Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated? (1412.7102v3)

Abstract: Massive MIMO is a promising technique to increase 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 $K$.

• The paper demonstrates that allocating up to half the coherence block for pilots significantly enhances spectral efficiency in massive MIMO systems.
• It derives closed-form expressions for spectral efficiency, comparing processing schemes like MR, ZF, and the novel full-pilot zero-forcing (P-ZF).
• Simulation results reveal that a practical user-to-antenna ratio of less than 10 optimizes performance, challenging conventional resource allocation approaches.

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

The paper "Massive MIMO for Maximal Spectral Efficiency: How Many Users and Pilots Should Be Allocated?" presents a comprehensive analysis of optimal resource allocation strategies in massive MIMO systems. The authors, Emil Bjornson, Erik G. Larsson, and Merouane Debbah, focus on determining the optimal number of users and pilots to maximize spectral efficiency (SE) in cellular networks, employing large antenna arrays at base stations.

Key Contributions

The paper derives novel analytical expressions for SE, taking into account various system parameters such as the number of antennas, users, and pilots, as well as factors like power control and pilot contamination. The investigation also considers hardware impairments, uplink (UL) and downlink (DL) channel estimation, and diverse linear processing schemes, including maximum ratio (MR), zero-forcing (ZF), and a novel full-pilot zero-forcing (P-ZF) scheme.

Analytical Framework

1. System Model and Assumptions:
   • The network model features massive MIMO setups where the base stations are equipped with large antenna arrays, providing significant array gains.
   • The paper considers scenarios where the channel state information (CSI) is acquired through pilot signaling, which is constrained by the channel coherence block.
2. Spectral Efficiency Analysis:
   • The authors derive expressions for SE that are independent of user locations by assuming random user distributions and applying power control.
   • The closed-form SE expressions facilitate efficient evaluation of the SE of different processing schemes and pilot allocations.
3. Pilot and User Scheduling:
   • A significant insight from the analysis is that up to half of the coherence block should be allocated to pilot signals. The optimal user-to-antenna ratio was found to be less than 10 in practical scenarios, challenging conventional wisdom.
4. Interference Management:
   • To mitigate the effects of pilot contamination, the paper proposes P-ZF, a distributed coordinated beamforming technique that offers robust suppression of inter-cell interference.

Numerical and Simulation Results

• Simulation Scenarios:
  • The authors consider hexagonal grid networks and examine different interference scenarios to optimize SE concerning the number of antennas and scheduled users.
  • The effectiveness of different pilot reuse strategies and their impact on the network's SE are analyzed.
• Performance Metrics:
  • The paper reports that massive MIMO can achieve up to 40 times the SE required by IMT-Advanced standards under certain conditions, illustrating the potency of the technology in achieving high SE.

Implications and Future Work

The results of this paper have significant implications for the deployment and operation of massive MIMO systems in real-world settings. The findings suggest that a balance between pilot overhead and active user scheduling is crucial for optimizing SE. Future work may build on these insights to explore adaptive scheduling algorithms and the integration of these strategies in next-generation networks.

In summary, this paper provides a detailed investigation into the SE-maximization problem in massive MIMO systems, offering valuable guidance on user and pilot allocation strategies. The analytical and simulation insights enhance the understanding of how to harness the full potential of massive MIMO technology.