arXiv subjects

Francois Gagnon

Publications and source records attributed to Francois Gagnon.

16 recordsLinked to original sources

arXiv2017

A Joint Code-Frequency Index Modulation for Low-complexity, High Spectral and Energy Efficiency Communications

A relatively simple low complexity multiuser communication system based on simultaneous code and frequency index modulation (CFIM) is proposed in this paper. The proposed architecture reduces the emitted energy at the transmitter as well as the peak-to-average-power ratio (PAPR) of orthogonal frequency-division multiplexing (OFDM)- based schemes functions without relegating data rate. In the scheme we introduce here, we implement a joint code- frequency- index modulation (CFIM) in order to enhance spectral and energy efficiencies. After introducing and analysing the structure with respect to latter metrics, we derive closed-form expressions of the bit error rate (BER) performance over Rayleigh fading channels and we validate the outcome by simulation results. Simulation are used verify the analyses and show that, in terms of BER, the proposed CFIM outperforms the existing index modulation (IM) based systems such as spatial modulation (SM), OFDM-IM and OFDM schemes significantly. To better exhibit the particularities of the proposed scheme, PAPR, complexity, spectral efficiency (SE) and energy efficiency (EE) are thoroughly examined. Results indicate a high SE while ensuring an elevated reliability compared to the aforementioned systems. In addition, the concept is extended to synchronous multiuser communication networks, where full functionality is obtained. With the characteristics demonstrated in this work, the proposed system would constitute an exceptional nominee for Internet of Things (IoT) applications where low-complexity, low-power consumption and high data rate are paramount.

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arXiv2017

On Optimal Latency of Communications

In this paper we investigate the optimal latency of communications. Focusing on fixed rate communication without any feedback channel, this paper encompasses low-latency strategies with which one hop and multi-hop communication issues are treated from an information theoretic perspective. By defining the latency as the time required to make decisions, we prove that if short messages can be transmitted in parallel Gaussian channels, for example, via orthogonal frequency-division multiplexing (OFDM)-like signals, there exists an optimal low-latency strategy for every code. This can be achieved via early-detection schemes or asynchronous detections. We first provide the optimal achievable latency in additive white Gaussian noise (AWGN) channels for every channel code given a probability block error $ε$. This can be obtained via sequential ratio tests or a "genie" aided, \textit{e.g}. error-detecting codes. Results demonstrate the effectiveness of the approach. Next, we show how early-detection can be effective with OFDM signals while maintaining its spectral efficiency via random coding or pre-coding random matrices. Finally, we explore the optimal low-latency strategy in multi-hop relaying schemes. For amplify-and-forward (AF) and decode-and-forward (DF) relaying schemes there exist an optimal achievable latency. In particular, we first show that there exist a better low-latency strategy, for which AF relays could transmit while receiving. This can be achieved by using amplify and forward combined with early detection.

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arXiv2013

Lower Bound on the BER of a Decode-and-Forward Relay Network Under Chaos Shift Keying Communication System

This paper carries out the first-ever investigation of the analysis of a cooperative Decode-and-Forward (DF) relay network with Chaos Shift Keying (CSK) modulation. The performance analysis of DF-CSK in this paper takes into account the dynamical nature of chaotic signal, which is not similar to a conventional binary modulation performance computation methodology. The expression of a lower bound bit error rate (BER) is derived in order to investigate the performance of the cooperative system under independently and identically distributed (i.i.d.) Gaussian fading wireless environments. The effect of the non-periodic nature of chaotic sequence leading to a non constant bit energy of the considered modulation is also investigated. A computation approach of the BER expression based on the probability density function of the bit energy of the chaotic sequence, channel distribution, and number of relays is presented. Simulation results prove the accuracy of our BER computation methodology.

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arXiv2013

Design and Analysis of a Multi-Carrier Differential Chaos Shift Keying Communication System

A new Multi-Carrier Differential Chaos Shift Keying (MC-DCSK) modulation is presented in this paper. The system endeavors to provide a good trade-off between robustness, energy efficiency and high data rate, while still being simple compared to conventional multi-carrier spread spectrum systems. This system can be seen as a parallel extension of the DCSK modulation where one chaotic reference sequence is transmitted over a predefined subcarrier frequency. Multiple modulated data streams are transmitted over the remaining subcarriers. This transmitter structure increases the spectral efficiency of the conventional DCSK system and uses less energy. The receiver design makes this system easy to implement where no radio frequency (RF) delay circuit is needed to demodulate received data. Various system design parameters are discussed throughout the paper, including the number of subcarriers, the spreading factor, and the transmitted energy. Once the design is explained, the bit error rate performance of the MC-DCSK system is computed and compared to the conventional DCSK system under an additive white Gaussian noise (AWGN) and Rayleigh channels. Simulation results confirm the advantages of this new hybrid design.

