In this paper, we introduce a newly developed MMSE-based digital precoder, the called Tunable MMSE (T-MMSE), to address cross-interference (CI) among user equipments (UEs) in a multi-user (MU) massive multiple-input multiple-output (mMIMO) downlink (DL) communication scenario. Compared to the conventional MMSE precoder, our approach adds a tunable constraint that enables the base station (BS) to regulate CI affecting specific UEs. After deriving the theoretical expression for the proposed optimal T-MMSE, we evaluate the influence of the tuning parameter on the performance of the communication. On top of our proposal, we also introduce a sub-optimal version with significantly reduced computational complexity. Simulation results show its strong flexibility in CI regulation, making it a superior solution to MMSE in various real-world communication scenarios.

This paper deals with discrete Fourier transform (DFT)-based modulation and demodulation techniques for affine frequency division multiplexing (AFDM), as opposed to using the discrete affine Fourier transform (DAFT). This allows for a simple (de)modulation process based on the usual DFT, enabling the interpretation of AFDM as a precoded orthogonal frequency division multiplexing (OFDM) waveform. This makes the AFDM modulation scheme backward compatible with existing OFDM systems. Furthermore, the sampling frequency of the modulated AFDM signal can be finely tuned using the suggested methods, whereas the usual DAFT leads to signals sampled at the Nyquist rate. To achieve this, a DFT-based AFDM modulation technique is introduced, along with a corresponding demodulation method. The introduction considers necessary conditions on the AFDM signal parameters, albeit at the cost of reduced flexibility in parameter settings, as only a limited set of parameters can be considered. The validity of the presented method is supported by mathematical developments and proofs, and validated through simulations. Furthermore, a complexity analysis is conducted.

In this paper, we study the behavior of a multiple-input multiple-output (MIMO) full-duplex (FD) system according to two different models of the self-interference (SI) channel inherent to the FD communication strategy: the spherical wave model (SWM) and the planar wave model (PWM). More precisely, we evaluate the received SI power at the receiver antenna array by changing the relative geometrical position of the transmitter antenna array in respect to the latter. Our study shows a significant difference between the two models. In particular we theoretically show as well as through simulation that the SWM for the SI channel is more precise than the PWM, and should then be considered for practical applications of the FD concept.

Abstract This article deals with peak to average power (PAPR) reduction in a single and multi‐user orthogonal chirp division multiplexing (OCDM) context. Two methods for PAPR reduction based on the selection of the frequency variation (up or down) of the chirps are first presented in a single user system. The first technique consists in considering two OCDM signals generated with up and down chirps, respectively, and selecting the one offering lowest PAPR. The second PAPR reduction method is based on usual clipping, and in that case the chirp selection aims to reduce the clipping noise. An adapted receiver is presented, based on the maximum likelihood estimation of the frequency variation (up or down) of the chirp. Then, a general procedure for multi‐user OCDM transmission is introduced, where a sub‐band of the available bandwidth is dedicated to each user, whose frequency of the chirps varies within this sub‐band. Next, the PAPR reduction techniques are generalised to this multi‐user OCDM system. Moreover, a performance analysis of the first PAPR reduction method is developed, and it is shown through simulations that theoretical and numerical results match for both Nyquist rate and oversampled signals. It is also shown that the chirp selection reduces the clipping noise, and improves the bit error rate performance compared with clipping only.

This article deals with time and frequency synchronization in the Long Range (LoRa) system based on the preamble symbols. A thorough analysis of the maximum-likelihood (ML) estimator of the delay (time offset) and the frequency offset shows that the resulting cost function is not concave. As a consequence thea priorisolution to the maximization problem consists in exhaustively searching over all the possible values of both the delay and the frequency offset. Furthermore, it is shown that these parameters are intertwined and therefore they must be jointly estimated, leading to an extremely complex solution. Alternatively, we show that it is possible to recover the concavity of the cost function, from which we suggest a low-complexity synchronization algorithm, whose steps are described in detail. Simulations results show that the suggested method reaches the same performance as the ML exhaustive search, while the complexity is drastically reduced, allowing for a real-time implementation of an LoRa receiver.

This paper deals with the computation of integrals of centred bivariate Gaussian densities over any domain defined as an angular sector of ℝ2. Based on an accessible geometrical approach of the problem, we suggest to transform the double integral into a single one, leading to a tractable closed-form expression only involving trigonometric functions. This solution can also be seen as the angular cumulative distribution of bivariate centered Gaussian variables (X, Y). We aim to provide a didactic approach of our results, and we validate them by comparing with those of the literature.

