Baptiste Vrigneau

Extension of the MIMO Precoder Based on the Minimum Euclidean Distance: A Cross-Form Matrix

Under full channel state information at the transmitter side (Tx-CSI), MIMO precoders can be designed by the optimization of many pertinent criteria, like, for example, the maximizing post-processing signal-to-noise ratio (max-SNR or beamforming solution), or the minimizing weighted mean square error between transmit and receive vector-symbols (W-MMSE solution). These solutions decouple the MIMO channel into b parallel independent datastreams. This diagonal structure reduces the complexity of the maximum likelihood (ML) decisions but the diversity order of these schemes is limited. Recently, we proposed a precoder, max-dmjn solution, which optimizes the exact expression of the minimum Euclidean distance and leads to a non diagonal structure allowing to achieve maximum diversity order. However, the result is available only for two transmit datastreams (6 = 2) and BPSK and QPSK modulations. In this paper, we propose a heuristic method to deal with the case b > 2, which provides a suboptimal, but good solution to this general problem. The new precoder, Equal-dm;n (E-dmin), is based on a non diagonal cross-form structure. It significantly enhances the transmit diversity in the eigen-subchannels. We demonstrate that the achieved diversity order is greater than that of precoders with diagonal structure for the same number of datastreams despite a tradeoff between rate and diversity. This design can also ensure quality of service (QoS) by using an adapted power allocation strategy. Performance comparisons show the BER improvement for MIMO and MIMO-OFDM systems.

Minimum Distance Based Precoder for MIMO-OFDM Systems Using a 16-QAM Modulation

A precoder based on the exact optimization of the minimum Euclidean distance dmin between signal points at the receiver side is proposed for MIMO-OFDM systems using a 16-QAM modulation. Assuming that channel state information (CSI) can be made available at the transmitter, the channel is diagonalized and a precoder can be derived. A numerical approach shows that the precoder design depends on the channel characteristics, leading to 8 different precoder expressions. Comparisons with maximum signal-to-noise ratio (SNR) strategy and other precoders based on criteria, such as water-filling (WF), minimum mean square error (MMSE), and maximization of the minimum singular value of the global channel matrix, are performed to illustrate the significant bit-error-rate (BER) improvement of the proposed precoder. In order to make its implementation easier, it is shown that it can be expressed by only two ways without significant performance degradation.

Impacts of impulsive noise from partial discharges on wireless systems performance: application to MIMO precoders

To satisfy the smart grid electrical network, communication systems in high-voltage substations have to be installed in order to control equipments. Considering that those substations were not necessarily designed for adding communication networks, one of the most appropriate solutions is to use wireless sensor network (WSN). However, the high voltage transported through the station generates a strong and specific radio noise. In order to prepare for such a network, the electromagnetic environment has to be characterized and tests in laboratories have to be performed to estimate the communication performances. This paper presents a method for measuring the noise due to high voltage and more particularly the impulsive noise. In the laboratory, we generate the impulsive noise using two specimens, and we show that these laboratory measurements validate the field measurements of Pakala et al. For the two specimens, it aims to link the noise characteristics (magnitude and frequency) with the specimen parameters (power supply and geometric dimensions) to predict the environments where wireless communications can be troublesome. By using different sets of this measured noise, we show that the statistical model of Middleton Class A can be used to model the impulsive noise in high-voltage substations better than the Gaussian model. We consider a cooperative multiple-input-multiple-output (MIMO) system to achieve the wireless sensor communication. This system uses recent MIMO techniques based on precoding like max-dmin and P-OSM precoders. The MIMO precoder-based cooperative system is a potential candidate for energy saving in WSN since energy efficiency optimization is a very important critical issue. Since MIMO precoders are with Gaussian noise assumption, we evaluate the performance of several MIMO precoders in the presence of impulsive noise using estimated parameters from the measured noise.

Statistical comparison between max-dmin, max-SNR and MMSE precoders

In this study, we considered a MIMO system with available channel state information at the transmitter side and compared three known precoders based on different and pertinent criteria: the post processing signal-to-noise ratio (max-SNR), the mean square error between transmitted and received symbols (MMSE) and the minimum distance of the received constellation (max-dmin). We demonstrate that, alike the max-SNR and contrarily to the MMSE, the max-dmin gives the maximum diversity order for a Rayleigh channel. An upper- bound of the MMSE diversity order is given. On the other hand, dmin of the three precoders will be statistically studied as a function of the number of antennas. In addition, BER simulations showed that the best precoder is the max-dmin.

