Non-orthogonal Pilot Research Articles

Hybrid orthogonal and non-orthogonal pilot distribution based channel estimation in massive MIMO system

How to obtain accurate channel state information (CSI) at the transmitter with less pilot overhead for frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) system is a challenging issue due to the large number of antennas. To reduce the overwhelming pilot overhead, a hybrid orthogonal and non-orthogonal pilot distribution at the base station (BS), which is a generalization of the existing pilot distribution scheme, is proposed by exploiting the common sparsity of channel due to the compact antenna arrangement. Then the block sparsity for antennas with hybrid pilot distribution is derived respectively and can be used to obtain channel impulse response. By employing the theoretical analysis of block sparse recovery, the total coherence criterion is proposed to optimize the sensing matrix composed by orthogonal pilots. Due to the huge complexity of optimal pilot acquisition, a genetic algorithm based pilot allocation (GAPA) algorithm is proposed to acquire optimal pilot distribution locations with fast convergence. Furthermore, the Cramer Rao lower bound is derived for non-orthogonal pilot-based channel estimation and can be asymptotically approached by the prior support set, especially when the optimized pilot is employed.

Non-Orthogonal Pilot Designs for Joint Channel Estimation and Collision Detection in Grant-Free Access Systems

In this paper, we consider a densely deployed phantom cell system providing a low latency network for massive connectivity. Non-orthogonal pilot designs serve as a promising solution to support a large number of users, but fast collision detection at the receiver is needed for low latency networks. Recently, a nice solution based on an on–off type non-orthogonal pilot design with collision detection capability has been proposed. It can serve more users than the orthogonal pilot design but at the cost of degraded channel estimation performance compared to the orthogonal optimum pilot design. We propose a new non-orthogonal pilot design with collision detection capability and improved channel estimation performance. An optimum threshold-based detection criterion is developed. We further show that a dynamically calculated optimum threshold-based detection outperforms a fixed threshold-based detection. Next, we investigate non-orthogonal pilot designs for fractional bandwidth allocation. We propose two new non-orthogonal pilot designs for physical resource block based resource allocation. Both of the new designs support fast collision detection at the receiver. Performance evaluation results show that the proposed schemes provide equivalent or better channel estimation performance and support much more users than the orthogonal pilots defined in the current 4G standards. Finally, we explore sparse channel estimation with compressed sensing technique. We prove several propositions regarding compressed sensing based estimation performance. Using these propositions, two novel orthogonal pilot designs are developed for sparse channel estimation with optimized performances. Finally, utilizing these orthogonal pilot sets, we propose a non-orthogonal pilot design with collision detection capability for sparse channel estimation.

Eradication of pilot contamination and zero forcing precoding in the multi‐cell TDD massive MIMO systems

In massive multiple-input multiple-output (M-MIMO) systems, the base station (BS) estimates the downlink and uplink channels using the uplink pilot training in conjunction with channel reciprocity property of time division duplex (TDD) operation. However, this channel estimation is contaminated due to the use of non-orthogonal pilot sequences for the uplink training in neighbouring cells that results in inter-cell interference. This study proposes an effective pilot contamination elimination scheme along with zero forcing precoding for multi-cell TDD M-MIMO systems. In the proposed scheme, each BS is assigned with a specific orthogonal variable spreading factor (OVSF) code row and a set of Zadoff–Chu (ZC) sequences are used for uplink pilot training. Then, the set of ZC sequences is multiplied element-wise at each BS with its OVSF code row to generate the orthogonality among the pilot sequences across the neighbouring cells. The proposed method can promise uncontaminated channel estimation and interference free downlink transmission without requiring the knowledge of the channels’ second-order statistics and without increasing the training overhead by a factor equal to the number of interfering cells. The simulation results authenticate the effectiveness and superiority of the proposed scheme over other schemes.

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.

Artificial Noise-Aided Physical Layer Security in Underlay Cognitive Massive MIMO Systems with Pilot Contamination

In this paper, a secure communication model for cognitive multi-user massive multiple-input multiple-output (MIMO) systems with underlay spectrum sharing is investigated. A secondary (cognitive) multi-user massive MIMO system is operated by using underlay spectrum sharing within a primary (licensed) multi-user massive MIMO system. A passive multi-antenna eavesdropper is assumed to be eavesdropping upon either the primary or secondary confidential transmissions. To this end, a physical layer security strategy is provisioned for the primary and secondary transmissions via artificial noise (AN) generation at the primary base-station (PBS) and zero-forcing precoders. Specifically, the precoders are constructed by using the channel estimates with pilot contamination. In order to degrade the interception of confidential transmissions at the eavesdropper, the AN sequences are transmitted at the PBS by exploiting the excess degrees-of-freedom offered by its massive antenna array and by using random AN shaping matrices. The channel estimates at the PBS and secondary base-station (SBS) are obtained by using non-orthogonal pilot sequences transmitted by the primary user nodes (PUs) and secondary user nodes (SUs), respectively. Hence, these channel estimates are affected by intra-cell pilot contamination. In this context, the detrimental effects of intra-cell pilot contamination and channel estimation errors for physical layer secure communication are investigated. For this system set-up, the average and asymptotic achievable secrecy rate expressions are derived in closed-form. Specifically, these performance metrics are studied for imperfect channel state information (CSI) and for perfect CSI, and thereby, the secrecy rate degradation due to inaccurate channel knowledge and intra-cell pilot contamination is quantified. Our analysis reveals that a physical layer secure communication can be provisioned for both primary and secondary massive MIMO systems even with the channel estimation errors and pilot contamination.

