Massive MIMO is a promising technique for increasing the spectral efficiency (SE) of cellular networks, by deploying antenna arrays with hundreds or thousands of active elements at the base stations and performing coherent transceiver processing. A common rule-of-thumb is that these systems should have an order of magnitude more antennas $M$ than scheduled users $K$ because the users’ channels are likely to be near-orthogonal when $M/K > 10$ . However, it has not been proved that this rule-of-thumb actually maximizes the SE. In this paper, we analyze how the optimal number of scheduled users $K^\star$ depends on $M$ and other system parameters. To this end, new SE expressions are derived to enable efficient system-level analysis with power control, arbitrary pilot reuse, and random user locations. The value of $K^\star$ in the large- $M$ regime is derived in closed form, while simulations are used to show what happens at finite $M$ , in different interference scenarios, with different pilot reuse factors, and for different processing schemes. Up to half the coherence block should be dedicated to pilots and the optimal $M/K$ is less than 10 in many cases of practical relevance. Interestingly, $K^\star$ depends strongly on the processing scheme and hence it is unfair to compare different schemes using the same $K$ .

Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated?

Understand the fundamentals of wireless and MIMO communication with this accessible and comprehensive text. Viewing the subject through an information theory lens, but also drawing on other perspectives, it provides a sound treatment of the key concepts underpinning contemporary wireless communication and MIMO, all the way to massive MIMO. Authoritative and insightful, it includes over 330 worked examples and 450 homework problems, with solutions and MATLAB code and data available online. Altogether, this is an excellent resource for instructors and graduate students, as well as an outstanding reference for researchers and practicing engineers.

Foundations of MIMO Communication

In a communication system employing coherent reception, pilot symbols are used for estimating the channel state information (CSI) at the receiver. The amount of training, which is quantified by the fractional pilot duration for a fixed-length pilot-plus-data frame, should be kept as low as possible for saving bandwidth and increasing data rate. However, reducing training leads to degraded error performance due to poor CSI estimate although it increases data rate, while increasing training improves error performance but reduces data rate. Expressing the tradeoff between symbol error probability (SEP) and data rate by the normalized error-free data rate, we present an analytical framework for its maximization with respect to pilot symbol duration fraction in a pilot-aided single-input multiple-output wireless communication system with reception over independent and identically distributed flat Rayleigh fading diversity branches, employing $M$ -ary phase-shift keying, and using maximal-ratio combining. Closed-form expressions for the approximate optimal pilot symbol duration fraction are derived for the high signal-to-noise ratio (SNR) case. Numerical results are presented to highlight the system behavior with changes in parameters like SNR, pilot symbol quality, and number of receive diversity branches. It is found that the optimization maximizes normalized error-free data rate with close to minimum SEP.

Fractional Pilot Duration Optimization for SIMO in Rayleigh Fading With MPSK and Imperfect CSI

A signal processing perspective

For massive multiple-input multiple-output (MIMO) circumstances with time division duplex (TDD) protocol, pilot contamination becomes one of main system performance bottlenecks. This paper proposes an uplink pilot sequence assignment to alleviate this problem for spatially correlated massive MIMO circumstances. Firstly, a single-cell TDD massive MIMO model with multiple terminals in the cell is established. Then a spatial correlation between two channel response vectors is established by the large-scale fading variables and the angle of arrival (AOA) span with an infinite number of base station (BS) antennas. With this spatially correlated channel model, the expression for the achievable system capacity is derived. To optimize the achievable system capacity, a problem regarding uplink pilot assignment is proposed. In view of the exponential complexity of the exhaustive search approach, a pilot assignment algorithm corresponding to the distinct channel AOA intervals is proposed to approach the optimization solution. In addition, simulation results prove that the main pilot assignment algorithm in this paper can obtain a noticeable performance gain with limited BS antennas.

/pdf/pilot-sequence-assignment-for-spatially-correlated-massive-2pftia33fw.pdf

Pilot Sequence Assignment for Spatially Correlated Massive MIMO Circumstances.

We investigate the achievable uplink rate of multi-cell massive multi-input multi-output (MIMO) systems considering pilot reuse across cells. Based on tractable approximations for the achievable rates, we derive the optimal pilot length to maximize the sum rate per cell. Interestingly, it is found that, for moderately large numbers of base station (BS) antennas, the optimal pilot length is above the minimum feasible value, and the gains brought by the extra amount of training diminish as the reuse factor grows. Simulation results confirm the accuracy of our analysis.

Optimal pilot length for uplink massive MIMO systems with pilot reuse

Optimal optimal pilot length for uplink massive mimo systems with pilot reuse

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Optimal pilot length for uplink massive MIMO systems with pilot reuse

Optimal optimal pilot length for uplink massive mimo systems with pilot reuse