Source-linked AI summary
Capacity analysis of a multi-cell multi-antenna cooperative cellular network with co-channel interference
Xiaohu Ge, Kun Huang, Cheng-Xiang Wang, Xuemin Hong, Xi Yang
TL;DR
The paper addresses the lack of analytical co-channel interference models and exact capacity analysis for multi-cell multi-antenna cellular networks. It proposes an alpha stable interference model, derives MIMO and MISO cooperative capacity expressions, and finds that cooperation improves capacity while gains diminish as cooperative resources increase.
Problem
Exact normalized average capacity for multi-cell MIMO cellular networks with co-channel interference had not been investigated, while such interference was often treated simply as noise.
Method
The paper models co-channel interference using alpha stable processes and derives exact MIMO and closed-form cell-edge MISO cooperative downlink capacity expressions.
Results
Cooperative transmission improves capacity performance, while increasing cooperative antennas or base stations reduces the incremental capacity gain.
Takeaways & Limitations
Cooperative transmission is especially beneficial when the density of interfering base stations is high.
Takeaways & Limitations
The analysis assumes desired signals received by the user are uncorrelated and simplifies the system model through stated interference assumptions.
Abstract
from arXiv · showhide
Characterization and modeling of co-channel interference is critical for the design and performance evaluation of realistic multi-cell cellular networks. In this paper, based on alpha stable processes, an analytical co-channel interference model is proposed for multi-cell multiple-input multi-output (MIMO) cellular networks. The impact of different channel parameters on the new interference model is analyzed numerically. Furthermore, the exact normalized downlink average capacity is derived for a multi-cell MIMO cellular network with co-channel interference. Moreover, the closed-form normalized downlink average capacity is derived for cell-edge users in the multi-cell multiple-input single-output (MISO) cooperative cellular network with co-channel interference. From the new co-channel interference model and capacity, the impact of cooperative antennas and base stations on cell-edge user performance in the multi-cell multi-antenna cellular network is investigated by numerical methods. Numerical results show that cooperative transmission can improve the capacity performance of multi-cell multi-antenna cooperative cellular networks, especially in a scenario with a high density of interfering base stations. The capacity performance gain is degraded with the increased number of cooperative antennas or base stations.
I. INTRODUCTION
The paper addresses missing interference modeling and capacity analysis for realistic multi-cell multi-antenna networks. It proposes an analytical model and derives exact or closed-form capacity expressions, then examines cooperative transmission numerically.
- Existing interference models largely target single-antenna or single-cell scenarios, leaving multi-cell multi-antenna networks insufficiently represented.
- Previous capacity studies considered simplified settings, including finite interferers, flat Rayleigh fading, or single-cell systems.
- It derives the exact downlink average capacity for multi-cell MIMO networks and a closed-form normalized capacity for cell-edge users in cooperative multi-cell MISO networks.
- The paper proposes an analytical co-channel interference model for multi-cell MIMO networks with Poisson-distributed interferers, fading, and shadowing.
- Numerical analysis investigates cooperative antennas and base stations, finding improved capacity but diminishing gains as their numbers increase.
II. CO-CHANNEL INTERFERENCE MODELING AND PERFORMANCE ANALYSIS
The general model represents downlink interference using users with multiple receiving antennas and base stations with multiple transmitting antennas. Base-station locations follow a Poisson spatial distribution across an unbounded two-dimensional plane.
- The analysis focuses on downlink interference and retains only effective interferers in the general model.
- The model contains user equipment with Nr antennas and interfering base stations with Nt antennas.
- Base-station locations are modeled by a Poisson spatial distribution in a two-dimensional infinite plane, with one base station per cell.
- The resulting interference model is intended to describe interference signals in multi-cell cellular networks.
B. Interference Model of Multi-cell MIMO Cellular Networks
The multi-cell MIMO interference model aggregates signals from Poisson-distributed base stations through path loss, Nakagami-m fading, and Gamma shadowing. Its aggregate-interference distribution is modeled with an alpha stable process and expressed through a derived PDF.
- Interference signals undergo independent channel effects, including path loss, Nakagami-m fading, and shadowing.
- Each selected user receives aggregated interference from base stations distributed according to a Poisson process with density parameter λBS.
- The aggregated interference follows an alpha stable distribution characterized through its characteristic function.
- Each interfering base station has Nt antennas, producing Nt interference sub-streams received across the user's antennas.
