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As an essential part of mobile communication systems that beyond the fifth generation (B5G) and sixth generation (6G), ultra reliable low latency communication (uRLLC) places strict requirements on latency and reliability. In recent years, with the improvement of mobile communication network performance, centralized and distributed processing of cell-free mMIMO has been widely studied, and wireless access networks (RAN) have also become a widely studied topic in academia. This paper analyzes the performance of a novel scalable cell-free RAN (CF-RAN) architecture with multiple edge distributed units (EDUs) in the scenario of finite block length. The upper and lower bounds on its spectral efficiency (SE) performance are derived, and the complete set's formula and distributed processing can be used as their two exceptional cases, respectively. Secondly, the paper further considers the distribution of users and large-scale fading models and studies the position distribution of remote radio units (RRUs). It is found that a uniform distribution of RRUs is beneficial for improving the SE of finite block length under specific error rate performance, and RRUs need to be interwoven as much as possible under multiple EDUs. This is different from traditional multi-node clustering centralized collaborative processing. The paper compares the performance of Monte Carlo simulation and multi-RRU clustering group collaborative processing. At the same time, this article verifies the accuracy of the space-time exchange theory in the CF-RAN scenario. Through scalable EDU deployment, a trade-off between latency and reliability can be achieved in practical systems and exchanged with spatial degrees of freedom. This implementation can be seen as a distributed and scalable implementation of the space-time exchange theory.

Due to its ability of significantly improving data rate, intelligent reflecting surface (IRS) will be a potential crucial technique for the future generation wireless networks like 6G. In this paper, we will focus on the analysis of degree of freedom (DoF) in IRS-aided multi-user MIMO network. Firstly, the DoF upper bound of IRS-aided single-user MIMO network, i.e., the achievable maximum DoF of such a system, is derived, and the corresponding results are extended to the case of IRS-aided multiuser MIMO by using the matrix rank inequalities. In particular, in serious rank-deficient, also called low-rank, channels like line-of-sight (LoS), the network DoF may doubles over no-IRS with the help of IRS. To verify the rate performance gain from augmented DoF, three closed-form beamforming methods, null-space projection plus maximize transmit power and maximize receive power (NSP-MTP-MRP), Schmidt orthogonalization plus minimum mean square error (SO-MMSE) and two-layer leakage plus MMSE (TLL-MMSE) are proposed to achieve the maximum DoF. Simulation results shows that IRS does make a dramatic rate enhancement. For example, in a serious deficient channel, the sum-rate of the proposed TLL-MMSE aided by IRS is about twice that of no IRS. This means that IRS may achieve a significant DoF improvement in such a channel., Comment: 12 pages, 9 figures

Cell-free massive multiple-input-multiple-output (CF-mMIMO) is regarded as one of the promising technologies for next-generation wireless networks. However, due to its distributed architecture, geographically separated access points (APs) jointly serve a large number of user-equipments (UEs), there will inevitably be a discrepancies in the arrival time of transmitted signals. In this paper, we investigate millimeter-wave (mmWave) CF-mMIMO orthogonal frequency division multiplexing (OFDM) systems with asynchronous reception in a wide area coverage scenario, where asynchronous timing offsets may extend far beyond the cyclic prefix (CP) range. A comprehensive asynchronous beam-domain signal transmission model is presented for mmWave CF-mMIMO-OFDM systems in both downlink and uplink, incorporating phase offset, inter-carrier interference (ICI) and inter-symbol interference (ISI). To address the issue of asynchronous reception, we propose a novel per-beam timing advance (PBTA) hybrid precoding architecture and analyze the spectral efficiency (SE) in the beam domain for downlink and uplink asynchronous receptions. Both scalable centralized and distributed implementations are taken into account, and the asynchronous delay phase is utilized to design precoding/combining vectors. Furthermore, we formulate the sum rate maximization problem and develop two low-complexity joint beam selection and UE association algorithms considering the impact of asynchronous timing offset exceeding the CP range. Simulation results demonstrate that the performance will be severely limited by ICI and ISI, and our proposed PBTA hybrid precoding architecture effectively mitigates asynchronous interference compared to the nearest AAU/UE-based timing-advance scheme. Additionally, numerical results show that our proposed low-complexity joint beam selection and UE association algorithms achieve superior SE performance.