The cell identity (ID) estimation is one of the essential steps performed by the narrowband‐internet of things (NB‐IoT) user equipment (UE) during its initial access to the network. The cell ID value is carried by the narrowband secondary synchronisation signal (NSSS) that is periodically transmitted in even radio frames. In this study, the authors proposed a novel technique of cell ID estimation for the NB‐IoT UE. The proposed technique is based on a sub‐optimal estimator that applies auto‐correlation over the received observations and which is 30 times less complex than the optimal maximum likelihood (ML) estimator based on cross‐correlation. In addition, they presented three methods that allow the receiver to take advantage of the periodicity of the NSSS. Finally, the advantages and the drawbacks of the presented methods are discussed with a performance analysis through simulation results. Results show that these methods reach the performance of ML with lower overall complexity.

This study deals with the detection of unknown signals in white noise. The authors present a new detector, based on the difference of a deterministic function of the energy of the signal and the energy of the same signal, which has been filtered. Unlike usual energy detector (ED), the proposed detector consists in exploiting the behaviour of the energy of filtered white noise, which can be a priori determined since the used filter is known. Thus, if the measured energy differs from an expected value, the detector decides that a signal is present in the band. In order to have the same asymptotic complexity as ED, a simple two‐tap filter is used. The theoretical expressions of the probabilities of detection and false alarm are developed, and the optimal threshold is deduced. Simulations show that the proposed detector achieves better performance than ED, in both additive white Gaussian noise and Rayleigh channels. Furthermore, the relevance of the analytical results is proved through simulations.

The distribution of the peak-to-average power ratio (PAPR) of multicarrier systems is studied in the context of signals featuring low subcarriers number. Considering the mean power of the signal as a random variable, a general cumulative distribution function of the PAPR is suggested. We show that the new formulation is valid not only for low subcarriers number but also for larger subcarriers number. Thus, an asymptotic analysis using a large subcarriers number proves a perfect concordance between the suggested approach and the state-of-the-art derivations only valid for large subcarriers number. All the theoretical developments are supported through simulations, and we discuss the case of oversampled signals as well.

This study deals with the ergodic capacity in multi‐sector cells. Due to the presence of the antenna gain pattern in the expression of the capacity, the latter may be difficult to express analytically. To overcome this problem, the authors propose to approximate the antenna gain pattern by means of a piecewise linear function, which leads to a general closed‐form formulation of the capacity. The obtained expression is applicable for any used antenna. The simulations results are performed by using the long term evolution (LTE) TR 36.942 antenna specification, showing that the proposed closed‐form capacity almost matches the exact one. In addition, the authors provide a practical use case of the method, by considering a scenario where the users are clustered within the area covered by the antenna.

Linear minimum mean square error (LMMSE) is by definition the optimal channel estimator in the sense of mean square error criterion, but its practical application is limited by its high complexity. Furthermore, the LMMSE estimation method requires the knowledge of both the channel and the noise statistics, which are a priori unknown at the receiver. A wide range of techniques are proposed in the literature in order to overcome these two drawbacks. In this study, the authors give an overview of the LMMSE‐based channel estimation in an orthogonal frequency division multiplexing (OFDM) context. A didactic reminder concerning the basics of LMMSE estimation and its performance is provided, and a survey of techniques of the literature, which enable the practical application of LMMSE and the reduction of its complexity, is presented in both single‐input single‐output and multiple‐input multiple‐output contexts. Finally, some perspectives are provided, in particular the application of the LMMSE estimator to flexible waveforms beyond OFDM.

This study deals with a bit error rate (BER) floor performance analysis for orthogonal frequency division multiplexing (OFDM) systems using pilot‐aided channel estimation with polynomial interpolations. Such a performance analysis has been previously undertaken in the literature, but is limited to binary phase shift keying and 4‐quadrature amplitude modulation (4‐QAM) constellations. The main contribution of this study is then to analyse the BER floor achieved by a 16‐QAM OFDM signal in a Rayleigh channel. To achieve this, the binary error probability is obtained by carrying out the analysis on maximum significant bits (MSB) and least significant bits (LSB). The MSB leads to the similar results as those obtained in 4‐QAM, but very specific developments are required to obtain the error probability of the LSB. Numerical results show that the proposed BER performance analysis is valid for the 16‐QAM constellation.

