Non-orthogonal Pilot Sequences Research Articles

Analysis and optimization for non-orthogonal pilot sequence sets in massive MIMO systems

In modern wireless communication systems, orthogonal pilot signals has been generally employed in estimation of the channel state information. However, orthogonal pilot signals are inadequate for supporting the rapidly increasing requirements of communication throughput for 5G-and-beyond wireless environments, owing to the pilot contamination and short coherence times in high-mobility situations. To address these concerns, we present a new strategy for making use of non-orthogonal pilot sequences in channel estimation for multi-cell massive multiple-input multiple-output systems. First, we extend prior pilot assignment strategies based on the orthogonality of pilots to the general case of non-orthogonal pilot signals. Based on the proposed non-orthogonal pilot assignment strategy, we establish the minimal pilot length that fulfills a requirement for the channel estimate error, under a given degree of non-orthogonality. Then, we demonstrate validity of the pilot assignment strategy with the minimal length, which maximizes the entire network throughput. Simulation results show that our proposed method gives a significantly enhanced performance in terms of the net throughput compared to that with orthogonal pilot sequences. The performance gain becomes particularly significant with a higher density of users or shorter coherence time intervals.

A greedy algorithm for pilot contamination mitigation using LAP

In this paper, we propose a linear assignment problem (LAP) scheme using greedy algorithms to alleviate the intercell interference (ICI) in massive multi-input multiple-output (maMIMO) systems. ICI has been recognized as one of the main challenges of massive MIMO systems and occurs when pilot sequences (PSs) are reused across neighboring cells or using non-orthogonal PS, and this results in a phenomenon known as pilot contamination (PC). The proposed scheme uniquely assigns pilot sequences to mobile terminals to mitigate PC such that the optimal or near-optimal solution is achieved. This scheme attains maximum SINR by assigning pilot sequence to mobile terminals that will only produce the least PC. Results obtained from simulation showed that the proposed assignment scheme achieved a greater sum rate than some established assignment schemes when compared.

Covariance-Based Activity Detection With Orthogonal Pilot Sequences for Cell-Free Distributed Massive MIMO Systems

The grant-free random access (GFRA) has been the mainstream access scheme in the massive ultra-reliable low-latency communications (mURLLC). Device activity detection is the foremost issue in GFRA. Most of previous works assume unique non-orthogonal pilot sequence assignment in device activity detection which brings about severe inter-device interference and requires high-complexity access point (AP) coordination to eliminate interference. Taking advantage of the good cross-correlation characteristic of orthogonal pilot sequences and the sparsity in power domain of cell-free (CF) distributed massive multiple-input multiple-output (mMIMO) systems, this paper proposes a novel orthogonal pilot sequences based activity detection (OPSAD) algorithm to alleviate inter-device interference and thus improve device activity detection performance. In the proposed OPSAD algorithm, the min-max covariance interference (MMCI) pilot assignment algorithm considering AP selection and power control is introduced and a new interference metric is defined to efficiently capture the inter-device interference in this algorithm. Simulation results show that the proposed algorithm reduces computational complexity and achieves better performance than the benchmark algorithm utilizing non-orthogonal pilot sequences in practical mURLLC scenario.

Reconfigurable Intelligent Surface for Massive Connectivity: Joint Activity Detection and Channel Estimation

This paper considers the massive connectivity with the aid of a reconfigurable intelligent surface (RIS), where an enormous number of devices transmit sporadically to a base station (BS). The RIS establishes favorable signal propagation environments to enhance data transmission in massive connectivity in such a scenario. Nevertheless, the BS needs to detect active devices and estimate channels to support data transmission in RIS-assisted massive access systems. Furthermore, due to a large number of devices, it is impossible to assign orthogonal signature sequences to the devices as in most of the existing works on RIS-related channel estimation, which yields unique challenges. This paper shall consider a RIS-assisted uplink IoT network and solve the RIS-related activity detection and channel estimation problem. The BS detects the active devices and estimates the separated channels of the RIS-to-device link and the RIS-to-BS link by using non-orthogonal pilot sequences. Due to limited scattering between the RIS and the BS, we model the RIS-to-BS channel as a sparse channel. As a result, by simultaneously exploiting both the sparsity of sporadic transmission in massive connectivity and the RIS-to-BS channels, we formulate the RIS-related activity detection and channel estimation problem as a sparse matrix factorization problem. Furthermore, we develop an approximate message passing (AMP) based algorithm to solve the problem based on the Bayesian inference framework and reduce the computational complexity by approximating the algorithm with the central limit theorem and Taylor series expansion. Finally, extensive numerical experiments are conducted to verify the effectiveness of the proposed algorithm.