Optimal Semi-Persistent Uplink Scheduling Policy for Large-Scale Antenna Systems

In this paper, the uplink semi-persistent scheduling policy problem of minimizing network latency is considered for a training-based large-scale antenna system employing two simple linear receivers, a maximum ratio combiner and a zero-forcing receiver, while satisfying each user’s reliability and latency constraints under an energy constraint. The network latency is defined as the air-time requested either to serve all users with a minimum quality-of-service, including reliability constraints and minimum throughput levels, or to maximize the spectral efficiency. Optimal non-orthogonal pilots are used to decrease the network latency. An optimization algorithm for determining the latency-optimal uplink scheduling policy using binary-integer programming (BIP) with an exponential-time complexity is proposed. In addition, it is proven that a linear programming relaxation of the BIP can provide an optimal solution with a polynomial-time complexity. Numerical simulations demonstrate that the proposed scheduling policy can provide several times lower network latency in realistic environments than conventional policies. The proposed optimal semi-persistent scheduling policy provides critical guidelines for designing 5G and future cellular systems, particularly for their ultra-reliable low-latency communication services.

Non-orthogonal pilot pattern for sparse channel estimation in large-scale MIMO-OFDM system

From the perspective of compressed sensing (CS) theory, the channel estimation problem in large-scale multiple input multiple output (MIMO)-orthogonal frequency division multiplexing (OFDM) system is investigated. According to the theory, the smaller mutual coherence the reconstruction matrix has, the higher success probability the estimation can obtain. Aiming to design a pilot that can make the system reconstruction matrix having the smallest mutual coherence, this paper proposes a low complexity joint algorithm and obtains a kind of non-orthogonal pilot pattern. Simulation results show that compared with the conventional orthogonal pilot pattern, applying the proposed pattern in the CS channel estimation can obtain the better normalized mean square error performance. Moreover, the bit error rate performance of the large-scale MIMO-OFDM system is also improved.

Structured Compressive Sensing-Based Spatio-Temporal Joint Channel Estimation for FDD Massive MIMO

Massive MIMO is a promising technique for future 5G communications due to its high spectrum and energy efficiency. To realize its potential performance gain, accurate channel estimation is essential. However, due to massive number of antennas at the base station (BS), the pilot overhead required by conventional channel estimation schemes will be unaffordable, especially for frequency division duplex (FDD) massive MIMO. To overcome this problem, we propose a structured compressive sensing (SCS)-based spatio-temporal joint channel estimation scheme to reduce the required pilot overhead, whereby the spatio-temporal common sparsity of delay-domain MIMO channels is leveraged. Particularly, we first propose the non-orthogonal pilots at the BS under the framework of CS theory to reduce the required pilot overhead. Then, an adaptive structured subspace pursuit (ASSP) algorithm at the user is proposed to jointly estimate channels associated with multiple OFDM symbols from the limited number of pilots, whereby the spatio-temporal common sparsity of MIMO channels is exploited to improve the channel estimation accuracy. Moreover, by exploiting the temporal channel correlation, we propose a space-time adaptive pilot scheme to further reduce the pilot overhead. Additionally, we discuss the proposed channel estimation scheme in multi-cell scenario. Simulation results demonstrate that the proposed scheme can accurately estimate channels with the reduced pilot overhead, and it is capable of approaching the optimal oracle least squares estimator.

A Comprehensive Survey of Pilot Contamination in Massive MIMO—5G System

Massive MIMO has been recognized as a promising technology to meet the demand for higher data capacity for mobile networks in 2020 and beyond. Although promising, each base station needs accurate estimation of the channel state information (CSI), either through feedback or channel reciprocity schemes in order to achieve the benefits of massive MIMO in practice. Time division duplex (TDD) has been suggested as a better mode to acquire timely CSI in massive MIMO systems. The use of non-orthogonal pilot schemes, proposed for channel estimation in multi-cell TDD networks, is considered as a major source of pilot contamination in the literature due to the limitations of coherence time. Given the importance of pilot contamination in massive MIMO systems, we provide an extensive survey on pilot contamination, and identify other possible sources of pilot contamination, which include hardware impairment and non-reciprocal transceivers. We review established theories that have analyzed the effect of pilot contamination on the performance of massive MIMO systems, particularly on achievable rates. Next, we categorize the different proposed mitigation techniques for pilot contamination using the following taxonomy: pilot-based approach and subspace-based approach. Finally, we highlight the open issues, such as training overhead, deployment scenario, computational complexity, use of channel reciprocity, and conclude with broader perspective and a look at future trends in pilot contamination in massive MIMO systems.

