Pilot Sequence Length Research Articles

Pilot and data power optimization problems in multiple Aerial Relay Stations cell‐free communication systems

SummaryA cell‐free (CF) technology and unmanned aerial vehicles (UAVs) acting as aerial relay stations (ARSs) are gradually viewed as viable technologies for usage in sixth‐generation (6G) wireless networks owing to their outstanding advantages, such as large coverage, uniform service quality, huge connections, flexible deployment in all geographical areas, and high line‐of‐sight (LoS) probability. As a result, the combination of the CF model and UAVs is suitable for densely populated urban areas, shopping malls, festivals, and locations with complex geography. Furthermore, the integration of the CF model and UAV communication can improve system quality and is considered an entirely new research direction as there is no comprehensive investigation of this combined model. In this study, we investigate the quality of the multi‐ARS CF communication system, where ARSs are equipped with multiple antennas and stochastic distribution within a specific region to simultaneously serve numerous ground users. We establish a closed‐form formulation for the uplink and downlink throughput of individual users by using the matched filtering method and conjugate beamforming technology, respectively. Moreover, we propose a novel method to optimize the pilot and data transmission power coefficients for improving channel estimation and increasing throughput per user, thereby ensuring a high quality of service. The power optimization method is executed via the successive convex approximation (SCA) method, second‐order cone program (SOCP), and linear program. We evaluate system performance according to the cumulative distribution function (CDF) of user throughput based on various parameters, such as the number of users, the number of ARSs, and the length of pilot sequences. The analytical findings also reveal that the system with the proposed power optimization method is always superior to the system without the proposed method in both uplink and downlink.

Developing Uplink Power Optimization and ARS Selection Algorithm for Multi-ARS Small Cell Communication System

Small Cell (SC) models and unmanned aerial vehicles (UAVs) acting as aerial relay stations (ARSs) are both promising advancements in the development of upcoming wireless networks that contribute significantly to improving the overall service quality. In this work, we rely on the Multi-ARS Cell-Free (CF) model, where a large number of ARS coordinated by the ground base station (GBS) and cooperate to serve a large number of users within the same frequency and time resources, to develop the uplink of a multi-ARS SC system, in which each user is served by only one ARS. The time division duplex (TDD) mechanism is used for communication protocol, and the Minimum Mean Square Error (MMSE) method is implemented to estimate the uplink channel. We derive an closed-form expression for uplink user throughput. In addition, we introduce the ARS selection method based on channel conditions and propose the Bisection algorithm to optimize uplink power. The system performance is evaluated by the cumulative distribution function (CDF) of user throughput according to different parameters, such as changing the number of ARS, the number of users, the number of antennas, and the length of pilot sequences with/without power optimization. The results reveal that the ARS selection method is effectively resolved to reduce complexity and improve the practicality of the proposed system, and the power optimization problem for better throughput is non-optimization.

Channel estimation using hybrid optimizer based recurrent neural network long short term memory for MIMO communications in 5G network

In the fifth-generation (5G) networks, multiple input multiple-output (MIMO) systems are further developed to enhance transmission reliability. However, channel estimation is one of the major challenges which needs focus for improved data transmission in MIMO. Although efficient estimation techniques have been recently proposed, estimation accuracy needs to be upgraded further. Hence, an optimized Recurrent Neural Network-Long Short-Term Memory (RNN-LSTM) network is presented in this paper for channel estimation. At first, history of channel responses of pilot block is collected or estimated using Least Square (LS) channel estimation method. Using these collected channel responses, the proposed RNN-LSTM is trained where weight parameters are chosen optimally using hybrid Particle Swarm Optimization (PSO)-Adam optimizer. Using the trained PSO-Adam optimizer based RNN-LSTM, the current channel response is predicted or estimated. The performance of the proposed channel estimation scheme is analysed by varying pilot sequence length and number of antennas to evaluate the metrics Bit Error Rate (BER) and Mean Square Error (MSE). Complexity analysis of the proposed scheme is compared with standard estimators like LS and Minimum Mean-Square Error (MMSE).