In the research of next-generation wireless communication technologies, orthogonal time frequency space (OTFS) modulation is emerging as a promising technique for high-speed mobile environments due to its superior efficiency and robustness in doubly selective channels. Additionally, the cell-free architecture, which eliminates the issues associated with cell boundaries, offers broader coverage for radio access networks. By combining cell-free network architecture with OTFS modulation, the system may meet the demands of massive random access required by machine-type communication devices in high-speed scenarios. This paper explores a massive random access scheme based on OTFS modulation within a cell-free architecture. A transceiver model for uplink OTFS signals involving multiple access points (APs) is developed, where channel estimation with fractional channel parameters is approximated as a block sparse matrix recovery problem. Building on existing superimposed and embedded preamble schemes, a hybrid preamble scheme is proposed. This scheme leverages superimposed and embedded preambles to respectively achieve rough and accurate active user equipment (UEs) detection (AUD), as well as precise channel estimation, under the condition of supporting a large number of access UEs. Moreover, this study introduces a generalized approximate message passing and pattern coupling sparse Bayesian learning with Laplacian prior (GAMP-PCSBL-La) algorithm, which effectively captures block sparse features after discrete cosine transform (DCT), delivering precise estimation results with reduced computational complexity. Simulation results demonstrate that the proposed scheme is effective and provides superior performance compared to other existing schemes.

This paper studies the large-scale cell-free networks where dense distributed access points (APs) serve many users. As a promising next-generation network architecture, cell-free networks enable ultra-reliable connections and minimal fading/blockage, which are much favorable to the millimeter wave and Terahertz transmissions. However, conventional beam management with large phased arrays in a cell is very time-consuming in the higher-frequencies, and could be worsened when deploying a large number of coordinated APs in the cell-free systems. To tackle this challenge, the spatial-spectral cell-free networks with the leaky-wave antennas are established by coupling the propagation angles with frequencies. The beam training overhead in this direction can be significantly reduced through exploiting such spatial-spectral coupling effects. In the considered large-scale spatial-spectral cell-free networks, a novel subchannel allocation solution at sub-terahertz bands is proposed by leveraging the relationship between cross-entropy method and mixture model. Since initial access and AP clustering play a key role in achieving scalable large-scale cell-free networks, a hierarchical AP clustering solution is proposed to make the joint initial access and cluster formation, which is adaptive and has no need to initialize the number of AP clusters. After AP clustering, a subchannel allocation solution is devised to manage the interference between AP clusters. Numerical results are presented to confirm the efficiency of the proposed solutions and indicate that besides subchannel allocation, AP clustering can also have a big impact on the large-scale cell-free network performance at sub-terahertz bands.

By deploying antenna arrays at the transmitter/receiver to provide additional spatial-domain degrees of freedom (DoFs), multi-antenna technology greatly improves the reliability and efficiency of wireless communication. Meanwhile, the application of multi-antenna technology in the radar field has achieved spatial angle resolution and improved sensing DoF, thus significantly enhancing wireless sensing performance. However, wireless communication and radar sensing have undergone independent development over the past few decades. As a result, although multi-antenna technology has dramatically advanced in these two fields separately, it has not been deeply integrated by exploiting their synergy. A new opportunity to fill up this gap arises as the integration of sensing and communication has been identified as one of the typical usage scenarios of the 6G communication network. Motivated by the above, this article aims to explore the multi-antenna technology for 6G ISAC, with the focus on its future development trends such as continuous expansion of antenna array scale, more diverse array architectures, and more flexible antenna designs. First, we introduce several new and promising antenna architectures, including the centralized antenna architectures based on traditional compact arrays or emerging sparse arrays, the distributed antenna architectures exemplified by the cell-free massive MIMO, and the movable/fluid antennas with flexible positions and/or orientations in a given 3D space. Next, for each antenna architecture mentioned above, we present the corresponding far-field/near-field channel models and analyze the communication and sensing performance. Finally, we summarize the characteristics of different antenna architectures and look forward to new ideas for solving the difficulties in acquiring CSI caused by the continuous expansion of antenna array scale and flexible antenna designs., Comment: in Chinese language

