Multi-user Massive MIMO Communication Systems Based on Irregular Antenna Arrays

Abstract: In practical mobile communication engineering applications, surfaces of antenna array deployment regions are usually uneven. Therefore, massive multi-input-multi-output (MIMO) communication systems usually transmit wireless signals by irregular antenna arrays. To evaluate the performance of irregular antenna arrays, the matrix correlation coefficient and ergodic received gain are defined for massive MIMO communication systems with mutual coupling effects. Furthermore, the lower bound of the ergodic achievable rate, symbol error rate (SER) and average outage probability are firstly derived for multi-user massive MIMO communication systems using irregular antenna arrays. Asymptotic results are also derived when the number of antennas approaches infinity. Numerical results indicate that there exists a maximum achievable rate when the number of antennas keeps increasing in massive MIMO communication systems using irregular antenna arrays. Moreover, the irregular antenna array outperforms the regular antenna array in the achievable rate of massive MIMO communication systems when the number of antennas is larger than or equal to a given threshold.

• The paper demonstrates that employing irregular antenna arrays can optimize the achievable rate by balancing antenna count against spatial correlation.
• The paper develops a comprehensive channel model that accounts for mutual coupling and fading effects, validated by simulation results fitting normal distributions.
• The paper quantifies performance metrics such as SER and outage probability, revealing significant energy savings and improved spectral efficiency in multi-user scenarios.

Multi-user Massive MIMO Communication Systems Based on Irregular Antenna Arrays

The advancement in mobile communication technology, specifically the evolution towards 5G networks, necessitates significant enhancements in spectrum efficiency and energy savings. "Multi-user Massive MIMO Communication Systems Based on Irregular Antenna Arrays" (1604.04968) addresses these challenges by investigating massive multi-input-multi-output (MIMO) systems that use irregular antenna arrays. This essay explores the key contributions, methodologies, results, and implications illustrated in the paper.

Introduction

Massive MIMO technology, integral for fifth-generation wireless communication systems, offers significant potential in enhancing network capacity and energy efficiency. Contemporary studies demonstrate its ability to escalate spectrum efficiency by 10 to 20 bit/s/Hz and energy savings by factors of 10 to 20 in wireless systems. However, a significant challenge lies in the deployment of the sheer number of antennas required, often constrained by physical space limitations, resulting in the non-uniform spacing characteristic of irregular antenna arrays. This paper examines the performance of multi-user massive MIMO communication systems that adopt such irregular arrays, considering the critical aspect of mutual coupling which significantly affects the system's performance due to changes in phase and amplitude of antenna response vectors.

System Model

The paper introduces a model for a single-cell multi-user massive MIMO system where base station (BS) antennas, limited by uneven deployment surfaces, form an irregular antenna array. A channel model was formulated which includes various factors such as mutual coupling, irregular antenna arrays, array steering, and fading models that can further influence the performance of massive MIMO systems. The channel matrix, defined as:

$\mathbf{G} = \mathbf{CAHD}^{1/2},$

captures these effects, where $\mathbf{C}$ represents mutual coupling, $\mathbf{A}$ is the array steering matrix, $\mathbf{H}$ is the small scale fading matrix, and $\mathbf{D}$ represents large scale fading.

Impact of Mutual Coupling

In massive MIMO systems, particularly those installed on irregular surfaces, the mutual coupling effect and channel correlation significantly affect system performance. The paper examines these influences through the matrix correlation coefficient $\eta$ and ergodic received gain $\mathbb{G}\left( {M,R} \right)$. The coefficient $\eta$ is used to quantify the channel's correlation strength by assessing the relationship between the sum of squared off-diagonal elements and diagonal elements within the channel correlation matrix. Meanwhile, the ergodic received gain $\mathbb{G}(M,R)$ considers both antenna count and array size, capturing the supposed antagonistic relationship between spatial distance and antenna count within a constrained deployment area.

Numerical Analysis and Results

Through simulations, the paper highlights that irregular antenna arrays display unique channel correlation properties compared to regular arrays. The eigenvalue distribution of the correlation matrix for such arrays is shown to fit a sum of normal distributions well, as evidenced by Figure 1. This distribution plays a crucial role in evaluating system metrics like achievable rate and SER under channel correlation and mutual coupling effects.

The results underline the existence of an optimal number of antennas maximizing the achievable rate, beyond which the rate diminishes. For example, when operating under the specified conditions, irregular antenna arrays outperformed regular arrays when the antenna count exceeded a certain threshold. Additionally, the relation of mutual coupling and irregular array size to the achievable rate and outage probability is critically examined. Increasing array size while maintaining a fixed number of antennas results in a decreased spatial correlation and enhanced spectral efficiency.

Performance Metrics Analysis

Several analytical propositions are developed within the paper to derive performance metrics for irregular antenna array systems, considering the mutual coupling effect:

1. Achievable Rate: A lower bound for the ergodic achievable rate is formulated based on the matrix correlation and channel conditions, providing a headroom for what can be achieved asymptotically.
2. Symbol Error Rate (SER): The paper derives the equation for the average SER, demonstrating its decay trend with both increasing channel quality and antenna count while noting the dependence on modulation schemes.
3. Outage Probability: An expression for the average outage probability is articulated with respect to the UTs’ transmit SNR and the number of BS antennas, further distinguishing between scenarios of regular and non-regular antenna arrays.

Conclusions

This paper makes substantial contributions towards understanding the impact of irregular antenna arrays in massive MIMO systems with mutual coupling effects. It reveals that while irregular arrays can lead to a maximum achievable rate at a certain antenna threshold, they also complicate the correlation structure, thus influencing the performance of multi-user scenarios. This work provides valuable insights into antenna deployment strategies for efficient massive MIMO communication systems in both theoretical and practical dimensions, indicating prospects for future research into multi-cell environments with even greater numbers of antennas.