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arXiv2013

On Convexity of Error Rates in Digital Communications

Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations, bit mapping and coding. Earlier results obtained for the AWGN channel are extended to a wide class of noise densities, including unimodal and spherically-invariant noise. Under these broad conditions, symbol and bit error rates are shown to be convex functions of the SNR in the high-SNR regime with an explicitly-determined threshold, which depends only on the constellation dimensionality and minimum distance, thus enabling an application of the powerful tools of convex optimization to such digital communication systems in a rigorous way. It is the decreasing nature of the noise power density around the decision region boundaries that insures the convexity of symbol error rates in the general case. The known high/low SNR bounds of the convexity/concavity regions are tightened and no further improvement is shown to be possible in general. The high SNR bound fits closely into the channel coding theorem: all codes, including capacity-achieving ones, whose decision regions include the hardened noise spheres (from the noise sphere hardening argument in the channel coding theorem) satisfies this high SNR requirement and thus has convex error rates in both SNR and noise power. We conjecture that all capacity-achieving codes have convex error rates. Convexity properties in signal amplitude and noise power are also investigated. Some applications of the results are discussed. In particular, it is shown that fading is convexity-preserving and is never good in low dimensions under spherically-invariant noise, which may also include any linear diversity combining.

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arXiv2013

Multi-User Multi-Carrier Differential Chaos Shift Keying Communication System

In this paper, a multi user Multi-Carrier Differential Chaos Shift Keying (MC-DCSK) modulation is presented. The system endeavors to provide a good trade-off between robustness, energy efficiency and high data rate, while still being simple. In this architecture of MC-DCSK system, for each user, chaotic reference sequence is transmitted over a predefined subcarrier frequency. Multiple modulated data streams are transmitted over the remaining subcarriers allocated for each user. This transmitter structure saves energy and increases the spectral efficiency of the conventional DCSK system.

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arXiv2013

An Enhanced Spectral Efficiency Chaos-Based Symbolic Dynamics Transceiver Design

Chaotic synchronization performs poorly in noisy environments, with the main drawback being that the coherent receiver cannot be implemented in realistic communication channels. In this paper, we focus our study on a promising communication system based on chaotic symbolic dynamics. Such modulation shows a high synchronization quality, without the need for a complex chaotic synchronization mechanism. Our study mainly concerns an improvement of the bandwidth efficiency of the chaotic modulator. A new chaotic map is proposed to achieve this goal, and a receiver based on the maximum likelihood algorithm is designed to estimate the transmitted symbols. The performance of the proposed system is analyzed and discussed.

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arXiv2010

Error Rates of Capacity-Achieving Codes Are Convex

Motivated by a wide-spread use of convex optimization techniques, convexity properties of bit error rate of the maximum likelihood detector operating in the AWGN channel are studied for arbitrary constellations and bit mappings, which also includes coding under maximum-likelihood decoding. Under this generic setting, the pairwise probability of error and bit error rate are shown to be convex functions of the SNR and noise power in the high SNR/low noise regime with explicitly-determined boundary. Any code, including capacity-achieving ones, whose decision regions include the hardened noise spheres (from the noise sphere hardening argument in the channel coding theorem) satisfies this high SNR requirement and thus has convex error rates in both SNR and noise power. We conjecture that all capacity-achieving codes have convex error rates.

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arXiv2010

A performance analysis of multi-hop ad hoc networks with adaptive antenna array systems

Based on a stochastic geometry framework, we establish an analysis of the multi-hop spatial reuse aloha protocol (MSR-Aloha) in ad hoc networks. We compare MSR-Aloha to a simple routing strategy, where a node selects the next relay of the treated packet as to be its nearest receiver with a forward progress toward the final destination (NFP). In addition, performance gains achieved by employing adaptive antenna array systems are quantified in this paper. We derive a tight upper bound on the spatial density of progress of MSR-Aloha. Our analytical results demonstrate that the spatial density of progress scales as the square root of the density of users, and the optimal contention density (that maximizes the spatial density of progress) is independent of the density of users. These two facts are consistent with the observations of Baccelli et al., established through an analytical lower bound and through simulations.