Joint Transceiver Design for Incremental Channel Estimation in Distributed MIMO Systems

When nonorthogonal pilot sequences are used in cellular systems, channel estimation would be impaired by intercell interference. To tackle this problem, we exploit the slowly varying characteristics of some special channel statistics (large-scale fading and spatial correlation) for incremental channel estimation. By using the block coordinate descent (BCD) method, a joint design of pilot power allocation at the transmitter and spatial filtering at the receiver in a multicell distributed multiple-input multiple-output (D-MIMO) system is proposed, with the demonstration of its convergence. Simulation results illustrate the superiority and validity of the proposed joint transceiver design.

Wireless Information and Power Transfer in Multiway Massive MIMO Relay Networks

Simultaneous wireless information and power transfer techniques for multiway massive multiple-input multiple-output (MIMO) relay networks are investigated. By using two practically viable relay receiver designs, namely 1) the power splitting receiver and 2) the time switching receiver, asymptotic signal-to-interference-plus-noise ratio (SINR) expressions are derived for an unlimited number of antennas at the relay. These asymptotic SINRs are then used to derive asymptotic symmetric sum rate expressions in closed form. Notably, these asymptotic SINRs and sum rates become independent of radio frequency-to-direct current (RF-to-DC) conversion efficiency in the limit of infinitely many relay antennas. Moreover, tight average sum rate approximations are derived in closed form for finitely many relay antennas. The fundamental tradeoff between the harvested energy and the sum rate is quantified for both relay receiver structures. Notably, the detrimental impact of imperfect channel state information (CSI) on the MIMO detector/precoder is investigated, and thereby, the performance degradation caused by pilot contamination, which is the residual interference due to nonorthogonal pilot sequence usage in adjacent/cochannel systems, is quantified. The presence of cochannel interference (CCI) can be exploited to be beneficial for energy harvesting at the relay, and consequently, the asymptotic harvested energy is an increasing function of the number of cochannel interferers. Notably, in the genie-aided perfect CSI case, the detrimental impact of CCI for signal decoding can be cancelled completely whenever the number of relay antennas grows without bound. Nevertheless, the pilot contamination severely degrades the sum rate performance even for infinitely many relay antennas.

Pilot Design for Sparse Channel Estimation in Large-Scale MIMO-OFDM System

The pilot design problem in large-scale multi-input-multioutput orthogonal frequency division multiplexing (MIMO-OFDM) system is investigated from the perspective of compressed sensing (CS). According to the CS theory, the success probability of estimation is dependent on the mutual coherence of the reconstruction matrix. Specifically, the smaller the mutual coherence is, the higher the success probability is. Based on this conclusion, this paper proposes a pilot design algorithm based on alternating projection and obtains a nonorthogonal pilot pattern. Simulation results show that applying the proposed pattern gives the better performance compared to applying conventional orthogonal one in terms of normalized mean square error (NMSE) of the channel estimate. Moreover, the bit error rate (BER) performance of the large-scale MIMO-OFDM system is improved.

Spatially Common Sparsity Based Adaptive Channel Estimation and Feedback for FDD Massive MIMO

This paper proposes a spatially common sparsity based adaptive channel estimation and feedback scheme for frequency division duplex based massive multi-input multi-output (MIMO) systems, which adapts training overhead and pilot design to reliably estimate and feed back the downlink channel state information (CSI) with significantly reduced overhead. Specifically, a nonorthogonal downlink pilot design is first proposed, which is very different from standard orthogonal pilots. By exploiting the spatially common sparsity of massive MIMO channels, a compressive sensing (CS) based adaptive CSI acquisition scheme is proposed, where the consumed time slot overhead only adaptively depends on the sparsity level of the channels. In addition, a distributed sparsity adaptive matching pursuit algorithm is proposed to jointly estimate the channels of multiple subcarriers. Furthermore, by exploiting the temporal channel correlation, a closed-loop channel tracking scheme is provided, which adaptively designs the nonorthogonal pilot according to the previous channel estimation to achieve an enhanced CSI acquisition. Finally, we generalize the results of the multiple-measurement-vectors case in CS and derive the Cramér-Rao lower bound of the proposed scheme, which enlightens us to design the nonorthogonal pilot signals for the improved performance. Simulation results demonstrate that the proposed scheme outperforms its counterparts, and it is capable of approaching the performance bound.

