# Pilot Sequence Allocation Schemes in Massive MIMO Systems Using Heuristic Approaches
## 1 Introduction
### Related Works  
Among different studies whose objectives are to minimize the pilot sequence contamination in TDD Massive MIMO systems, there is a considerable selection of methods, tools and techniques already tested, e.g., greedy and tabu search, smart pilot assignment, genetic algorithm (GA), deep learning, hybrid solutions and multi-objective approaches. To situate the contributions of this work, we present a chronological list of related work:  
* In [6], the authors approach the pilot contamination on Massive MIMO systems with low complexity evolutionary algorithms comparing the performance in macro-cell scenarios: greedy search, tabu search and a hybrid solution. * In [7], the authors proposed a new algorithm named Smart Pilot Assignment. The algorithm goal is to maximize all user signals to interference plus noise ratio (SINR) within a cell. The base station calculates the cell observed interference for each of the pilot sequences which users from neighbors' cells cause. The algorithm then assigns the pilot sequences following the rule: the user with the worst channel state receives the pilot sequence with the smallest observed interference. This process is repeated until each user has been assigned a pilot sequence, or the system has no pilot sequences to assign. * In [8], the authors proposed a greedy search. At each iteration, a number of users are randomly selected from each cell to be assigned the same pilot sequence. The selection is made such that the group chosen maximizes their transmission rate. As the iterations grow, the number of selected users also grows. Likewise, the number of possible selected users at each iteration shortens due to the already accomplished pilot sequence assignments of previous iterations. * In a different approach [9], the authors proposed the mitigation to pilot sequence contamination modeling the problem as an Epsilon-restricted optimization problem and then solving an eigenvalue decomposition problem through linear complexity. * In [10], the authors proposed a simple pilot assignment algorithm based on the water-filling algorithm. The users with the best channels received the pilot sequences under the lowest interference effect. To achieve such, at each base station, both channel state information (CSI) array, which contains each user CSI, as well as the inter-cell interference observed by each pilot sequence, are sorted such that one is in increasing order and the other in decreasing order. The pilot assignment is the combination of indexes of these two arrays. * In [11], the author used different algorithms to solve the pilot sequence assignment problem. The main objective is to maximize the system throughput where the GA was capable of obtaining the average maximum rate user with a smaller complexity. Furthermore, the GA solution as well as random assignment and exhaustive search are compared with the proposed schemes of [6]. * In [12], the authors proposed the assignment of orthogonal pilot sequences along with sectorization. The pilot sequences are re-utilized in the same cell, reducing sizes of the pilot sequence and optimizing spectral efficiency (SE), and Bayesian estimation is used to eliminate pilot contamination. * In [13], the authors present an adaptive pilot sequence allocation algorithm which separate the users in a cell into two groups: one for users who suffer high interference from other cells and one for users under a low interference regime. The algorithm then assigns mutually orthogonal pilot sequences for all the users under the interference regime, while the other group of users shares the same set of pilot sequences. * In [14], the pilot sequence allocation problem is solved using deep learning in the form a 3-layer perception neural network. The proposed scheme reaches 99.38% of the theoretical upper-bound performance and takes only 0.92 milliseconds to compute. * In [15], an algorithm of clustering divides users into two groups, low and high interference.