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arXiv2010

Performance of Optimum Combining in a Poisson Field of Interferers and Rayleigh Fading Channels

This paper studies the performance of antenna array processing in distributed multiple access networks without power control. The interference is represented as a Poisson point process. Desired and interfering signals are subject to both path-loss fading (with an exponent greater than 2) and to independent Rayleigh fading. Using these assumptions, we derive the exact closed form expression for the cumulative distribution function of the output signal-to-interference-plus-noise ratio when optimum combining is applied. This results in a pertinent measure of the network performance in terms of the outage probability, which in turn provides insights into the network capacity gain that could be achieved with antenna array processing. We present and discuss examples of applications, as well as some numerical results.

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arXiv2009

Bit Error Rate is Convex at High SNR

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arXiv2009

Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications

Motivated by a recent surge of interest in convex optimization techniques, convexity/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex/concave for arbitrary multi-dimensional constellations. In particular, the SER is convex in SNR for any one- and two-dimensional constellation, and also in higher dimensions at high SNR. Pairwise error probability and bit error rate are shown to be convex at high SNR, for arbitrary constellations and bit mapping. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, an implication for fading channels ("fading is never good in low dimensions") and optimization of a unitary-precoded OFDM system. For example, the error rate bounds of a unitary-precoded OFDM system with QPSK modulation, which reveal the best and worst precoding, are extended to arbitrary constellations, which may also include coding. The reported results also apply to the interference channel under Gaussian approximation, to the bit error rate when it can be expressed or approximated as a non-negative linear combination of individual symbol error rates, and to coded systems.

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arXiv2009

The Ergodic Capacity of The MIMO Wire-Tap Channel

This paper has been withdrawn to provide a more rigorous proof of the converse of Theorem 1 and Lemma 1 as well.

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arXiv2008

Amendment to "Performance Analysis of the V-BLAST Algorithm: An Analytical Approach." [1]

An analytical technique for the outage and BER analysis of the nx2 V-BLAST algorithm with the optimal ordering has been presented in [1], including closed-form exact expressions for average BER and outage probabilities, and simple high-SNR approximations. The analysis in [1] is based on the following essential approximations: 1. The SNR was defined in terms of total after-projection signal and noise powers, and the BER was analyzed based on their ratio. This corresponds to a non-coherent (power-wise) equal-gain combining of both the signal and the noise, and it is not optimum since it does not provide the maximum output SNR. 2. The definition of the total after-projection noise power at each step ignored the fact that the after-projection noise vector had correlated components. 3. The after-combining noises at different steps (and hence the errors) were implicitly assumed to be independent of each other. Under non-coherent equal-gain combining, that is not the case. It turns out that the results in [1] hold also true without these approximations, subject to minor modifications only. The purpose of this note is to show this and also to extend the average BER results in [1] to the case of BPSK-modulated V-BLAST with more than two Rx antennas (eq. 18-20). Additionally, we emphasize that the block error rate is dominated by the first step BER at the high-SNR mode (eq. 14 and 21).

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arXiv2008

On Outage and Error Rate Analysis of the Ordered V-BLAST

Outage and error rate performance of the ordered BLAST with more than 2 transmit antennas is evaluated for i.i.d. Rayleigh fading channels. A number of lower and upper bounds on the 1st step outage probability at any SNR are derived, which are further used to obtain accurate approximations to average block and total error rates. For m Tx antennas, the effect of the optimal ordering at the first step is an m-fold SNR gain. As m increases to infinity, the BLER decreases to zero, which is a manifestation of the space-time autocoding effect in the V-BLAST. While the sub-optimal ordering (based on the before-projection SNR) suffers a few dB SNR penalty compared to the optimal one, it has a lower computational complexity and a 3 dB SNR gain compared to the unordered V-BLAST and can be an attractive solution for low-complexity/low-energy systems. Uncoded D-BLAST exhibits the same outage and error rate performance as that of the V-BLAST. An SNR penalty of the linear receiver interfaces compared to the BLAST is also evaluated.

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arXiv2007

Symbol Error Rates of Maximum-Likelihood Detector: Convex/Concave Behavior and Applications

Convexity/concavity properties of symbol error rates (SER) of the maximum likelihood detector operating in the AWGN channel (non-fading and fading) are studied. Generic conditions are identified under which the SER is a convex/concave function of the SNR. Universal bounds for the SER 1st and 2nd derivatives are obtained, which hold for arbitrary constellations and are tight for some of them. Applications of the results are discussed, which include optimum power allocation in spatial multiplexing systems, optimum power/time sharing to decrease or increase (jamming problem) error rate, and implication for fading channels.

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