Index Modulation-Based Non-Coherent Transmission in Grant-Free Massive Access

In this paper, the non-coherent transmission in grant-free massive machine-type-communication-enabled random access is studied, and a new index modulation (IM)-based non-coherent data transmission scheme is presented. In the proposed scheme, each user is allocated $N (N>1)$ non-orthogonal pilot sequences. When the user is active, $N_a (1\leq N_a out of the $N$ allocated pilot sequences are activated to generate transmit signal, where the indices of these active pilot sequences are employed to carry information based on the IM principle. At receiver, first, exact and approximated presentations of the covariance matrix of received signals for the cases of $N_a=1$ and $N_a>1$ are derived, respectively. Then, the non-Bayesian maximum-likelihood (ML) estimator is employed to detect user activity along with embedded information bits. Finally, simulation results are given to demonstrate the performance of the proposed scheme.

Pilot Contamination Attack Detection for 5G MmWave Grant-Free IoT Networks

Grant-free random access is an emerging technology for providing massive connectivity for 5G massive machine-type communications (mMTC), where non-orthogonal pilot sequences are used to simultaneously detect active users and estimate channels. However, grant-free 5G IoT networks are vulnerable to pilot contamination attacks (PCA), where the attacker can send the same pilots as legitimate IoT users to harm the active user detection and channel estimation. To defend against this attack, in this article, we propose a physical-layer countermeasure based on the channel virtual representation (CVR). CVR can emphasize the unique characteristics of mmWave channels that are sensitive to the location of the sender. This can be utilized to counter PCA no matter if the attacker's pilots are superimposed to that of the victim or not. Based on this observation, to achieve an efficient PCA detection, a single-hidden-layer multiple measurement (SHMM) Siamese network is employed. This solution tackles the challenges of channel randomness and massive connectivity in mMTC IoT networks, and supports small sample learning. Simulation results evaluate and confirm the effectiveness of the proposed detection scheme under various scenarios. The detection accuracy can approach 99% with 128 antennas at the receiver and reach above 95% even with only 50 training samples.

Covariance-Aided CSI Acquisition With Non-Orthogonal Pilots in Massive MIMO: A Large-System Performance Analysis

Massive multiple-input multiple-output (MIMO) systems use antenna arrays with a large number of antenna elements to serve many different users simultaneously. The large number of antennas in the system makes, however, the channel state information (CSI) acquisition strategy design critical and particularly challenging. Interestingly, in the context of massive MIMO systems, channels exhibit a large degree of spatial correlation which results in strongly rank-deficient spatial covariance matrices at the base station (BS). With the final objective of analyzing the benefits of covariance-aided uplink multi-user CSI acquisition in massive MIMO systems, here we compare the channel estimation mean-square error (MSE) for (i) conventional CSI acquisition, which does not assume any knowledge on the user spatial covariance matrices and uses orthogonal pilot sequences; and (ii) covariance-aided CSI acquisition, which exploits the individual covariance matrices for channel estimation and enables the use of non-orthogonal pilot sequences. We apply a large-system analysis to the latter case, for which new asymptotic MSE expressions are established under various assumptions on the distributions of the pilot sequences and on the covariance matrices. We link these expressions to those describing the estimation MSE of conventional CSI acquisition with orthogonal pilot sequences of some equivalent length. This analysis provides insights on how much training overhead can be reduced with respect to the conventional strategy when a covariance-aided approach is adopted.

Pilot decontamination in massive multiuser MIMO systems based on low‐rank matrix approximation

In multi-cell massive multiuser multi-input multi-output (MU-MIMO) systems, the channel estimation performance is degraded by the pilot contamination problem. This effect occurs when non-orthogonal pilot sequences are reused by other users in the adjacent cells. In this study, two channel estimation methods based on low-rank matrix approximation technique are proposed to mitigate pilot contamination problem in time division duplex multi-cell massive MU-MIMO systems. In the first method, the massive MU-MIMO channel estimation is formulated as the nuclear norm (NN) optimisation problem and solved by using a novel estimation algorithm proposed in this study. In the second method, the iterative weighted NN (IWNN) is proposed to improve the NN estimation performance. Consequently, the regularisation parameter of both optimisation methods is selected based on the cross-validation curve method. The simulation results show that both proposed methods outperform the traditional least square method in terms of the normalised mean square error. Moreover, the IWNN estimation method demonstrates substantial improvement over the NN estimation method in the presence of strong pilot contamination problem.

