Weighted-Graph-Coloring-Based Pilot Decontamination for Multicell Massive MIMO Systems

In this paper, we consider secure downlink transmission in a multi-cell massive multiple-input multiple-output (MIMO) system where the numbers of base station (BS) antennas, mobile terminals, and eavesdropper antennas are asymptotically large. The channel state information of the eavesdropper is assumed to be unavailable at the BS and hence, linear precoding of data and artificial noise (AN) are employed for secrecy enhancement. Four different data precoders (i.e., selfish zero-forcing (ZF)/regularized channel inversion (RCI) and collaborative ZF/RCI precoders) and three different AN precoders (i.e., random, selfish/collaborative null-space based precoders) are investigated and the corresponding achievable ergodic secrecy rates are analyzed. Our analysis includes the effects of uplink channel estimation, pilot contamination, multi-cell interference, and path-loss. Furthermore, to strike a balance between complexity and performance, linear precoders that are based on matrix polynomials are proposed for both data and AN precoding. The polynomial coefficients of the data and AN precoders are optimized respectively for minimization of the sum mean squared error of and the AN leakage to the mobile terminals in the cell of interest using tools from free probability and random matrix theory. Our analytical and simulation results provide interesting insights for the design of secure multi-cell massive MIMO systems and reveal that the proposed polynomial data and AN precoders closely approach the performance of selfish RCI data and null-space based AN precoders, respectively.

As a combination of spatial modulation (SM) system and massive multiple-input multiple-output (MIMO) system, massive SM aided MIMO (SM-MIMO) system is recently proposed. In broadband scenarios, single-carrier (SC) modulation is introduced to massive SM-MIMO system, thus massive SC-SM MIMO system is proposed for uplink multi-user transmission over frequency-selective fading channels. In this study, the uplink spectral efficiency (SE) of multi-cell massive SC-SM MIMO system is analysed, meanwhile the pilot contamination effect is taken into consideration. A tight SE lower bound of multi-cell massive SC-SM MIMO system is proposed with maximum ratio (MR) combining, which also takes into account the imperfect channel estimation, transmit antenna correlation and path loss. The tightness of the authors' proposed closed-form SE lower bound is shown via simulation results. The optimal pilot reuse factor can be determined with different system configurations by simulations, and the pilot reuse factor that is larger than one is more suitable for less TAs and user equipments.

In this paper, we study the problem of secure transmission in the downlink of a multi-cell massive multiple-input multiple-output (MIMO) system, where pilot contamination is considered due to non-orthogonal uplink training sequence. The channel state information (CSI) of the eavesdropper is assumed to be unavailable at the base station (BS) and hence, the BS cooperation and an artificial noise(AN) are investigated for secrecy enhancement. Based on regularized channel inversion (RCI), we derive a closed-form expression for ergodic secrecy sum rate in the large-system regime, in which the number of users per cell K, the number of antenna at BS N and the number of antenna at eavesdropper N E tend to infinity. Our analysis shows that the secrecy sum-rate saturates at high signal-to-noise ratio (SNR) with BSs cooperation and AN under pilot contamination.

We propose a novel algorithm to design user load-achieving pilot sequences that mitigate pilot contamination in multi-cell massive multiple-input multiple-output (MIMO) networks. To this end, we first derive expressions for the user load and the load region of the network considering both small-scale and large-scale propagation effects. We then develop the pilot sequence algorithm for multi-cell massive MIMO networks as per the rules of generalized Welch bound equality design. Notably, we find that our algorithm and the corresponding downlink power allocation ensure that the user load is achieved when the signal-to-interference-plus-noise ratio (SINR) requirements for the users lie within the load region. Furthermore, we demonstrate the performance advantage of our proposed design relative to the existing designs, in terms of a larger load region and a higher maximum permitted SINR. Finally, we show that our proposed design can satisfy the pre-defined SINR requirements for users with a finite number of antennas at the base station (BS), while the existing designs cannot satisfy the same requirements even with an infinite number of antennas at the BS.

In this paper, we analyze the spectral efficiency of multicell massive multiple-input-multiple-output (MIMO) systems with downlink training and a new pilot contamination precoding (PCP) scheme. First, we analyze the spectral efficiency of the beamforming training (BT) scheme with maximum-ratio transmission (MRT) precoding. Then, we derive an approximate closed-form expression of the spectral efficiency to find the optimal lengths of uplink and downlink pilots. Simulation results show that the achieved spectral efficiency can be improved due to channel estimation at the user side, but in comparison with a single-cell scenario, the spectral efficiency per cell in multicell scenario degrades because of pilot contamination. We focus on the practical case where the number of base station (BS) antennas is large but still finite and propose the BT and PCP (BT-PCP) transmission scheme to mitigate the pilot contamination with limited cooperation between BSs. We confirm the effectiveness of the proposed BT-PCP scheme with simulation, and we show that the proposed BT-PCP scheme achieves higher spectral efficiency than the conventional PCP method and that the performance gap from the perfect channel state information (CSI) scenario without pilot contamination is small.