This paper presents a preamble-based linear minimum mean square error (LMMSE) estimation technique for filter bank multicarrier (FBMC) modulations. Orthogonal frequency division multiplex (OFDM) systems have been extensively used in digital communication systems, for they are extremely efficient in terms of channel estimation and equalization. Estimation being a crucial part of digital communication systems, techniques have been developed to reduce the impact of noise on the channel estimation process, the optimal one being the LMMSE one. Until recently, non-orthogonal multicarrier modulations such as FBMC, were unable to use OFDM-like estimation techniques due to the non-orthogonality. The interference approximation method (IAM) is one of the most popular method among preamblebased estimation techniques with a limited complexity. This paper present a combination of IAM and a LMMSE-based algorithm that makes possible to achieve a LMMSE estimation in FBMC.

This paper focuses on the use of a long term evolution (LTE)- like broadband system using filter bank multicarrier (FBMC) PHY layer in professional mobile radio (PMR) communication band. PMR communication systems have been designed for emergency, security, and disaster relief communications in the 400 MHz band. The main goal is to deploy a broadband LTE-like system to coexist without causing harmful interferences with actually deployed PMR systems in unused bands. Besides the use of FBMC scheme, some additional modifications on the resource block size and the pilot pattern structure have been introduced in LTE standard to be adapted and able to operate in PMR communication environment. Obtained results through simulations demonstrated the suitability of proposed changes in terms of achieved bit error rates compared with defined structure in LTE system.

In this study, the performance of different preamble‐based channel estimation techniques is analysed for orthogonal frequency division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) modulation systems. Three pilot allocation methods, the pair of pilot, the interference cancellation method, and the interference approximation method are considered. A theoretical expression of the estimation mean square error (MSE) is performed for each of them, which considers the selectivity of the channel and the interferences from all the neighbouring time–frequency positions. Moreover, an application of the linear minimum MSE estimator in OFDM/OQAM is investigated and an analysis of its MSE performance is provided as well. It is shown that, due to the intrinsic interference, the MSE of the channel estimation inevitably reaches an error floor whatever the applied method is. Numerical results show that the theoretical MSE assessments match those obtained by simulation. In addition to the MSE, the bit error rate performance for the different channel estimators is depicted.

In this paper, the authors provide an analytical expression of the mean square error (MSE) and the bit error rate (BER) lower bound of an orthogonal frequency division multiplexing signal transmission over a multipath Rayleigh channel considering estimation errors. For some pilot arrangements, an interpolation is required to perform the channel estimation. Owing to their low complexity, polynomial based interpolations are usually applied at the receiver, which induces estimation and signal errors. Based on a statistical analysis of these errors, the exact MSE expression of the channel estimation is provided. Furthermore, with a geometrical study of the constellation, an analytical BER limit is derived. For a given channel, it is shown that the errors are perfectly characterised by the interpolation method and the frequency gap between the pilot tones. All the steps of the analytical developments are validated through simulations. The proposed analysis then predicts the performance of the receiver, thus enabling the latter to a priori select the interpolation method with minimum complexity, according to a given channel and a BER target.

This paper deals with the minimum mean square error (MMSE)-based multipath channel and noise variance estimation in the case of a pilot-aided orthogonal frequency division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) system. The theoretical expression of the LMMSE channel estimation is formulated and a simpler closed-form is derived. The MSE analysis shows that LMMSE inevitably reaches an error floor due to the interference inherent to OFDM/OQAM modulation. Furthermore, an algorithm for the joint MMSE estimation of both the channel and the noise variance (J-MCNE) is proposed and features a reduced complexity thanks to the low-rank approximation method. The noise level estimation represents a challenge as it is concealed in the intrinsic interferences generated by the OFDM/OQAM. Simulations reveal the capability of the proposed J-MCNE method to estimate the noise variance and show that the achieved bit error rate (BER) is close to that of the perfect estimation.

In this article, the authors study the convergence of an iterative algorithm for the joint estimation of the signal‐to‐noise ratio (SNR) and the transmission channel in orthogonal frequency division multiplexing context. At each step of the algorithm, the authors use the minimum‐mean‐square error (MMSE)‐based SNR estimation, which feeds the linear MMSE channel estimation. Reciprocally, this efficient channel estimation is used to perform the SNR estimation. The authors provide a proof of convergence of the algorithm to a single value. Furthermore, we derive an accurate approximation of the bias of the estimation. Simulations show that the algorithm converges quickly and verifies the theoretical results. They also show the efficiency of both SNR and channel estimation. By comparing with the existing methods, the authors show that the tradeoff between the number of required pilots in the preamble and the performance of the SNR estimation were improved. Furthermore, for a fixed bit error rate, the SNR gap between the proposed channel estimation and the perfect one is <0.5 dB.