method has been successfully used in OFDM communications. In this thesis, an SLM method employing GDFT with closed form phase functions rather than fixed DFT for PAPR reduction is introduced. The performance improvements of GDFT based SLM PAPR reduction for various OFDM communications scenarios including the WiMAX standard based system are evaluated by simulations. Moreover, an efficient implementation of GDFT based SLM method reducing computational cost of multiple transform operations is forwarded. Performance simulation results show that power efficiency of non-linear RF amplifier in an OFDM system employing proposed method significantly improved

Software Defined Radio Implementation of Carrier and Timing Synchronization for Distributed Arrays

The communication range of wireless networks can be greatly improved by using distributed beamforming from a set of independent radio nodes. One of the key challenges in establishing a beamformed communication link from separate radios is achieving carrier frequency and sample timing synchronization. This paper describes an implementation that addresses both carrier frequency and sample timing synchronization simultaneously using RF signaling between designated master and slave nodes. By using a pilot signal transmitted by the master node, each slave estimates and tracks the frequency and timing offset and digitally compensates for them. A real-time implementation of the proposed system was developed in GNU Radio and tested with Ettus USRP N210 software defined radios. The measurements show that the distributed array can reach a residual frequency error of 5 Hz and a residual timing offset of 1/16 the sample duration for 70 percent of the time. This performance enables distributed beamforming for range extension applications.Comment: Submitted to 2019 IEEE Aerospace Conferenc

Compressive Sensing for Spread Spectrum Receivers

With the advent of ubiquitous computing there are two design parameters of wireless communication devices that become very important power: efficiency and production cost. Compressive sensing enables the receiver in such devices to sample below the Shannon-Nyquist sampling rate, which may lead to a decrease in the two design parameters. This paper investigates the use of Compressive Sensing (CS) in a general Code Division Multiple Access (CDMA) receiver. We show that when using spread spectrum codes in the signal domain, the CS measurement matrix may be simplified. This measurement scheme, named Compressive Spread Spectrum (CSS), allows for a simple, effective receiver design. Furthermore, we numerically evaluate the proposed receiver in terms of bit error rate under different signal to noise ratio conditions and compare it with other receiver structures. These numerical experiments show that though the bit error rate performance is degraded by the subsampling in the CS-enabled receivers, this may be remedied by including quantization in the receiver model. We also study the computational complexity of the proposed receiver design under different sparsity and measurement ratios. Our work shows that it is possible to subsample a CDMA signal using CSS and that in one example the CSS receiver outperforms the classical receiver.Comment: 11 pages, 11 figures, 1 table, accepted for publication in IEEE Transactions on Wireless Communication

Golden Modulation: a New and Effective Waveform for Massive IoT

This paper considers massive Internet of Things systems, especially for LoW Power Wide Area Networks, that aim at connecting billions of low-cost devices with multi-year battery life requirements. Current systems for massive Internet of Things exhibit severe problems when trying to pursue the target of serving a very large number of users. In this paper, a novel asynchronous spread spectrum modulation, called Golden Modulation, is introduced. This modulation provides a vast family of equivalent waveforms with very low cross-interference even in asynchronous conditions, hence enabling natural multiuser operation without the need for inter-user synchronization or for interference cancellation receivers. Thanks to minimal interference between waveforms, coupled with the absence of coordination requirements, this modulation can accommodate very high system capacity. The basic modulation principles, relying on spectrum spreading via direct Zadoff-Chu sequences modulation, are presented and the corresponding theoretical bit error rate performance in an additive white Gaussian noise channel is derived and compared by simulation with realistic Golden Modulation receiver performance. The demodulation of the Golden Modulation is also described, and its performance in the presence of uncoordinated multiple users is characterized.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