Massive multiple-input multiple-output (MIMO) systems are expected to achieve substantial gains in frequency efficiency compared to conventional MIMO systems. However, these promising gains are limited by the pilot contamination in multicell scenario, which results from reusing the same set of pilot sequences in neighboring cells. This paper proposes a clustering based pilot allocation (CPA) algorithm to mitigate the effects of pilot contamination. Specifically, we first define the inter-cell interference (ICI) relationship between users, based on which the users are divided into high and low ICI groups. Then, the users in low ICI group reuse pilots randomly, while the users in high ICI group are clustered by affinity propagation (AP) clustering method. Finally, we perform different pilot allocation strategies according to the types of user clusters. Simulation results show that the proposed algorithm can significantly improve the pilot efficiency compared to the existing pilot allocation algorithms using grouping ideas.

This paper strives to reduce pilot contamination, a bottleneck for massive multiple-input multiple-output (MIMO) systems, by exploiting channel sparsity. Considering that typical wideband massive MIMO channel is correlated in both space and frequency domains, we employ Karhunen–Loeve Transform (KLT) and Discrete Fourier Transform (DFT) to capture the hidden sparsity of the channel. KLT basis is optimal in extracting the uncorrelated information from channel, but requires channel statistical information. As a suboptimal alternative, DFT basis can be determined without channel statistics, which is more viable for practical use. By representing the channel with DFT basis, we find that the subspaces of the desired and interference channels are approximately orthogonal, even when the number of antennas is not so large. Inspired by this observation, we propose a pilot decontamination method, where a pilot assignment policy is designed to help identify the subspace of the desired channel, and a desired channel subspace aware least square channel estimator is derived to remove the pilot contamination. The proposed method does not need channel statistics and pilot co-ordination. By exploiting channel stationary, the method does not introduce extra training overhead. Simulation results demonstrate substantial sum rate gain of the proposed method over existing methods.

This paper proposes a novel heuristic algorithm that mitigates pilot contamination in Massive MIMO (multiple-input, multiple-output) systems by optimizing the allocation of pilots, which are a shared resource among base stations (BSs). The goal is to minimize the effect of pilot contamination caused by interference from reusing the same pilot sequence from multiple user equipment (UE) in different cells. Specifically, we aim to maximize the minimum uplink signal to interference ratio (SIR) through the network by assigning the same pilot to the UEs in different cells that cause the least amount of interference. For this purpose, the algorithm starts with two cells that have the worst arithmetic mean of the potential SIR between their users. Then the algorithm continues the assignment procedure for the rest of the cells depending on the arithmetic mean of the worst potential SIR of the users of a cell and the users of the already assigned cells. The simulation results showed that our results are very close to the optimal solution where the exhaustive search is feasible, and outperforms the results obtained from recently published related work which served as a benchmark when the exhaustive search could not be applied to the search space size.

Massive Multiple-Input-Multiple-Output (MIMO) systems, where the base station (BS) is equipped with hundred antennas, is expected to be one of the key technologies for the next generation wireless systems. Pilot contamination is one of performance degradation factors for massive MIMO. This paper aims to eliminate this pilot contamination impact. High time resolution carrier interferometry (HTRCI) was previously proposed which can perform highly accurate channel estimation with reducing the number of pilot signals. The original HTRCI generated the impulses in 1/4 equal interval. With regarding the current OFDM system design, more fine and variable impulse allocation is available, e.g. the guard interval (GI) length of Long-Term-Evolution-Advanced (LTE-A) is 1/8 or 1/16 of the OFDM symbol duration. This paper proposes the modified HTRCI with variable pulse generation at 1/8 interval which can estimate channel state information (CSI) of the 4 access per received antenna. This paper expands the concept of HTRCI to estimate more channels and these CSIs can be separated by time-domain signal processing in the same manner. It is applied to the pilot de-contamination on downlink multi-cell MIMO transmission. Computer simulation results confirm that the BER performance can be improved as compared with the conventional method.