Performance Analysis of Scalable User-Centric HC-RAN Over Rician Fading Channels

In this paper, we analyze the uplink performance of a scalable user-centric heterogeneous cloud-radio access network (HC-RAN) implemented by using dynamic cooperative clustering (DCC) framework over a Rician fading channel with phase shifts. This channel describes various practical aspects, such as a deterministic line of sight (LoS) component and random non-LoS (N-LoS) components. To account for the phase shifts due to user mobility, the phase of the LoS component is modeled as a uniformly distributed random variable. We assume that phase information is available at each remote radio head (RRH). We derived the phase aware-minimum mean square error (PA-MMSE) and phase unaware Linear-MMSE estimators and obtained the channel state information (CSI). We derived a closed-form expression for the achievable spectral efficiency (SE) to evaluate the system performance with both estimators. To address the effect of coherent interference in the ultra-dense networks, we developed a two-layer decoding scheme in uplink in which maximum ratio (MR) combining is performed at the RRH and large-scale fading decoding is performed at the base-band unit (BBU) pool. Based on the obtained results, the proposed method enhanced the uplink performance in an ultra-dense scenario. It is validated by comparing it with the simulation results. Moreover, the performance loss caused by the lack of phase knowledge will depend on the pilot sequence length.

QoE Driven VR 360° Video Massive MIMO Transmission

Massive multiple-input and multiple-output (MIMO) enables ultra-high throughput and low latency for tile-based adaptive virtual reality (VR) 360° video transmission in wireless network. In this paper, we consider a massive MIMO system where multiple users in a single-cell theater watch an identical VR 360° video. Based on tile prediction, base station (BS) deliveries the tiles in predicted field of view (FoV) to users. By introducing practical supplementary transmission for missing tiles and unacceptable VR sickness, we propose the first stable transmission scheme for VR video. we formulate an integer non-linear programming (INLP) problem to maximize users’ average quality of experience (QoE) score. Moreover, we derive the achievable spectral efficiency (SE) expression of predictive tile groups and the approximately achievable SE expression of missing tile groups, respectively. Analytically, the overall throughput is related to the number of tile groups and the length of pilot sequences. By exploiting the relationship between the structure of viewport tiles and SE expression, we propose a multi-lattice multi-stream grouping method aimed at improving the overall throughput for VR video transmission. Moreover, we analyze the relationship between QoE objective and number of predictive tile. We transform the original INLP problem into an integer linear programming problem by setting the predictive tiles groups as some constants. With variable relaxation and recovery, we obtain the optimal average QoE. Extensive simulation results validate that the proposed algorithm effectively improves QoE.

Deep Learning for Massive MIMO With 1-Bit ADCs: When More Antennas Need Fewer Pilots

This letter considers uplink massive MIMO systems with 1-bit analog-to-digital converters (ADCs) and develops a deep-learning based channel estimation framework. In this framework, the prior channel estimation observations and deep neural networks are leveraged to learn the non-trivial mapping from quantized received measurements to channels. For that, we derive the sufficient length and structure of the pilot sequence to guarantee the existence of this mapping function. This leads to the interesting, and counter-intuitive, observation that when more base-station antennas are employed, our proposed deep learning approach achieves better channel estimation performance, for the same pilot sequence length. Equivalently, for the same channel estimation performance, this means that when more antennas are employed, fewer pilots are required. This observation is also analytically proved for some special channel models. Simulation results confirm our observations and show that more antennas lead to better channel estimation in terms of the normalized mean squared error and the receive signal-to-noise ratio per antenna.

