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Vertex Graph-Coloring-Based Pilot Assignment With Location-Based Channel Estimation for Massive MIMO Systems

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Trọng Hiếu at University of Ulsan
Trọng Hiếu
Sunghwan Kim
Sunghwan Kim
Sunghwan Kim
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Abstract and Figures

Massive multiple-input multiple-output (MIMO) is considered as a promising technique in wireless communication systems, which contains cellular base stations (BS) equipped with a very large number of antennas to serve multiple users. However, the performance of massive MIMO is limited by the impact of pilot contamination (PC) due to inter-cell interference (ICI). In conventional massive MIMO systems, pilot sequences are randomly assigned to users without any further consideration. In this paper, a vertex graph coloring-based pilot assignment (VGC-PA) algorithm is proposed in conjunction with the existing post-processing discrete Fourier transform (DFT) filtering channel estimation to mitigate the inter-cell interference between users with the same pilot sequence in the channel estimation process to improve the capacity of the whole system. Specifically, we propose a metric to measure the potential ICI strength between any two users in the system based on their angle of arrival (AoA), correlation, and distances to construct a ICI graph where each user is regarded as a node. This ICI graph denotes the potential ICI strength relationship among all users in the system. Then, we propose a VGC-PA algorithm to mitigate the ICI relationship between users with same pilot sequences by assigning different pilots to connected users with high ICI metric based on some criteria. After the pilot assignment process, we apply the existing post-processing DFT filtering in the channel estimation process. The simulation results show the significant improvement of our proposed VGC-PA algorithm compared with existing methods.
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Vertex Graph-Coloring-Based Pilot Assignment With Location-Based Channel Estimation for Massive MIMO Syste
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... For PC mitigation, several conventional algorithms based on pilot assignment have been proposed [3][4][5]. In [3], a vertex graph-coloring-based pilot assignment was proposed, in which pilot sequences were assigned to mobile terminals based on the ICI graph. ...
... For PC mitigation, several conventional algorithms based on pilot assignment have been proposed [3][4][5]. In [3], a vertex graph-coloring-based pilot assignment was proposed, in which pilot sequences were assigned to mobile terminals based on the ICI graph. The evaluation of an ICI graph is dependent on both the angle of arrival (AoA) correlation and the distance between the mobile terminals, but the problem with the scheme is that it needs a second-order channel information to function effectively. ...
... We considered the source of ICI throughout the pilot assignment, which is the fundamental cause of the PC in maMIMO systems, in contrast to the works mentioned in [4,15]. The availability of some factors, such as mobile terminal location, AoA, or LoS interference, is difficult to estimate, and it is a requirement for pilot assignment in some other works [3,[5][6][7], while in our proposed scheme, we only need large-scale fading coefficients that are easy to track because they do not change quickly during the coherence interval. Our proposed scheme is not computationally intensive and can be easily implemented in large-scale systems. ...
A greedy algorithm for pilot contamination mitigation using LAP
Article
Full-text available
  • Jun 2023
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.
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... In addition to that, the graph coloring algorithms, being minimization techniques, have been implemented to reduce the interference in mobile communications [24,25]. Reference [26] proposes a pilot assignment algorithm based on vertex graph-coloring problem to model reusing UL pilots between multiple cells in cellular networks. Precisely, in [26], UL pilot contamination occurs only between cells because a pilot can be used once within one cell. ...
... Reference [26] proposes a pilot assignment algorithm based on vertex graph-coloring problem to model reusing UL pilots between multiple cells in cellular networks. Precisely, in [26], UL pilot contamination occurs only between cells because a pilot can be used once within one cell. ...