Channel feedback is essential in frequency division duplexing (FDD) massive\nmultiple-input multiple-output (MIMO) systems. Unfortunately, previous work on\nmultiuser MIMO has shown that the codebook size for channel feedback should\nscale exponentially with the number of base station (BS) antennas, which is\ngreatly increased in massive MIMO systems. To reduce the codebook size and\nfeedback overhead, we propose an angle-of-departure (AoD)-adaptive subspace\ncodebook for channel feedback in FDD massive MIMO systems. Our key insight is\nto leverage the observation that path AoDs vary more slowly than the path\ngains. Within the angle coherence time, by utilizing the constant AoD\ninformation, the proposed AoD-adaptive subspace codebook is able to quantize\nthe channel vector in a more accurate way. We also provide performance analysis\nof the proposed codebook in the large-dimensional regime, where we prove that\nto limit the capacity degradation within an acceptable level, the required\nnumber of feedback bits only scales linearly with the number of resolvable\n(path) AoDs, which is much smaller than the number of BS antennas. Moreover, we\ncompare quantized channel feedback using the proposed AoD-adaptive subspace\ncodebook with analog channel feedback. Extensive simulations that verify the\nanalytical results are provided.\n

Interference alignment scheme for massive MIMO system

Channel estimation is crucial for massive multiple-input multiple-output (MIMO) systems to scale up multi-user MIMO, providing significant improvement in spectral and energy efficiency. In this paper, we present a simple and practical channel estimator for multipath multi-cell massive MIMO time division duplex systems with pilot contamination, which poses significant challenges to channel estimation. The proposed estimator addresses performance under moderate to strong pilot contamination without previous knowledge of the inter-cell large-scale fading coefficients and noise power. Additionally, we derive and assess an approximate analytical mean square error (MSE) expression for the proposed channel estimator. We show through simulations that the proposed estimator performs asymptotically as well as the minimum MSE estimator with respect to the number of antennas and multipath coefficients.

Cell-Free (CF) massive multiple-input multiple-output (MIMO) system is a distributed antenna system, wherein a large number of access points wish to simultaneously communicate with a relatively small number of users. Similar to co-located massive MIMO system, pilot contamination and multi-user interference are two major impediments to CF massive MIMO network performance improvement. One can mitigate the detrimental effect of pilot contamination and multi-user interference through judicious resource allocation. In this work, we formulate and investigate the problem of frequency assignment for a CF massive MIMO. The formulated optimization problem is proven to be generally NP-hard. Local optima can be found by approaches such as the Lagrangian method that however, has considerably slow rates of convergence. To circumvent this issue, we propose an alternative solution being of two-folds. Firstly, we reformulate the problem as a grouping strategy which enables to attenuate the effect of intra-group multi-user interference. In the second fold, frequencies are assigned in a non-overlapping fashion to each scheduled group to palliate the effect of inter-group interference and pilot contamination. To further improve the performance of the proposed approach, power coefficients are allocated to the users via a sequential convex approximation (SCA)-based framework. The effectiveness of the proposed algorithms is then verified through extensive numerical simulations which demonstrate a non-negligible improvement in the performance of the studied scenario.

Massive multiple-input multiple-output (MIMO) communication is a promising technology for increasing spectral efficiency in wireless networks. Two of the main challenges massive MIMO systems face are degraded channel estimation accuracy due to pilot contamination and increase in computational load and hardware complexity due to the massive number of antennas. In this paper, we focus on the problem of channel estimation in massive MIMO systems, while addressing these two challenges: We jointly design the pilot sequences to mitigate the effect of pilot contamination and propose an analog combiner which maps the high number of sensors to a low number of RF chains, thus reducing the computational and hardware cost. We consider a statistical model in which the channel covariance obeys a Kronecker structure, and treat two special cases, corresponding to fully- and partially-separable correlations. We prove that under these models, the analog combiner design can be performed independently of the pilot sequences. Given the resulting combiner, we derive a closed-form expression for the optimal pilot sequences in the fully-separable case and suggest a greedy sum of ratio traces maximization (GSRTM) method for designing sub-optimal pilots in the partially-separable scenario. We demonstrate via simulations that our pilot design framework achieves lower mean squared error than the common pilot allocation framework previously considered for pilot contamination mitigation.

In this letter, we propose a novel way to mitigate the notorious pilot contamination in massive multiple-input multiple-output (MIMO) systems by exploiting the intelligent reflecting surfaces (IRSs). Particularly, we intentionally break the uplink (UL) and downlink (DL) channel reciprocity in time-division duplexing (TDD) systems by configuring the phases of the IRSs differently during the UL training phase and the DL data transmission phase. In this way, we show that the pilot contamination is mitigated and can be eliminated in some cases. Meanwhile, we analyze the signal-to-interference-plus-noise ratio (SINR) performance due to the non-reciprocal UL and DL channels. We further show the asymptotic optimality of our proposed decontamination scheme. The analytical results are also corroborated by numerical simulations.