A Unifying View of Loosely Time-Triggered Architectures

Cyber-Physical Systems require distributed architectures to support safety critical real-time control. Hermann Kopetz' Time-Triggered Architecture (TTA) has been proposed as both an architecture and a comprehensive paradigm for systems architecture, for such systems. TTA offers the programmer a logical discrete time compliant with synchronous programming, together with timing bounds. A clock synchronization protocol is required, unless the local clocks used themselves provide the recquired accuracy. To relax the strict requirements on synchronization imposed by TTA, Loosely Time-Triggered Architectures (LTTA) have been proposed. In LTTA, computation and communication units are all triggered by autonomous, unsynchronized, clocks. Communication media act as shared memories between writers and readers and communication is non blocking. This is at the price of communication artifacts (such as duplication or loss of data), which must be compensated for by using some "LTTA protocol". In this paper we pursue our previous work by providing a unified presentation of the two variants of LTTA (token- and time-based), with simplified analyses. We compare these two variants regarding performance and robustness and we provide ways to combine them. This report was prepared for a lecture in Gérard Berry's seminar series at the Collège de France, March 5, 2014; it is a corrected version of a paper, which appeared at Emsoft'2010. It is dedicated to our close friend Paul Caspi who died in April 2012.Les infrastructures de calcul distribuées pour le contrôle des systèmes embarqués critiques requièrent des propriétés particulières destinées à préserver les caractéristiques attendues du contrôleur. Les architectures TTA (Time-Triggered Architectures) ont été proposées par Hermann Kopetz, à la fois comme une architecture de calcul et comme une méthodologie de conception des systèmes. TTA offre au programmeur un temps logique conforme à celui de la programmation synchrone, avec en outre un contrôle strict du temps. Il requiert un protocole de synchronisation entre les horloges du système réparti. Pour affaiblir ces hypothèses, les architectures LTTA (Loosely Time-Triggered Architectures) ont été proposées récemment. Dans LTTA, les calculs et les communications sont rythmées par des horloges locales, non synchronisées. Les supports de communication se comportent comme des mémoires partagées. La communication est donc non-bloquante. Ce type de communiccation crée évidemment des artefacts à combattre par un protocole dit "LTTA". Dans cet article nous présentons une approche unifiée des deux techniques connues pour ce type de protocole, reposant sur l'usage, soit de jetons, soit du temps. On compare ces deux variantes et on étudie leur performance. Le présent rapport est une version corrigée d'un article paru à Emsoft'2010. Il est dédié à notre très cher ami Paul Caspi, décédé en Avril 2012

Quickest Sequence Phase Detection

A phase detection sequence is a length-$n$ cyclic sequence, such that the location of any length-$k$ contiguous subsequence can be determined from a noisy observation of that subsequence. In this paper, we derive bounds on the minimal possible $k$ in the limit of $n\to\infty$, and describe some sequence constructions. We further consider multiple phase detection sequences, where the location of any length-$k$ contiguous subsequence of each sequence can be determined simultaneously from a noisy mixture of those subsequences. We study the optimal trade-offs between the lengths of the sequences, and describe some sequence constructions. We compare these phase detection problems to their natural channel coding counterparts, and show a strict separation between the fundamental limits in the multiple sequence case. Both adversarial and probabilistic noise models are addressed.Comment: To appear in the IEEE Transactions on Information Theor

Fast Decoder for Overloaded Uniquely Decodable Synchronous CDMA

We consider the problem of designing a fast decoder for antipodal uniquely decodable (errorless) code sets for overloaded synchronous code-division multiple access (CDMA) systems where the number of signals K_{max}^a is the largest known for the given code length L. The proposed decoder is designed in a such a way that the users can uniquely recover the information bits with a very simple decoder, which uses only a few comparisons. Compared to maximum-likelihood (ML) decoder, which has a high computational complexity for even moderate code length, the proposed decoder has a much lower computational complexity. Simulation results in terms of bit error rate (BER) demonstrate that the performance of the proposed decoder only has a 1-2 dB degradation at BER of 10^{-3} when compared to ML