Pilot allocation in downlink for cell-free communication systems
Thesis
  • Dec 2020
In Cell-Free massive Multiple-Input-Multiple-Output (Cell-Free massive MIMO) systems, we distribute in a coverage area a massive number of access points, mastered by central processing units (CPUs), to simultaneously serve much smaller number of user equipments (UEs) over the same time/frequency resources. In contrast to the centralized massive MIMO, cell-free massive MIMO is characterized by a channel hardening not sufficiently accentuated, thus, it will be appropriate to include downlink (DL) pilots to estimate the DL channel. This thesis considers a DL pilot assignment for the cell-free massive MIMO systems by defining a metric, involving the inter-user interference (IUI). This metric gives insights about DL pilot contamination. A threshold is then defined to optimize the number of DL pilots, which maximizes the minimum per-user DL throughput. This approach gives a conflict graph, where each UE is regarded as a vertex of the graph. It consists in a combinatorial optimization problem that can be approximated using a graph coloring algorithm. It is a greedy algorithm whose steps are described as follows. By fixing the adequate threshold, maximizing the minimum per-user DL throughput, a conflict or interference graph is constructed. It models the potential interference among interfering UEs, the UEs between which there is an edge are in conflict, i.e., present a high IUI. Then, the proposed scheme mitigates the potential IUI by appointing different DL pilots to connected UEs with high IUI and same DL pilots to UEs with low IUI in the conflict graph in accordance with some coloring rules. The simulation results validate that the minimum per-user DL throughput based on the proposed approach outperforms the conventional methods, i.e., statistical channel state information, the orthogonal and the random pilot assignment in the DL training. Our analysis underlines also the reduction of the DL pilot overhead ratio using the DL pilot assignment based on our proposed scheme, compared to the conventional methods aforementioned.
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... In addition to that, the graph-colouring algorithms, being minimization techniques, have been implemented to reduce the interference in mobile communications [27,28]. Reference [29] proposes a pilot assignment algorithm based on vertex graphcolouring problem to model reusing UL pilots between multiple cells in cellular networks. Precisely, in [29], UL PC occurs only between cells because a pilot can be used once within one cell. ...
... Reference [29] proposes a pilot assignment algorithm based on vertex graphcolouring problem to model reusing UL pilots between multiple cells in cellular networks. Precisely, in [29], UL PC occurs only between cells because a pilot can be used once within one cell. The graph-theoretic approach was also used to assign DL training pilots in order to reduce the pilot overhead in centralized MMIMO systems [28]. ...
Graph‐colouring based pilot assignment to mitigate downlink pilot contamination for cell‐free massive MIMO systems
Article
Full-text available
  • Jun 2021
Abstract In cell‐free massive multiple‐input‐multiple‐output (CF‐MMIMO) systems, a massive number of access points, mastered by central processing units are distributed in a coverage area to serve much smaller number of user equipments (UEs) simultaneously over the same time/frequency resources. In opposition to the centralized MMIMO, CF‐MMIMO particularity is that its channel hardening degree is not sufficiently accentuated, thus, it will be judicious to include downlink (DL) pilots in order for the DL channel to be estimated. This paper considers the DL pilot assignment for the CF‐MMIMO systems by defining a metric, involving the inter‐user interference. This metric gives insights into DL pilot contamination. A threshold is then defined to optimize the number of DL pilots, which maximizes the minimum per‐user DL throughput. This approach gives a conflict graph, where each UE is regarded as a vertex of the graph. This is a combinatorial optimization problem that can be approximated using graph‐colouring algorithms. The simulation results reveal that the proposed method outperforms interestingly, in terms of per‐user DL throughput, the existing methods such as statistical channel state information, the orthogonal, and the random pilot assignment in the DL training.
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... To verify the performance of the proposed GC-LI algorithm, we compared it with the WGC-PD algorithm in [23], the GC-PA algorithm in [24], and the VGC-PA algorithm in [31]. The WGC-PD algorithm and the GC-PA algorithm only use the large-scale fading coefficients to construct the interference graphs, which are not pinpoint enough. ...
Pilot Assignment Based on Graph Coloring and Location Information in Multicell Multiuser Massive MIMO Systems
Article
Full-text available
  • Jul 2021
  • WIREL COMMUN MOB COM
A massive multiple-input multiple-output (MIMO) system uses a large number of antennas in the base station (BS) to serve multiple users, which significantly improves the capacity of the system. However, in time division duplex (TDD) mode, the pilot contamination (PC) is inevitable due to the multiplexing of pilots. This paper proposed a pilot assignment based on graph coloring and location information (GC-LI) to improve the performance of users. Specifically, based on graph coloring, the proposed GC-LI algorithm combines location information like the angle of arrival (AoA), distance, and correlation to construct an interference graph. Then, we calculate the interference between any two users and use the postprocessing discrete Fourier transform (DFT) filtering process to effectively distinguish the users with nonoverlapping AoAs. Finally, according to the interference graph, the GC-LI algorithm is proposed to mitigate the intercell interference (ICI) between users with the same pilot by assigning different pilots to connected users with high ICI metrics based on some regulation. Simulation results show that the GC-LI algorithm is suitable for various types of cells. In addition, compared with the existing pilot assignment algorithms based on graph coloring, users’ average signal-to-interference-plus-noise ratio (SINR) and uplink achievable sum rate (ASR) are significantly improved.
