This paper deals with the potential of affine frequency division multiplexing (AFDM) to operate within a multiuser multi-input multi-output (MU-MIMO) system, facilitated by spatial precoding preformed in frequency domain. To this end, we take advantage of the fact that AFDM based on discrete affine Fourier transform (DAFT) can be rewritten as a discrete Fourier transform (DFT)-based precoded orthogonal frequency division multiplexing (OFDM) waveform. By considering the wellknown zero-forcing (ZF) precoder and white noise, we show that MU-MIMO AFDM achieves the same performance as MU-MIMO OFDM in terms of both sum rate and bit error rate (BER).

In this paper we introduce projection-based precoders for secure transmission in cell-free massive multiple-input multipleoutput (MIMO) systems. Assuming that the channel state information (CSI) of both legitimate users (referred to as Bob) and passive eavesdroppers (Eve) is known, we derive three secure precoder designs using well-known linear precoders, such as maximum ratio transmission (MRT), zero-forcing (ZF) and minimum mean square error (MMSE). The first method projects these linear precoders onto the orthogonal complement space of Eve. The second method processes Bob's channel with the same projection operator before applying linear precoding to this newly formed "secure" channel matrix. Additionally, we propose a novel MMSE-based precoder with added security constraints, designed to reduce energy leaked towards Eve. By reformulating the proposed precoders, we provide several interpretations of the latter, which result in simpler expressions and equivalent projected precoding schemes. Analytical results are supported by simulations in realistic environments, and demonstrate that the proposed methods can completely eliminate Eve's received power. It results in improved secrecy performance compared to their non-secrecy aware counterparts.

This paper deals with the minimum mean square error (MMSE) digital beamforming techniques at both transmitter (precoding) and receiver (combining) sides in multiuser multiple input multiple output (MU-MIMO) systems, under errors of channel state information (CSI). We consider very general system models in both downlink and uplink cases, where the number of transmit and receive antennas can take any values, and the CSI errors are random samples. Based on this model, we analyze the performance of the MMSE beamforming methods considering imperfect CSI in the construction of the beamforming matrices, reflecting possible errors of channel estimation. We theoretically show that the additional inter-user interference power due to the CSI errors is quadratically proportional to the square of a parameter α quantifying the CSI errors. This analytic result is supported by simulations, and we also show the effect of the CSI errors on the achievable bit error rate (BER), considering multipath and free space line-of-sight channel models. In both cases, simulations and theoretical results match, and highlight that the MMSE beamforming methods experience few dB loss in presence of potentially high CSI errors compared to perfect CSI.

In this paper, we evaluate the performance of a newly developed spatial domain zero-forcing (ZF) based selfinterference cancellation (SIC) method in a generic multiple-input multiple-output (MIMO) full-duplex (FD) system. To this end, we theoretically evaluate the influence of channel state information (CSI) error on the SIC performance of our considered approach, and we validate our results through simulations. In particular, we show that the additional received self-interference (SI) power due to the CSI errors is quadratically proportional to a particular parameter α, quantifying the level of CSI errors. Furthermore, simulations results show that the increase of SI power has a negligible impact on the overall system performance in terms of spectral efficiency (SE), which proves the robustness of our considered SIC method.

This paper introduces a new spatial domain-based self-interference cancellation (SIC) precoding method named constrained minimum mean square error (C-MMSE) for an asymmetric massive multiple-input multiple-output (mMIMO) full-duplex (FD) system. The main idea is to translate the commonly used singular value decomposition (SVD)-based null-space projection approach, which is unfeasible in our considered system model, into an optimization problem under MMSE criterion, where additional constraints are implemented to perform SIC. Theoretical derivation of the C-MMSE precoder is presented, followed by performance comparison with conventional MMSE precoding, where no constraints are added for SIC. We theoretically show that the C-MMSE scheme outperforms the conventional one in terms of SIC, and allows the FD system to work under an almost interference-free environment. Additionally, we also assess the performance of the proposed method under imperfect channel state information (CSI), to further evaluate the robustness of our spatial precoder in more realistic conditions. We show that the C-MMSE precoder outperforms MMSE in terms of interference suppression ratio (ISR), even in CSI imperfection. Additionally, the C-MMSE achieves the same spectral efficiency (SE) as an hypothetical perfect SIC in a wide SNR range, whereas the MMSE is upper bounded in large SNR range.