On Design of Non-Orthogonal Pilot Signals for a Multi-Cell Massive MIMO System

In this letter, the error variance of the Minimal Mean-Square Error (MMSE) channel estimator is analyzed, and its analytic formula is given. Based on the analytic formula, a designing criterion on the pilot signals is proposed. When training time slots can be large enough, our criterion confirms the well-known fact that orthogonal pilot signals are optimal. But if training time slots are not enough to support this orthogonality, our results show that the error variance is lower-bounded away from zero, no matter what kind of pilot signals are used. In this case, the design of pilot signals should be implemented by using the line packing on a complex Grassmannian manifold.

Outage-Constrained Beamforming for Two-Tier Massive MIMO Downlink with Pilot Reuse

Massive multiple-input multiple-output (MIMO) systems and small cell networks are both regarded as promising candidates to meet the exponential growth of mobile data traffic for the next generation (5G) wireless communications. Hence, a new kind of multitier networks which combine massive MIMO macro cells with a secondary tier of small cells is proposed to resolve the contradiction of large network coverage and high data rate. In such multitier networks, it is inevitable to allocate nonorthogonal uplink pilot sequences to user equipment (UE) due to the large number of users. We propose a pilot reuse scheme by exploiting the unique architecture of this networks and analyse the special mixed channel state information (CSI) yielded by the pilot reuse scheme. Based on the mixed CSI, we formulate a downlink transmit beamforming problem of minimizing the total power consumption while satisfying the quality of service (QoS) requirements with outage constraints. After decomposing the original problem into simpler subproblems, we provide an efficient algorithm to combine these subproblems and solve them iteratively for generating the beamforming vectors. Monte Carlo simulations show that the average power consumption of the proposed pilot reuse scheme and its associated beamforming algorithm is close to that of the perfect CSI case.

Increasing the Sum-Throughput of Cells With a Sectorization Method for Massive MIMO

In massive multiple-input multiple-output time division duplex systems, the number of users simultaneously served by the base station (BS) is heavily limited if uplink orthogonal pilots are used. This difficulty can be alleviated by introducing non-orthogonal pilots through exploiting second-order channel statistics and sectorization. In this paper, we consider the large uniform linear array and propose a novel sectorization method with low complexity, in which multiple users per sector can be simultaneously served as if there were multiple BS antennas with identical directional characteristics in each sector. Numerical results show that the sum-throughput can be greatly increased compared to the typical massive MIMO architecture.

An Overview of Massive MIMO: Benefits and Challenges

Massive multiple-input multiple-output (MIMO) wireless communications refers to the idea equipping cellular base stations (BSs) with a very large number of antennas, and has been shown to potentially allow for orders of magnitude improvement in spectral and energy efficiency using relatively simple (linear) processing. In this paper, we present a comprehensive overview of state-of-the-art research on the topic, which has recently attracted considerable attention. We begin with an information theoretic analysis to illustrate the conjectured advantages of massive MIMO, and then we address implementation issues related to channel estimation, detection and precoding schemes. We particularly focus on the potential impact of pilot contamination caused by the use of non-orthogonal pilot sequences by users in adjacent cells. We also analyze the energy efficiency achieved by massive MIMO systems, and demonstrate how the degrees of freedom provided by massive MIMO systems enable efficient single-carrier transmission. Finally, the challenges and opportunities associated with implementing massive MIMO in future wireless communications systems are discussed.

UWB Sparse/Diffuse Channels, Part II: Estimator Analysis and Practical Channels

In this two-part paper, the problem of channel estimation in Ultra Wide-Band (UWB) systems is investigated. In Part I, a novel Hybrid Sparse/Diffuse (HSD) model is proposed for the UWB channel, and new channel estimation strategies are designed for this model. In this paper (Part II), a Mean-Squared Error (MSE) analysis of the Generalized MMSE and Generalized Thresholding Estimators developed in Part I is performed, for the asymptotic regimes of low and high SNR. The analysis quantifies the achievable MSE performance of these schemes over unstructured estimators. Specifically, we prove that it is beneficial to be conservative in the estimation of the sparse component, i.e., to assume that the sparse component is sparser than it actually is. Moreover, we analyze the scenario with a non-orthogonal pilot sequence, and establish a connection between the Generalized Thresholding estimator and conventional sparse approximation algorithms proposed in the literature. In addition to the theoretical analysis, these channel estimation schemes are evaluated in a more realistic geometry-based channel emulator, for which the HSD model developed in Part I is an approximation. The numerical results are shown to match the expected asymptotic MSE behavior. Moreover, the proposed estimation techniques are shown to outperform conventional unstructured and purely sparse estimators, from both an MSE and a bit error rate perspectives, even for the realistic geometry-based channel model.