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... Simulation results show that the channel estimation is enhanced by overcoming pilot contamination, and the performance of the system is improved in terms of Bit Error Rate (BER). In [42], graph colouring-based pilot assignment (VGC-PA) algorithm in combination with the existing post-processing discrete Fourier transform (DFT) filtering is proposed for channel estimation to enhance the system capacity and mitigate inter-cell interference between users sharing the same pilots. A channel estimation algorithm based on joint singular value decomposition (SVD) and iterative least square with projection (SVD-ILSP) is proposed in [43]. ...
Massive MIMO Systems for 5G: A Systematic Mapping Study on Antenna Design Challenges and Channel Estimation Open Issues
Article
Full-text available
  • Mar 2021
The next generation of mobile networks (5G) is expected to achieve high data rates, reduce latency, as well as improve the spectral and energy efficiency of wireless communication systems. Several technologies are being explored to be used in 5G systems. One of the main promising technologies that is seen to be the enabler of 5G is massive multiple-input multiple-output (mMIMO) systems. Numerous studies have indicated the utility of mMIMO in upcoming wireless networks. However, there are several challenges that needs to be unraveled. In this paper, the latest progress of research on challenges in mMIMO systems is tracked, in the context of mutual coupling, antenna selection, pilot contamination and feedback overhead. The results of a systematic mapping study performed on 63 selected primary studies, published between the year 2017 till the second quarter of 2020, are presented. The main objective of this secondary study is to identify the challenges regarding antenna design and channel estimation, give an overview on the state-of-the-art solutions proposed in the literature, and finally, discuss emerging open research issues that need to be considered before the implementation of mMIMO systems in 5G networks.
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Channel Charting Aided Pilot Reuse for Massive MIMO Systems With Spatially Correlated Channels
Article
Full-text available
  • Jan 2022
Massive multiple-input multiple-output (mMIMO) technology is a way to increase spectral efficiency and provide access to the Internet of things (IoT) and machine-type communication (MTC) devices. To exploit the benefits of large antenna arrays, accurate channel estimation through pilot signals is needed. Massive IoT and MTC systems cannot avoid pilot reuse because of the enormous numbers of connected devices. We propose a pilot reuse algorithm based on channel charting (CC) to mitigate pilot contamination in a multi-sector single-cell mMIMO system having spatially correlated channels. We show that after creating an interference map via CC, a simple strategy to allocate the pilot sequences can be implemented. The simulation results show that the CC-based pilot reuse strategy improves channel estimation accuracy, which subsequently improves the symbol detection performance and increases the spectral efficiency compared to other existing schemes. Moreover, the performance of the CC pilot assignment method approaches that of exhaustive search pilot assignment for small network setups.
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Pilot Reuse for mMTC with Spatially Correlated MIMO Channels: A Channel Charting Approach
Preprint
  • Mar 2022
Massive multiple-input multiple-output (mMIMO) technology is a way to increase the spectral efficiency of machine-type communications (MTC). To exploit the benefits from large antenna arrays, accurate channel estimation through pilot signals is needed. Massive MTC systems cannot avoid pilot reuse due to the enormous numbers of connected devices. We propose a pilot reuse algorithm based on channel charting (CC) to mitigate pilot contamination in a multi-sector single-cell massive MTC system having spatially correlated channels. We show that after creating an interference map via CC, a simple strategy to allocate the pilot sequences can be implemented. The simulation results show that the CC-based pilot reuse strategy improves channel estimation accuracy, which subsequently improves the symbol detection performance and increases the spectral efficiency compared to other existing schemes. Moreover, the performance of the CC pilot assignment method approaches that of exhaustive search pilot assignment for small network setups.
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Power Allocation for Energy Efficiency Maximization in Massive MIMO Systems
Article
  • Oct 2021
In this work, we investigate the power allocation needed to maximize the energy efficiency (EE) of a massive multiple-input-multiple-output (MIMO) system. We first derive a closed-form expression for the user rate with the presence of pilot contamination caused by inter-cell interference during the channel estimation phase. From the definition of system EE, we propose a maximization problem with two constraints: limited power for pilot and data signals and a minimum value for every user rate. The proposed maximization problem is a fractional programming problem and is very hard to solve directly. Therefore, we propose the first iterative algorithm to transform the original problem into subtractive form. Moreover, we propose the second iterative algorithm to solve the subtractive form maximization problem by approximating it as a convex problem. The convergence and feasibility of the two proposed algorithms are also discussed. Finally, the effectiveness of our scheme is shown by simulation results.