Multi-static integrated sensing and communication (ISAC) technology, which can achieve a wider coverage range and avoid self-interference, is an important trend for the future development of ISAC. Existing multi-static ISAC designs are unable to support the asymmetric uplink (UL)/downlink (DL) communication requirements in the scenario while simultaneously achieving optimal sensing performance. This paper proposes a design for multi-static ISAC based on network-assisted full-duplex (NAFD) cell-free networks can well solve the above problems. Under this design, closed-form expressions for the individual comunication rate and localization error rate are derived under imperfect channel state information, which are respectively utilized to assess the communication and sensing performances. Then, we propose a deep Q-network-based accesss point (AP) duplex mode optimization algorithm to obtain the trade-off between communication and sensing from the UL and DL perspectives of the APs. Simulation results demonstrate that the NAFD-based ISAC system proposed in this paper can achieve significantly better communication performance than other ISAC systems while ensuring minimal impact on sensing performance. Then, we validate the accuracy of the derived closed-form expressions. Furthermore, the proposed optimization algorithm achieves performance comparable to that of the exhaustion method with low complexity.

This paper analyzes the impact of pilot-sharing scheme on synchronization performance in a scenario where several slave access points (APs) with uncertain carrier frequency offsets (CFOs) and timing offsets (TOs) share a common pilot sequence. First, the Cramer-Rao bound (CRB) with pilot contamination is derived for pilot-pairing estimation. Furthermore, a maximum likelihood algorithm is presented to estimate the CFO and TO among the pairing APs. Then, to minimize the sum of CRBs, we devise a synchronization strategy based on a pilot-sharing scheme by jointly optimizing the cluster classification, synchronization overhead, and pilot-sharing scheme, while simultaneously considering the overhead and each AP's synchronization requirements. To solve this NP-hard problem, we simplify it into two sub-problems, namely cluster classification problem and the pilot sharing problem. To strike a balance between synchronization performance and overhead, we first classify the clusters by using the K-means algorithm, and propose a criteria to find a good set of master APs. Then, the pilot-sharing scheme is obtained by using the swap-matching operations. Simulation results validate the accuracy of our derivations and demonstrate the effectiveness of the proposed scheme over the benchmark schemes., Comment: Submitted to IEEE Journal for pos

The classical theory of Kosambi-Cartan-Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in terms of five geometrical invariants, of which the second corresponds to the so-called Jacobi stability of the system. Different from that of the Lyapunov stability that has been studied extensively in the literature, the analysis of the Jacobi stability has been investigated more recently using geometrical concepts and tools. It turns out that the existing work on the Jacobi stability analysis remains theoretical and the problem of algorithmic and symbolic treatment of Jacobi stability analysis has yet to be addressed. In this paper, we initiate our study on the problem for a class of ODE systems of arbitrary dimension and propose two algorithmic schemes using symbolic computation to check whether a nonlinear dynamical system may exhibit Jacobi stability. The first scheme, based on the construction of the complex root structure of a characteristic polynomial and on the method of quantifier elimination, is capable of detecting the existence of the Jacobi stability of the given dynamical system. The second algorithmic scheme exploits the method of semi-algebraic system solving and allows one to determine conditions on the parameters for a given dynamical system to have a prescribed number of Jacobi stable fixed points. Several examples are presented to demonstrate the effectiveness of the proposed algorithmic schemes., Comment: Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation (ISSAC 2024)