In this paper, we propose and evaluate a spatial domain self-interference cancellation (SIC) method based on the principle of zero-forcing (ZF) beamforming for a generic multiple-input multiple-output (MIMO) full-duplex (FD) transceiver system in a large-scale communication scenario. The core of the proposed SIC method is to implement an additional radio-frequency (RF) chain at the receiver (RX) to induce an additional dimension on the channel matrix, so that the inversion of the channel matrix becomes feasible. To this end, we adapt, as an example, a simple ZF digital combiner in our system model to simultaneously perform SIC and enhance the communication link performance. Simulations results further confirm our proposal. In particular, our method demonstrates a strong SIC capability, even with an erroneous knowledge of the channel state information (CSI), and effectively improves the communication link performance of the FD system.

This paper deals with a massive multiple-input multiple- output (mMIMO) full-duplex (FD) communication system. We propose new spatial domain self-interference cancellation (SIC) techniques. The main idea is to treat the self-interference (SI) signal emitted from the FD node as another spatial stream that needs to be precoded in the null space of the MIMO channel that includes that node as an output. To this end, an additional RF chain is needed at the transmitter to cancel the SI signal. On this basis, we derive the expressions of the spatial precoders with respect to the conventional zero forcing (ZF) and minimum mean square error precoding (MMSE) criteria. Furthermore, the originality of the analysis lies in the consideration of SWM for modeling the SI channel, which is justified by the close proximity of the transmit and receive antenna panels in the FD node. Simulations show the relevance of the study. We verify the SIC efficiency in the spatial domain using the derived ZF and MMSE precoders by analyzing their relative performance in terms of spectral efficiency. We also highlight the robustness of our SWM-based SI channel compared to classic planar wave model (PWM) and therefore the need for using it.

This paper deals with discrete Fourier transform (DFT)-based modulation and demodulation techniques for affine frequency division multiplexing (AFDM) instead of discrete affine Fourier transform (DAFT). This allows for a simple (de)modulation process based on the usual DFT, such that the AFDM can be interpreted as a precoded orthogonal frequency division multiplexing (OFDM) waveform, making the AFDM modulation scheme backward compliant with existing OFDM systems. Furthermore, the sampling frequency of the modulated AFDM signal can be finely tuned using the suggested methods while the usual DAFT leads to signals sampled at Nyquist rate. To achieve this, four different DFT-based AFDM modulation techniques are introduced, as well as one demodulation method, according to necessary conditions on the AFDM signal parameters, to the cost of a loss of flexibility on the parameters setting. All the presented methods are supported by mathematical developments and proofs, and validated through simulations.

This paper deals with the computation of integrals of centred bivariate Gaussian densities over any domain defined as an angular sector of R^2. 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.

This paper deals with the implementation of a light fifth generation (5G) base station (gNB) intended  for specific use cases requiring an airborne deployment of the network. We focus on the radio unit (RU) and give details on the components, the implementations, and the technical choices that have been made, driven by the strong constraints inherent to the considered use cases.

This paper deals with a new spatial domain-based self-interference cancellation (SIC) method called constrained minimum mean square error (C-MMSE) for massive multiple-input multiple-output (mMIMO) full-duplex (FD) communication systems. The main idea is to treat the self-interference (SI) signal emitted from an FD node as a particular spatial stream arriving at the receiver part of that same FD node which needs to be spatially postcoded along with other useful signals coming from other transmitters, so that it falls into the null space of the MIMO channel that includes the FD node transmitter part as an input. On this basis, we first adapt the expressions of the spatial combiners with respect to the conventional zero forcing (ZF) and minimum mean square error combining (MMSE) criteria and show that the latter is not capable to efficiently cancel the SI signal unless an additional constraint is added to properly perform SIC. We hence design the new so-called C-MMSE combiner and derive its expression. In addition to our proposal, the originality of our work lies in the consideration of spherical wave model (SWM) for modeling the SI channel, which is justified by the close proximity of the transmit and receive antenna panels in the FD node. We examine and compare the SIC performance of the adapted ZF combiner, the adapted MMSE combiner and the newly introduced C-MMSE combiner by evaluating the obtained spectral efficiency (SE). We also highlight the robustness of the SWM-based SI channel modelling compared to conventional planar wave modelling (PWM) and therefore the relevance of using it.

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.