Decentralized Joint Precoding With Pilot-Aided Beamformer Estimation

Downlink beamforming techniques with low beamformer training overhead are proposed for joint processing (JP) coordinated multipoint transmission (CoMP). The objective is to maximize the weighted sum rate within joint transmission clusters without centralized beamformer processing, while accounting for uncertainty in the underlying channels. The proposed methods use time-division duplexing and pilot-based training with, possibly, nonorthogonal pilot sequences. The beamformer training is done without the explicit channel state information estimation, which greatly improves the robustness to pilot contamination. Best response and gradient-based decentralized algorithms are proposed and provide a tradeoff between computational complexity and fast convergence rate. The impact of feedback/backhaul quantization is also considered. The results show that JP CoMP is feasible with slow fading conditions and limited backhaul capacity by employing decentralized beamformer processing.

Massive Connectivity With Massive MIMO—Part II: Achievable Rate Characterization

This two-part paper aims to quantify the cost of device activity detection in an uplink massive connectivity scenario with a large number of devices but device activities are sporadic. Part I of this paper shows that in an asymptotic massive multiple-input multiple-output (MIMO) regime, device activity detection can always be made perfect. Part II of this paper subsequently shows that despite the perfect device activity detection, there is nevertheless significant cost due to device detection in terms of overall achievable rate, because of the fact that non-orthogonal pilot sequences have to be used in order to accommodate the large number of potential devices, resulting in significantly larger channel estimation error as compared to conventional massive MIMO systems with orthogonal pilots. Specifically, this paper characterizes each active user's achievable rate using random matrix theory under either maximal-ratio combining (MRC) or minimum mean-squared error (MMSE) receive beamforming at the base-station (BS), assuming the statistics of their estimated channels as derived in Part I. The characterization of user rate also allows the optimization of pilot sequences length. Moreover, in contrast to the conventional massive MIMO system, the MMSE beamforming is shown to achieve much higher rate than the MRC beamforming for the massive connectivity scenario under consideration. Finally, this paper illustrates the necessity of user scheduling for rate maximization when the number of active users is larger than the number of antennas at the BS.

Massive Connectivity With Massive MIMO—Part I: Device Activity Detection and Channel Estimation

This two-part paper considers an uplink massive device communication scenario in which a large number of devices are connected to a base-station (BS), but user traffic is sporadic so that in any given coherence interval, only a subset of users are active. The objective is to quantify the cost of active user detection and channel estimation and to characterize the overall achievable rate of a grant-free two-phase access scheme in which device activity detection and channel estimation are performed jointly using pilot sequences in the first phase and data is transmitted in the second phase. In order to accommodate a large number of simultaneously transmitting devices, this paper studies an asymptotic regime where the BS is equipped with a massive number of antennas. The main contributions of Part I of this paper are as follows. First, we note that as a consequence of having a large pool of potentially active devices but limited coherence time, the pilot sequences cannot all be orthogonal. However, despite the non-orthogonality, this paper shows that in the asymptotic massive multiple-input multiple-output (MIMO) regime, both the missed device detection and the false alarm probabilities for activity detection can always be made to go to zero by utilizing compressed sensing techniques that exploit sparsity in the user activity pattern. Part II of this paper further characterizes the achievable rates using the proposed scheme and quantifies the cost of using non-orthogonal pilot sequences for channel estimation in achievable rates.

On modeling and performance analysis of non-cooperative multi-antenna multi-user MIMO systems

This work presents modeling and performance analysis of beamforming in non-cooperative multi-user multiple-input multiple-output (MU-MIMO) cellular systems using stochastic geometry based abstraction models. Particularly, a downlink MU-MIMO system is investigated in which an array of antenna elements at the base stations (BS) serves several user devices. We derive the closed-form expression of the complimentary cumulative distribution function (CCDF) of signal-to-interference-plus-noise ratio (SINR) representing the coverage probability for orthogonal pilot sequences and thereby characterize a number of related special cases. Moreover, closed-form expressions are also obtained for the CCDF of signal-to-interference ratio (SIR) for non-orthogonal pilot sequences and we also derive useful special cases of it and identify the support region of our analysis. Lastly, we define the numerical expression of ergodic capacity and utilize a partial fraction expansion to solve a simple form. Our contribution in this work is twofold, we not only provide a pedagogical tutorial-like exposition of stochastic geometry technique to model terrestrial networks, but also augment the existing literature in the field with aspects of frequency reuse factor, an indicator function for pilot usage, and the effect of pilot contamination. Simulation results are presented to support the theoretical part.

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.

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.

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.

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.