This paper investigates the network-assisted full-duplex (NAFD) cell-free millimeter-wave (mmWave) networks, where the distribution of the transmitting access points (T-APs) and receiving access points (R-APs) across distinct geographical locations mitigates cross-link interference, facilitating the attainment of a truly flexible duplex mode. To curtail deployment expenses and power consumption for mmWave band operations, each AP incorporates a hybrid digital-analog structure encompassing precoder/combiner functions. However, this incorporation introduces processing intricacies within channel estimation and precoding/combining design. In this paper, we first present a hybrid multiple-input multiple-output (MIMO) processing framework and derive explicit expressions for both uplink and downlink achievable rates. Then we formulate a power allocation problem to maximize the weighted bidirectional sum rates. To tackle this non-convex problem, we develop a collaborative multi-agent deep reinforcement learning (MADRL) algorithm called multi-agent twin delayed deep deterministic policy gradient (MATD3) for NAFD cell-free mmWave networks. Specifically, given the tightly coupled nature of both uplink and downlink power coefficients in NAFD cell-free mmWave networks, the MATD3 algorithm resolves such coupled conflicts through an interactive learning process between agents and the environment. Finally, the simulation results validate the effectiveness of the proposed channel estimation methods within our hybrid MIMO processing paradigm, and demonstrate that our MATD3 algorithm outperforms both multi-agent deep deterministic policy gradient (MADDPG) and conventional power allocation strategies., Comment: 14 pages, 9 figures, published on Physical Communication

The integration of sensing capabilities into communication systems, by sharing physical resources, has a significant potential for reducing spectrum, hardware, and energy costs while inspiring innovative applications. Cooperative networks, in particular, are expected to enhance sensing services by enlarging the coverage area and enriching sensing measurements, thus improving the service availability and accuracy. This paper proposes a cooperative integrated sensing and communication (ISAC) framework by leveraging information-bearing orthogonal frequency division multiplexing (OFDM) signals transmitted by access points (APs). Specifically, we propose a two-stage scheme for target localization, where communication signals are reused as sensing reference signals based on the system information shared at the central processing unit (CPU). In Stage I, we propose a twodimensional fast Fourier transform (2D-FFT)-based algorithm to measure the ranges of scattered paths induced by targets, through the extraction of delay and Doppler information from the sensing channels between APs. Then, the target locations are estimated in Stage II based on these range measurements. Considering the potential occurrence of ill-conditioned measurements with large error during the extraction of time-frequency information, we propose an efficient algorithm to match the range measurements with the targets while eliminating ill-onditioned measurements, achieving high-accuracy target localization. In addition, based on the transmission configurations defined in the fifth generation (5G) standards, we elucidate the performance trade-offs in both communication and sensing, and extend the proposed sensing scheme for general scenarios. Finally, numerical results confirm the effectiveness of our sensing scheme and the cooperative gain of the ISAC framework.

For a rational parameterization of a curve, it is desirable that its angular speed is as uniform as possible. Hence, given a rational parameterization, one wants to find re-parameterization with better uniformity. One natural way is to use piecewise rational reparameterization. However, it turns out that the piecewise rational reparameterization does not help when the angular speed of the given rational parameterization is zero at some points on the curve. In this paper, we show how to overcome the challenge by using piecewise radical reparameterization., Comment: In Proceedings ADG 2023, arXiv:2401.10725

This paper investigates how to achieve integrated sensing and communication (ISAC) based on a cell-free radio access network (CF-RAN) architecture with a minimum footprint of communication resources. We propose a new passive sensing scheme. The scheme is based on the radio frequency (RF) fingerprint learning of the RF radio unit (RRU) to build an RF fingerprint library of RRUs. The source RRU is identified by comparing the RF fingerprints carried by the signal at the receiver side. The receiver extracts the channel parameters from the signal and estimates the channel environment, thus locating the reflectors in the environment. The proposed scheme can effectively solve the problem of interference between signals in the same time-frequency domain but in different spatial domains when multiple RRUs jointly serve users in CF-RAN architecture. Simulation results show that the proposed passive ISAC scheme can effectively detect reflector location information in the environment without degrading the communication performance., Comment: 11 pages, 6 figures, submitted on 28-Feb-2023, China Communication, Accepted on 14-Sep-2023

In this paper, we combine the network-assisted full-duplex (NAFD) technology and distributed radar sensing to implement integrated sensing and communication (ISAC). The ISAC system features both uplink and downlink remote radio units (RRUs) equipped with communication and sensing capabilities. We evaluate the communication and sensing performance of the system using the sum communication rates and the Cramer-Rao lower bound (CRLB), respectively. We compare the performance of the proposed scheme with other ISAC schemes, the result shows that the proposed scheme can provide more stable sensing and better communication performance. Furthermore, we propose two power allocation algorithms to optimize the communication and sensing performance jointly. One algorithm is based on the deep Q-network (DQN) and the other one is based on the non-dominated sorting genetic algorithm II (NSGA-II). The proposed algorithms provide more feasible solutions and achieve better system performance than the equal power allocation algorithm., Comment: 14 pages, 7 figures,submit to China Communication February 28, 2023, date of major revision July 09, 2023