Limited Feedback Unitary Matrix applied to MIMO dmin-based Precoder

In spatial multiplexing systems, transmission reliability is enhanced by the full channel state information (CSI) used to design optimum linear precoders, but in practice a full CSI is often unrealistic. Indeed, a higher number of transmitters and/or receivers elevates the coefficient numbers of the estimated channel, and the precision on coefficients depends on the rate of the feedback stream. An interesting alternative is to return a limited amount of information to the transmitter; this led us to design a dmin precoder based on the use of i) a finite codebook known by the receiver and the transmitter and ii) feedback of only one quantized real-valued parameter. The selection criteria employed to find the optimal precoding matrix are presented. Then, the performances about BER are compared under different criteria and amounts of feedback and confronted to Alamouti code.

Theoretical Results about MIMO Minimal Distance Precoder and Performances Comparison

This study deals with two linear precoders: the maximization of the minimum Euclidean distance between received symbol-vectors, called here max-dmin, and the maximization of the post-processing signal-to-noise ratio termed max-SNR or beamforming. Both have been designed for reliable MIMO transmissions operating over uncorrelated Rayleigh fading channels. Here, we will explain why performances in terms of bit error rates show a significant enhancement of the max-dmin over the max-SNR whenever the number of antennas is increased. Then, from theoretical developments, we will demonstrate that, like the max-SNR precoder, the max-dmin precoder achieves the maximum diversity order, which is warrant of reliable transmissions. The current theoretical knowledge will be applied to the case-study of a system with two transmit- or two receive-antennas to calculate the probability density functions of two channel parameters directly linked to precoder performances for uncorrelated Rayleigh fading channels. At last, this calculation will allow us to quickly get the BER of the max-dmin precoder further to the derivation of a tight semi-theoretical approximation.

Performance Analysis of Closed-Loop MIMO Precoder Based on the Probability of Minimum Distance

Linear closed-loop MIMO precoders are attractive owing to their scalability. They can significantly improve the received signal via optimization of pertinent criterion. The solution of max-dmin precoding is optimal for 4-QAM as it utilizes the channel state information at the transmitter (CSIT) to minimize the system error probability making it very attractive. However, as M increases the solution which is dependent on channel angle gets complex, due to its multi-form precoder search. Motivated by a requirement to provide MIMO system evaluation parameters to upper layer protocol(s) as a function of precoder optimization criterion, we propose deriving a general expression for the probability density function (pdf) of max-dmin. Our approach applies numerical approximations to derive the system bit error rate (BER) and ergodic capacity for any values of M, nr, and nt, and with b = 2 data streams. Results show that the performance of our numerical approximation approach is close to the analytical simulation method.

Order statistics based diagonal precoding for 4 × 1 MISO system with real orthogonal space time block codes

In this paper, we discuss a quantized feedback based diagonal precoder for 4 × 1 multiple-input single-output (MISO) system employing real orthogonal space-time block code (ROSTBC). Precoding improves the coding gain of the MISO system by exploiting channel state information at transmitter. ROSTBC helps in achieving full spatial diversity, full rate, and symbol-wise decoding for arbitrary number of transmit antennas in MISO system. An accurate closed-form expression of the symbol error rate (SER) of considered MISO system is derived with erroneous feedback by using the order statistics. Optimized transmit weights are obtained by minimizing the average SER of the precoding scheme. Simulated and analytical results show that the proposed scheme achieves significant improvement over MISO system employing ROSTBC only. Further, the scheme remains insensitive to the feedback errors.

Green communication via HARQ protocols using message-passing decoder over AWGN channels

In this paper, we study the effect of optimal power allocation on the performance of communication systems using hybrid-automatic repeat request (HARQ) protocols with a limited maximum number of transmission rounds. We formulate the optimization problem aiming to minimize the total average power consumption in order to achieve a target performance constraint, where the total power consumption stands for the sum of the transmission power and the processing power consumed in the decoding. Our analysis relies on the characterization of an information-theoretic bound on the decoding power of any modern code to achieve a specified bit error probability while operating at a certain gap from the capacity. As this bound is built on the sphere-packing analysis, the present study focuses on message-passing decoders. We find that the implementation of power-adaptive HARQ reduces the total average power consumption even when taking decoding power into consideration, compared with reference systems.

l1-Norm minimization based algorithm for non-intrusive load monitoring

Non-Intrusive Load Monitoring (NILM) plays an important role in energy management and energy reduction in buildings and homes. An NILM system does not need a large amount of deployed power meters to monitor the power usage of home devices. Instead, only one meter on the main power line is necessary to detect and identify the operating devices. There are many approaches to solve the problem of device determination in NILM. The features applied in low-frequency based approach essentially include the step-change (or edge) and the steady state. This paper introduces three algorithms to solve the l1-norm minimization problem in NILM and results on power measurements obtained from a real appliance deployment. With a small number of devices, the obtained precision varies from 75% to 99%, depending on the tolerance criterion to determine the steady state of a given device.