Spectral efficiency analysis for massive MIMO systems in Ricean fading channels

This study focuses on the spectral efficiency of massive multiple-input–multiple-output (MIMO) systems over Ricean fading channels. Assuming the channel reciprocity of uplink and downlink transmissions, the channels are estimated through uplink pilot sequence with least minimum mean square error (MMSE) estimator, which facilitates the investigation of equivalent channel model. With the equivalent channel model, adopting joint MMSE receiver, the uplilnk achievable sum-rate is studied, and finally, the asymptotic expression of spectral efficiency is obtained. Based on the proposed asymptotic spectral efficiency, numerical results give some guidelines about system parameters design: the authors should choose a proper length of the block fading channels to reduce the effect of pilot overhead, and an optimal length of pilot sequence always exists to guarantee a satisfying system performance in terms of spectral efficiency. Furthermore, the simulation results show that when fixing the number of users, shrinking the cell serving area and increasing the number of antennas can improve the system performance.

Channel estimation with Bayesian framework based on compressed sensing algorithm in multimedia transmission system

With the emergence of Wireless multimedia transmission system, the distribution of multimedia contents has now become a reality. To solve the problem of stability in the process of transmission, this paper proposes an improved channel estimation with Bayesian framework based on compressed sensing algorithm in multimedia transmission system. The algorithm uses the sparse characteristics of the channel and can reduce the pilot sequence length under the same conditions. Due to the high complexity of the support agnostic Bayesian matching pursuit algorithm, our algorithm improves the support set, which proposed Expectation Prune Matching Pursuit algorithm in the paper. At each sparsity level of the channel, an expanded support set is given by adding some positions corresponding to the atoms that have a larger inner product value with the current residual signal. Then the best support set is obtained by removing the wrong positions and adopting the idea of Bayesian estimation algorithm in the expanded support set. The estimated channel and the relative probability of the best support set at each sparse level are calculated. Finally, the expectation of the channel is calculated and regarded as the estimation of the channel. Compared with comparison algorithm in the error and bit error rate under different SNR conditions, our proposed algorithm can reduce the computational complexity while maintaining the estimation accuracy.

Performance Analysis of Massive MIMO Two-Way Relay Networks With Pilot Contamination, Imperfect CSI, and Antenna Correlation

We consider a multicell two-way relay network consisting of single-antenna user nodes and amplify-and-forward relay nodes having very large antenna arrays. We investigate the combined impact of co-channel interference (CCI), imperfect channel state information (CSI), pilot contamination, and the antenna correlation at the massive multiple-input multiple-output (MIMO) node. By using a large number of antennas at the relay, we can completely mitigate the effect of CCI. However, the effects of imperfect CSI and pilot contamination degrade the performance even with a large antenna array. Yet, the use of massive MIMO allows power scaling at the user nodes and relay, and thus, even with channel imperfections, the benefits of employing a massive-MIMO-enabled relay on transmit power savings are significant. Furthermore, we derive closed-form approximations for the sum rate when CCI and pilot contamination are absent and CSI is perfect. This result helps to decide the required number of relay antennas to obtain a certain percentage of the asymptotic sum rate. Also, our analysis of antenna correlation shows that it can be mitigated by using a large antenna array. We also find the optimal pilot sequence length to maximize the sum rate of the system.

Spectral and Energy Efficiency of Superimposed Pilots in Uplink Massive MIMO

Next-generation wireless networks aim at providing substantial improvements in spectral efficiency (SE) and energy efficiency (EE). Massive MIMO has been proved to be a viable technology to achieve these goals by spatially multiplexing several users using many base station (BS) antennas. A potential limitation of massive MIMO in multicell systems is pilot contamination, which arises in the channel estimation process from the interference caused by reusing pilots in neighboring cells. A standard method to reduce pilot contamination, known as regular pilot (RP), is to adjust the length of pilot sequences while transmitting data and pilot symbols disjointly. An alternative method, called superimposed pilot (SP), sends a superposition of pilot and data symbols. This allows use of longer pilots which, in turn, reduces pilot contamination. We consider the uplink of a multicell massive MIMO network, with i.i.d. Rayleigh fading channels, using maximum ratio combining and compare RP and SP in terms of SE and EE. To this end, we derive rigorous closed-form achievable rates with SP under a practical random BS deployment. We prove that the reduction of pilot contamination with SP is outweighed by the additional coherent and non-coherent interference. Numerical results show that when both methods are optimized, RP achieves comparable SE and EE to SP in practical scenarios.