A future millimeter-wave (mmWave) massive multiple-input and multiple-output (MIMO) system may serve hundreds or thousands of users at the same time; thus, research on multiple access technology is particularly important.Moreover, due to the short-wavelength nature of a mmWave, large-scale arrays are easier to implement than microwaves, while their directivity and sparseness make the physical beamforming effect of precoding more prominent.In consideration of the mmWave angle division multiple access (ADMA) system based on precoding, this paper investigates the influence of the angle distribution on system performance, which is denoted as the angular multiplexing gain.Furthermore, inspired by the above research, we transform the ADMA user grouping problem to maximize the system sum-rate into the inter-user angular spacing equalization problem.Then, the form of the optimal solution for the approximate problem is derived, and the corresponding grouping algorithm is proposed.The simulation results demonstrate that the proposed algorithm performs better than the comparison methods.Finally, a complexity analysis also shows that the proposed algorithm has extremely low complexity., Comment: 12 pages,16 figures

This paper proposes a multi-level cooperative architecture to balance the spectral efficiency and scalability of cell-free massive multiple-input multiple-output (MIMO) systems. In the proposed architecture, spatial expansion units (SEUs) are introduced to avoid a large amount of computation at the access points (APs) and increase the degree of cooperation among APs. We first derive the closed-form expressions of the uplink user achievable rates under multi-level cooperative architecture with maximal ratio combination (MRC) and zero-forcing (ZF) receivers. The accuracy of the closed-form expressions is verified. Moreover, numerical results have demonstrated that the proposed multi-level cooperative architecture achieves a better trade-off between spectral efficiency and scalability than other forms of cell-free massive MIMO architectures., Comment: 5 pages, 3 figures

In this paper, we investigate network-assisted full-duplex (NAFD) cell-free millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems with digital-to-analog converter (DAC) quantization and fronthaul compression. We propose to maximize the weighted uplink and downlink sum rate by jointly optimizing the power allocation of both the transmitting remote antenna units (T-RAUs) and uplink users and the variances of the downlink and uplink fronthaul compression noises. To deal with this challenging problem, we further apply a successive convex approximation (SCA) method to handle the non-convex bidirectional limited-capacity fronthaul constraints. The simulation results verify the convergence of the proposed SCA-based algorithm and analyze the impact of fronthaul capacity and DAC quantization on the spectral efficiency of the NAFD cell-free mmWave massive MIMO systems. Moreover, some insightful conclusions are obtained through the comparisons of spectral efficiency, which shows that NAFD achieves better performance gains than co-time co-frequency full-duplex cloud radio access network (CCFD C-RAN) in the cases of practical limited-resolution DACs. Specifically, their performance gaps with 8-bit DAC quantization are larger than that with 1-bit DAC quantization, which attains a 5.5-fold improvement., Comment: accepted by China Communications

Open radio access network (ORAN) provides an open architecture to implement radio access network (RAN) of the fifth generation (5G) and beyond mobile communications. As a key technology for the evolution to the sixth generation (6G) systems, cell-free massive multiple-input multiple-output (CF-mMIMO) can effectively improve the spectrum efficiency, peak rate and reliability of wireless communication systems. Starting from scalable implementation of CF-mMIMO, we study a cell-free RAN (CF-RAN) under the ORAN architecture. Through theoretical analysis and numerical simulation, we investigate the uplink and downlink spectral efficiencies of CF-mMIMO with the new architecture. We then discuss the implementation issues of CF-RAN under ORAN architecture, including time-frequency synchronization and over-the-air reciprocity calibration, low layer splitting, deployment of ORAN radio units (O-RU), artificial intelligent based user associations. Finally, we present some representative experimental results for the uplink distributed reception and downlink coherent joint transmission of CF-RAN with commercial off-the-shelf O-RUs.