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A Smart Pilot Assignment in Multi-cell Massive MIMO Systems Using Virtual Modeling of Assigning Cost
Article
  • Apr 2021
In this paper, a smart pilot sequence assignment method is proposed to minimize inter-cell interference generated in a massive multi-input multi-output (MIMO) system due to pilot contamination in uplink TDD (Time Division Duplex) mode. The proposed method employs a zero-one integer linear programming method as the assignment algorithm. The amount of intercell interference imposed on the target cell users is considered as assigning cost. The introduced assigning cost is composed of the steering vectors of the desired users in the target cell, and the sum of the channel correlation matrices of interference users in adjacent cells. By exploiting the virtual channel modeling technique, we develop a simple alternative approach to calculate the assigning cost, which has low complexity. We prove that the new assigning cost, called virtual assigning cost, is equal to the assigning cost defined based on the physical channel model. Moreover, we develop a token-based protocol to manage the coupling between cells in the whole multicellular network based on a distributed manner without the need for data exchange between the BSs. Simulation results demonstrate that the proposed low complex smart pilot sequence assignment method achieves a good performance, which is better than those of some other related works in multicellular design regarding normalized mean square error (NMSE) and achievable rate criteria.
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A Performance Comparison of Graph Coloring Algorithms
Article
Full-text available
  • Dec 2016
Graph coloring problem (GCP) is getting more popular to solve the problem of coloring the adjacent regions in a map with minimum different number of colors. It is used to solve a variety of real-world problems like map coloring, timetabling and scheduling. Graph coloring is associated with two types of coloring as vertex and edge coloring. The goal of the both types of coloring is to color the whole graph without conflicts. Therefore, adjacent vertices or adjacent edges must be colored with different colors. The number of the least possible colors to be used for GCP is called chromatic number. As the number of vertices or edges in a graph increases, the complexity of the problem also increases. Because of this, each algorithm can not find the chromatic number of the problems and may also be different in their executing times. Due to these constructions, GCP is known an NP-hard problem. Various heuristic and metaheuristic methods have been developed in order to solve the GCP. In this study, we described First Fit (FF), Largest Degree Ordering (LDO), Welsh and Powell (WP), Incidence Degree Ordering (IDO), Degree of Saturation (DSATUR) and Recursive Largest First (RLF) algorithms which have been proposed in the literature for the vertex coloring problem and these algorithms were tested on benchmark graphs provided by DIMACS. The performances of the algorithms were compared as their solution qualities and executing times. Experimental results show that while RLF and DSATUR algorithms are sufficient for the GCP, FF algorithm is generally deficient. WP algorithm finds out the best solution in the shortest time on Register Allocation, CAR, Mycielski, Stanford Miles, Book and Game graphs. On the other hand, RLF algorithm is quite better than the other algorithms on Leighton, Flat, Random (DSJC) and Stanford Queen graphs.
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Optimal Pilot Design in Massive MIMO Systems Based on Channel Estimation
Article
Full-text available
  • Dec 2016
The performance of multicell massive multiple-input multiple-output (MIMO) systems is heavily affected by pilot contamination. This study considers the problem of pilot contamination and analytical expressions are presented on the normalised mean square error (NMSE) of the minimum mean square error channel estimation algorithm. Based on the NMSE of the massive MIMO systems, a pilot design criterion is proposed to design the optimal pilot sequences for mitigating the pilot contamination. Following this criterion, Chu sequence with perfect auto-correction and cross-correlation properties are employed to design the optimal pilot sequences. Then the performance of the proposed pilot design-based scheme is investigated, and the exact NMSE expressions are presented. The excellent performance of this pilot design scheme has been confirmed in the authors’ simulations.
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Location-aware channel estimation enhanced TDD based massive MIMO
Article
Full-text available
  • Nov 2016
Pilot contamination (PC) is a stumbling block in the way of realizing massive multi-input multi-output (MIMO) systems. This contribution proposes a location-aware channel estimation enhanced massive MIMO system employing timedivision duplexing protocol, which is capable of significantly reducing the inter-cell interference caused by PC and, therefore, improving the achievable system performance. Specifically, we present a novel location-aware channel estimation algorithm, which utilizes the property of the steering vector to carry out a fast Fourier transform based post-processing after the conventional pilot-aided channel estimation for mitigating PC. Our asymptotic analysis proves that this post processing is capable of removing PC from the interfering users with different angle-of-arrivals (AOAs). Since in practice the AOAs of some users may be similar, we further present a location-aware pilot assignment method to ensure that users utilizing the same pilot have distinguishable AOAs, in order to fully benefit from the location-aware channel estimation. Simulation results demonstrate that the proposed scheme can dramatically reduce the inter-cell interference caused by the re-use of the pilot sequence and improve the overall system performance significantly, while only imposing a modest extra computational cost, in comparison to the conventional pilot-aided channel estimation.