Hybrid Beamforming via the Kronecker Decomposition for the Millimeter-Wave Massive MIMO Systems

Despite its promising performance gain, the realization of mmWave massive MIMO still faces several practical challenges. In particular, implementing massive MIMO in the digital domain requires hundreds of RF chains matching the number of antennas. Furthermore, designing these components to operate at the mmWave frequencies is challenging and costly. These motivated the recent development of hybrid-beamforming where MIMO processing is divided for separate implementation in the analog and digital domains, called the analog and digital beamforming, respectively. Analog beamforming using a phase array introduces uni-modulus constraints on the beamforming coefficients, rendering the conventional MIMO techniques unsuitable and call for new designs. In this paper, we present a systematic design framework for hybrid beamforming for multi-cell multiuser massive MIMO systems over mmWave channels characterized by sparse propagation paths. The framework relies on the decomposition of analog beamforming vectors and path observation vectors into Kronecker products of factors being uni-modulus vectors. Exploiting properties of Kronecker mixed products, different factors of the analog beamformer are designed for either nulling interference paths or coherently combining data paths. Furthermore, a channel estimation scheme is designed for enabling the proposed hybrid beamforming. The scheme estimates the AoA of data and interference paths by analog beam scanning and data-path gains by analog beam steering. The performance of the channel estimation scheme is analyzed. In particular, the AoA spectrum resulting from beam scanning, which displays the magnitude distribution of paths over the AoA range, is derived in closed-form. It is shown that the inter-cell interference level diminishes inversely with the array size, the square root of pilot sequence length and the spatial separation between paths.

Multicell Multiway Massive MIMO Relay Networks

A generic performance analysis framework is developed for multicell amplify-and-forward (AF) multiway massive multiple-input multiple-output (MIMO) relay networks. The detrimental effects of imperfect channel state information (CSI), including channel estimation errors and outdated/delayed CSI for multicell massive MIMO AF multiway relay networks, are investigated. Thereby, for the first time in the open literature in the context of massive MIMO relay networks, the cumulative detrimental effects of pilot contamination and channel aging caused by the reuse of nonorthogonal pilot sequences and relative movements of user nodes, respectively, are quantified. The asymptotic signal-to-interference-plus-noise ratio and the achievable spectral efficiency expressions corresponding to three transmit power scaling laws at the user nodes and relay are derived whenever the number of antennas at the relay is substantially higher than the number of user nodes. The asymptotic performance analysis is generic in the sense that the individual effects of the practical transmission impairments, such as cochannel interference, pilot contamination, and channel aging, can be decomposed. The average symbol error rate (SER) and asymptotic SER are derived in closed form. The optimal pilot sequence length, which maximizes the achievable spectral efficiency, is derived in closed form. Our asymptotic analysis for the perfect CSI case reveals that the detrimental effects of cochannel interference can be asymptotically mitigated. Nevertheless, the performance degradation caused due to the cumulative effects of pilot contamination and channel aging cannot be mitigated, even in the limit of infinitely many relay antennas.

Space-Time Coding for Aeronautical Telemetry: Part I—Estimators

This paper derives and analyzes the estimators required for detection and decoding of Alamouti-encoded-shaped offset QPSK version TG (SOQPSK-TG). The joint maximum likelihood (ML) estimators for the frequency offset, channel delays, and channel gains are derived and analyzed. As a complexity-reducing technique, a sequential version of the ML estimators is developed. The Cramer–Rao bound for the parameters is derived and used to analyze the performance of the estimators to determine pilot sequence length. The complexity of the frequency estimator is reduced by applying the Zoom FFT algorithm in the coarse search. The complexity of the channel delay estimator was reduced by developing a novel version of the simplex search algorithm that operated on a discrete two-dimensional grid. These estimation algorithms were implemented in a prototype demodulator that was field tested at Edwards AFB.