Network-assisted full-duplex (NAFD) distributed massive multiple input multiple output (M-MIMO) enables the in-band full-duplex with existing half-duplex devices at the network level, which exceptionally improves spectral efficiency. This paper analyzes the impact of low-resolution analog-to-digital converters (ADCs) on NAFD distributed M-MIMO and designs an efficient bit allocation algorithm for low-resolution ADCs. The beamforming training mechanism relieves the heavy pilot overhead for channel estimation, which remarkably enhances system performance by guiding the interference cancellation and coherence detection. Furthermore, closed-form expressions for spectral and energy efficiency with low-resolution ADCs are derived. The multi-objective optimization problem (MOOP) for spectral and energy efficiency is solved by the deep Q network and the non-dominated sorting genetic algorithm II. The simulation results corroborate the theoretical derivation and verify the effectiveness of introducing low-resolution ADCs in NAFD distributed M-MIMO systems. Meanwhile, a set of Pareto-optimal solutions for ADC accuracy flexibly provide guidelines for deploying in a practical NAFD distributed M-MIMO system.

Downlink coherent multiuser transmission is an essential technique for cell-free massive multiple-input multiple output (MIMO) systems, and the availability of channel state information (CSI) at the transmitter is a basic requirement. To avoid CSI feedback in a time-division duplex system, the uplink channel parameters should be calibrated to obtain the downlink CSI due to the radio frequency circuit mismatch of the transceiver. In this paper, a design of a reference signal for over-the-air reciprocity calibration is proposed. The frequency domain generated reference signals can make full use of the flexible frame structure of the fifth generation (5G) new radio, which can be completely transparent to commercial off-the-shelf (COTS) remote radio units (RRUs) and commercial user equipments. To further obtain the calibration of multiple RRUs, an interleaved RRU grouping with a genetic algorithm is proposed, and an averaged Argos calibration algorithm is also presented. We develop a cell-free massive MIMO prototype system with COTS RRUs, demonstrate the statistical characteristics of the calibration error and the effectiveness of the calibration algorithm, and evaluate the impact of the calibration delay on the different cooperative transmission schemes.

Sixth-generation (6G) networks are evolving towards new features and order-of-magnitude enhancement of systematic performance metrics compared to the current 5G. In particular, the 6G networks are expected to achieve extreme connectivity performance with Tbps-scale data rate, Kbps/Hz-scale spectral efficiency, and $\mu$s-scale latency. To this end, an original three-layer 6G network architecture is designed to realise uniform full-spectrum cell-free radio access and provide task-centric agile proximate support for diverse applications. The designed architecture is featured by super edge node (SEN) which integrates connectivity, computing, AI, data, etc. On this basis, a technological framework of pervasive multi-level (PML) AI is established in the centralised unit to enable task-centric near-real-time resource allocation and network automation. We then introduce a radio access network (RAN) architecture of full spectrum uniform cell-free networks, which is among the most attractive RAN candidates for 6G TK$\mu$ extreme connectivity. A few most promising key technologies, i.e., cell-free massive MIMO, photonics-assisted Terahertz wireless access and spatiotemporal two-dimensional channel coding are further discussed. A testbed is implemented and extensive trials are conducted to evaluate innovative technologies and methodologies. The proposed 6G network architecture and technological framework demonstrate exciting potentials for full-service and full-scenario applications., Comment: 8 pages, 4 figures, in peer review with IEEE Wireless Communications Magazine