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A Performance Comparison of Graph Coloring Algorithms
Conference Paper
Full-text available
  • Sep 2016
Graph coloring problem (GCP) is getting more popular to solve the problem of coloring the adjacent regions in a map with minimum different number of colors. It is used to solve a variety of real-world problems like map coloring, timetabling and scheduling. Graph coloring is associated with two types of coloring as vertex and edge coloring. The goal of the both types of coloring is to color the whole graph without conflicts. Therefore, adjacent vertices or adjacent edges must be colored with different colors. The number of the least possible colors to be used for GCP is called chromatic number. As the number of vertices or edges in a graph increases, the complexity of the problem also increases. Because of this, each algorithm can not find the chromatic number of the problems and may also be different in their executing times. Due to these constructions, GCP is known an NP-hard problem. Various heuristic and metaheuristic methods have been developed in order to solve the GCP. In this study, we described First Fit (FF), Largest Degree Ordering (LDO), Welsh and Powell (WP), Incidence Degree Ordering (IDO), Degrees of Saturation (DSATUR) and Recursive Largest First (RLF) algorithms which have been proposed in the literature for the vertex coloring problem and these algorithms were tested on benchmark graphs provided by DIMACS. The performances of the algorithms were compared as their solution qualities and executing times. Experimental results show that while RLF and DSATUR algorithms are sufficient for the GCP, FF algorithm is generally deficient. WP algorithm finds out the best solution in the shortest time on Register Allocation, CAR, Mycielski, Stanford Miles, Book and Game graphs. On the other hand, RLF algorithm is quite better than the other algorithms on Leighton, Flat, Random (DSJC) and Stanford Queen graphs.
View
Graph Coloring Based Pilot Allocation to Mitigate Pilot Contamination for Multi-Cell Massive MIMO Systems
Article
Full-text available
  • Jul 2015
A massive multiple-input multiple-output (MIMO) system, which utilizes a large number of base station (BS) antennas to serve a set of users, suffers from pilot contamination due to the inter-cell interference (ICI). In this letter, a graph coloring based pilot allocation (GC-PA) scheme is proposed to mitigate pilot contamination for multi-cell massive MIMO systems. Specifically, by exploiting the large-scale characteristics of fading channels, an interference graph is firstly constructed to describe the potential ICI relationship of all users. Then, with the limited pilot resource, the proposed GC-PA scheme aims to mitigate the potential ICI by efficiently allocating pilots among users in the interference graph. The performance gain of the proposed scheme is verified by simulations.
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Smart pilot assignment for massive MIMO
Article
Full-text available
  • Jul 2015
A massive multiple-input multiple-output (MIMO) system, which utilizes a large number of antennas at the base station (BS) to serve multiple users, suffers from pilot contamination due to inter-cell interference. A smart pilot assignment (SPA) scheme is proposed in this letter to improve the performance of users with severe pilot contamination. Specifically, by exploiting the large-scale characteristics of fading channels, the BS firstly measures the inter-cell interference of each pilot sequence caused by the users with the same pilot sequence in other adjacent cells. Then, in contrast to the conventional schemes which assign the pilot sequences to the users randomly, the proposed SPA method assigns the pilot sequence with the smallest inter-cell interference to the user having the worst channel quality in a sequential way to improve its performance. Simulation results verify the performance gain of the proposed scheme in typical massive MIMO systems.
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Massive MIMO: Survey and future research topics
Article
  • May 2016
Massive multiple-input multiple-output technology has been considered a breakthrough in wireless communication systems. It consists of equipping a base station with a large number of antennas to serve many active users in the same time-frequency block. Among its underlying advantages is the possibility to focus transmitted signal energy into very short-range areas, which will provide huge improvements in terms of system capacity. However, while this new concept renders many interesting benefits, it brings up new challenges that have called the attention of both industry and academia: channel state information acquisition, channel feedback, instantaneous reciprocity, statistical reciprocity, architectures, and hardware impairments, just to mention a few. This paper presents an overview of the basic concepts of massive multiple-input multiple-output, with a focus on the challenges and opportunities, based on contemporary research.
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