Pilot Contamination Reduction in Multi-cell TDD Systems with Very Large MIMO Arrays

Very large multiple-input multiple-output (MIMO) technology has a potential of significantly improving the system performance of multi-cell time-division duplexing (TDD) networks, but in practice it is limited by pilot contamination. Different from the traditional channel estimation mean square error (MSE) expressions, the expressions that we derived have algebraic form, which no longer need hard matrix inversion as M, the number of the base station (BS) antennas, increasing. From them, we also found that the average transmitted power and length of training sequence almost does not help in enhancing the performance of MSE as $$M\rightarrow \infty $$ . Based on this, two pilot contamination reduction methods for the very large MIMO multi-cell TDD system were proposed. One is realized by grouping all the cells into two categories, using orthogonal pilots between these two types of cells or aligning the uplink pilot time slot of the cells in one category with the downlink data time slot of those cells in the neighboring categories. The other is to find the optimal division of pilot sequence length and the set of all users’s pilot transmission slots allocation through BSs’s coordination. The effectiveness of our proposed methods are verified via both theoretical analysis and numerical results.

Decision Aided Uplink Compressive Channel Estimation for Massive MIMO Systems

Thank to the observation that in massive multi-input multi-output systems, the channels associated with different base station antennas may share common sparse support, the significant path delays can be accurately captured by only few pilots, leading to a reduction of pilot overhead. However, when the number of pilots is small, the path gains can not be accurately estimated and this limits the system performance. To solve this problem, in this paper we propose a decision aided compressive sensing based channel estimation scheme, which utilizes the decoded data to refine the channel estimation. This scheme can effectively improve the channel estimation without increasing the length of pilot sequence, which is confirmed by both analyses and simulation results.

Multi-Cell Multiuser Massive MIMO Networks: User Capacity Analysis and Pilot Design

We propose a novel pilot sequence design to mitigate pilot contamination in multi-cell multiuser massive multiple-input multiple-output networks. Our proposed design generates pilot sequences in the multi-cell network and devises power allocation at base stations (BSs) for downlink transmission. The pilot sequences together with the power allocation ensure that the user capacity of the network is achieved and the pre-defined signal-to-interference-plus-noise ratio (SINR) requirements of all users are met. To realize our design, we first derive new closed-form expressions for the user capacity and the user capacity region. Built upon these expressions, we then develop a new algorithm to obtain the required pilot sequences and power allocation. We further determine the minimum number of antennas required at BSs to achieve certain SINR requirements of all users. Numerical results are presented to corroborate our analysis and to examine the impact of key parameters, such as the pilot sequence length and the total number of users, on the network performance. A pivotal conclusion is reached that our design achieves a larger user capacity region than the existing designs and needs less antennas at the BS to fulfill the pre-defined SINR requirements of all users in the network than the existing designs.

Joint Parameter Selection for Massive MIMO: An Energy-Efficient Perspective

In this paper, the energy-efficient massive MIMO design problem is investigated in both single-cell and multi-cell scenarios with the aim of selecting appropriate parameters to maximize the overall system energy utilization. To this end, a more realistic parameter selection model is established by considering the channel estimation error and pilot contamination (PC). In the proposed model, we not only optimize the number of antennas, the number of users, and the transmission power to balance the improved radiated energy efficiency and the increased circuit power consumption, but also optimize the length of pilot sequences to make a desired trade-off between improving channel estimation accuracy and reserving more resources for data transmission. We first focus on the single-cell scenario, and strictly prove the quasi-concavity of the objective function in each dimension after suitable variable transformation, based on which an alternative optimization plus bisection searching (AO-BS) algorithm is proposed to solve the problem quickly. Then, the research is extended into the multi-cell scenario by increasingly considering PC and multi-cell interference. Since PC is related to the relative pilot length, i.e., the ratio between the length of pilot sequences and the number of users, the formulated problem is difficult to deal with directly. For effective solving, we divide the original problem into multiple subproblems according to the setting of pilot reusing factor, and employ the proposed AO-BS algorithm to solve each subproblem. Through numerical simulations, it is observed that the proposed AO-BS algorithm converges rapidly and is almost able to achieve the globally optimal solution. Meanwhile, from the perspective of energy efficiency maximization, massive MIMO is more preferable in the case of large cell coverage, and selecting a large relative pilot length is beneficial, always resulting in higher energy utilization in both single-cell and multi-cell scenarios.