To improve the poor performance of distributed operation and non-scalability of centralized operation in traditional cell-free massive MIMO, we propose a cell-free distributed collaborative (CFDC) massive multiple-input multiple-output (MIMO) system based on a novel two-layer model to take advantages of the distributed cloud-edge-end collaborative architecture in beyond 5G (B5G) internet of things (IoT) environment to provide strong flexibility and scalability. We further ultilize the proposed CFDC massive MIMO system to support the low altitude three-dimensional (3-D) coverage scenario with unmanned aerial vehicles (UAVs), while accounting for 3-D Rician channel estimation, user-centric association and different scalable receiving schemes. Since coexisted UAVs and ground users (GUEs) cause greater interference, we ultilize user-centric association strategy and minimum-mean-square error (MMSE) channel state information (CSI) estimation to obtain the estimated CSI of UAVs and GUEs. Under the CFDC scenarios, scalable receiving schemes as maximum ratio combing (MRC), partial zero-forcing (P-ZF) and partial minimum-mean-square error (P-MMSE) can be performed at edge servers and the closed-form expressions for uplink spectral efficiency (SE) are derived. Based on the derived expressions, we propose an efficient power control algorithm by solving a multi-objective optimization problem (MOOP) between maximizing the average SE of UAVs and GUEs simultaneously with Deep Q-Network (DQN). Numerical results verify the accuracy of the derived closed-form expressions and the effectiveness of the coexisted UAVs and GUEs transmission scheme in CFDC massive MIMO systems. The SE analysis under various system parameters offers numerous flexibilities for system optimization., Comment: The work is further studied and the content of the paper is updated. So, temporarily withdrawn for these reasons

Ultra-reliable low latency communications (uRLLC) is adopted in the fifth generation (5G) mobile networks to better support mission-critical applications that demand high level of reliability and low latency. With the aid of well-established multiple-input multiple-output (MIMO) information theory, uRLLC in the future 6G is expected to provide enhanced capability towards extreme connectivity. Since the latency constraint can be represented equivalently by blocklength, channel coding theory at finite block-length plays an important role in the theoretic analysis of uRLLC. On the basis of Polyanskiy's and Yang's asymptotic results, we first derive the exact close-form expressions for the expectation and variance of channel dispersion. Then, the bound of average maximal achievable rate is given for massive MIMO systems in ideal independent and identically distributed fading channels. This is the study to reveal the underlying connections among the fundamental parameters in MIMO transmissions in a concise and complete close-form formula. Most importantly, the inversely proportional law observed therein implies that the latency can be further reduced at expense of spatial degrees of freedom.

This paper studies the number of limit cycles that may bifurcate from an equilibrium of an autonomous system of differential equations. The system in question is assumed to be of dimension $n$, have a zero-Hopf equilibrium at the origin, and consist only of homogeneous terms of order $m$. Denote by $H_k(n,m)$ the maximum number of limit cycles of the system that can be detected by using the averaging method of order $k$. We prove that $H_1(n,m)\leq(m-1)\cdot m^{n-2}$ and $H_k(n,m)\leq(km)^{n-1}$ for generic $n\geq3$, $m\geq2$ and $k>1$. The exact numbers of $H_k(n,m)$ or tight bounds on the numbers are determined by computing the mixed volumes of some polynomial systems obtained from the averaged functions. Based on symbolic and algebraic computation, a general and algorithmic approach is proposed to derive sufficient conditions for a given differential system to have a prescribed number of limit cycles. The effectiveness of the proposed approach is illustrated by a family of third-order differential equations and by a four-dimensional hyperchaotic differential system.

In this paper, we consider a joint unicast and multi-group multicast cell-free distributed massive multiple-input multiple-output (MIMO) system, while accounting for co-pilot assignment strategy based channel estimation, pilot contamination and different precoding schemes. Under the co-pilot assignment strategy, we derive the minimum-mean-square error (MMSE) channel state information (CSI) estimation for unicast and multicast users. Given the acquired CSI, the closed-form expressions for downlink achievable rates with maximum ratio transmission (MRT), zero-forcing (ZF) and MMSE beamforming are derived. Based on these expressions, we propose an efficient power allocation scheme by solving a multi-objective optimization problem (MOOP) between maximizing the minimum spectral efficiency (SE) of multicast users and maximizing the average SE of unicast users with non-dominated sorting genetic algorithm II (NSGA-II). Moreover, the MOOP is converted into a deep learning (DL) problem and solved by an unsupervised learning method to further promote computational efficiency. Numerical results verify the accuracy of the derived closed-form expressions and the effectiveness of the joint unicast and multigroup multicast transmission scheme in cell-free distributed massive MIMO systems. The SE analysis under various system parameters and the trade-off regions between these two conflicting optimization objectives offers numerous flexibilities for system optimization.