Spectral-Energy Efficiency Tradeoff in Relay-Aided Massive MIMO Cellular Networks With Pilot Contamination

This paper concerns with a relay-aided massive multiple input multiple output (MIMO) cellular network. The exact closed-form expressions of both spectral efficiency (SE) and energy efficiency (EE) are obtained for downlink single-cell multi-user multi-relay massive MIMO transmission in the pilot-contaminated regime, where the number of users is larger than the pilot sequence length. Based on the theoretical results of SE and EE, we investigate the effects of some system parameters [such as number of antennas at the base station (BS), transmit power at the BS, and transmit power of each relay station (RS)] on system performance, and achieve the tradeoff between SE and EE by power control. Specifically, the tradeoff problem is solved by joint optimization over transmit power $P$ of the BS and transmit power $p_{r}$ of each RS, so as to maximize EE while satisfying the SE requirement. With the proposition that EE function is strictly quasi-concave with either $P$ or $p_{r}$ , we propose two optimization methods: 1-D searching and alternate optimization. Comparatively, the former achieves a better performance, while the latter has a lower complexity. Simulation results validate the effectiveness of the two methods.

Pilot Contamination Mitigation via a Novel Time-Shift Pilot Scheme in Large-Scale Multicell Multiuser MIMO Systems

We propose a novel time-shift pilot scheme to mitigate the pilot contamination in large-scale multicell multiuser MIMO (LS-MIMO) systems. In the proposed scheme, the length of the uplink training pilot sequence is equal to the cell number; that is to say, the same pilot sequence is used within a cell, while for different cells, pilot sequences are mutually orthogonal. Moreover, users within a cell transmit the same pilot sequence in a time-shift manner during the channel estimation stage and in this way all user terminals’ channel state information can be estimated without contamination. The asymptotic channel orthogonality is studied in the LS-MIMO system, with which the mutual interference among cells caused by data and pilot sequences can be cancelled with the successive interference cancellation (SIC) method. We explore the superiority of the proposed scheme in channel coefficient estimation, uplink data detection, and downlink data transmission steps. Theoretical analysis and simulation results demonstrate that the proposed time-shift pilot design can alleviate the pilot contamination problem and improve the performance of the considered system significantly compared with the popular orthogonal pilots.

Energy-efficient beamforming for two-tier massive MIMO downlink

Heterogeneous networks (HetNets) consisting of macro cells with very large antenna arrays and a secondary tier of small cells with a few antennas each can well tackle the contradiction of large coverage of the network and high data rate at the hot spots. However, it is not permissible to assign orthogonal pilot sequences for all the supported users due to the large number. Hence, we propose a pilot reduction scheme based on the heterogeneous system configurations and the unique topology of this HetNet. The reusing of pilot sequences causes the presence of the contaminated channel state information (CSI) and results in receivers' Quality of Service (QoS) outage. With the contaminated CSI, we provide an energy-efficient beamforming based on minimizing the total power consumption while keeping the QoS constraints satisfied and restricting the QoS outage probability below a given specification. By applying the approach of Bernstein approximation and semi-definite relaxation, we transform the original intractable chance constrained program to a convex problem conservatively. Numerical results show that the average power consumption of the proposed beamforming for our pilot reduction scheme is close to that of the perfect CSI case. Since our scheme will greatly compress the length of pilot sequence especially for those highly densified network with large number of small cells, it will be crucially helpful to put such two-tier massive multiple-input and multiple-output (MIMO) systems into practice.