- Gamma shadowing and Nakagami-m fading are approximated by a Generalized-K process, enabling derivation of the interference PDF.
- An inverse Fourier transform yields a new PDF for received aggregate interference, with a specialized analytical model when σr = 4.
C. Performance Analysis
The performance analysis compares the proposed interference distribution with a Gaussian model and examines how channel and network parameters shape interference. The proposed model has heavy tails, while several parameters alter interference burstiness and probability across power ranges.
- The proposed interference PDF has an obvious heavy-tail characteristic compared with the conventional Gaussian interference model.
- Rare high-interference events have a non-ignorable impact on the alpha stable distribution.
- Increasing σdB raises the probability of interference between 0 and 3×10^-10 watt but lowers the tail probability above 3×10^-10 watt.
- Increasing λBS decreases low-power interference probability and increases high-power interference probability across the reported ranges.
- Increasing σr, Nt, or Nr reverses the interference-probability trend after reported power thresholds.
- The parameters σdB, λBS, σr, Nt, and Nr significantly influence aggregate-interference burstiness, whereas Nakagami shaping factor m has little influence on its power.
A. Cooperative System
The paper models a multi-cell cooperative network with Poisson-distributed interfering base stations and focuses capacity analysis on cell-edge users in cooperative transmission areas.
- The network contains infinite base stations with N_t antennas and user terminals with N_r antennas, with interfering base-station locations following a Poisson spatial distribution.
- Three adjacent base stations form a cooperative cluster arranged in a triangle, with corresponding adjacent sectors forming a hexagonal cluster structure.
- Cooperative transmission is limited to overlapping cell areas, while the remaining regions use traditional transmission.
- Capacity analysis is restricted to a cooperative cluster and focuses on downlink capacity for cell-edge users in the cooperative transmission area.
- In the cell-edge overlap, K users simultaneously receive expected signals from cooperative base stations, with N_b ∈[1, 3] representing different cooperative transmission solutions.
B. Downlink Capacity of Multi-cell MIMO Cooperative Cellular Network
This section formulates downlink capacity for a multi-cell MIMO network by combining desired-signal and co-channel-interference models under fading and path-loss assumptions, then derives an exact average-capacity expression.
- All wireless channels are modeled as Nakagami-m fading channels with path loss, and MRT/MRC is used to express the received SINR.
- The received signal model separates the desired signal, cooperative-cluster interference, other-cluster interference, and additive white Gaussian noise.
- The capacity expression uses Shannon theory with bandwidth B_w and the interference covariance matrix, while AWGN power may be neglected relative to received interference.
- The average-capacity derivation combines the PDFs of desired and aggregated interference powers under a statistical-independence assumption.
- An exact normalized downlink average capacity is derived for the multi-cell MIMO cellular network with co-channel interference.
C. Closed-form Downlink Capacity of Multi-cell MISO Cellular Network
This section derives a closed-form normalized downlink capacity for cell-edge users in a MISO cooperative network, using cooperative transmission and interference distributions under simplifying assumptions.
- A closed-form normalized downlink average capacity is derived for the multi-cell MISO cooperative cellular network with co-channel interference.
- Interference within a cooperative cluster is assumed negligible because cooperative base stations use orthogonal channels, and each antenna transmits normalized power P_ant = 1.
- The interference model represents interfering-base-station locations with a Poisson spatial distribution and fading variables with Nakagami-m distributions.
- The analysis targets cell-edge users in cooperative areas, where distances from cooperative base stations are approximated as equivalent and path loss is treated as constant.
- The derivation assumes m = 1 and i.i.d. zero-mean unit-variance complex Gaussian channel coefficients for desired and interfering signals.
- The integral expression is transformed using Meijer’s G-function to eliminate integral calculation and simplify parameters.
IV. NUMERICAL RESULTS AND DISCUSSION FOR MISO CAPACITY MODEL
Numerical analysis evaluates how cooperative antennas, cooperative base stations, and interfering-base-station density affect normalized downlink average capacity under the stated model assumptions. Cooperation improves capacity, but marginal gains decrease as antennas or cooperative base stations increase, while interference density strongly reduces capacity.
- Numerical setup: The analysis uses the derived co-channel-interference capacity model with specified channel parameters and cooperative-transmission assumptions.The numerical setup limits each base station to four cooperative-transmission antennas, uses two by default, and directly aggregates desired signals from multiple base stations.
- Cooperative antennas and BSs: 209% capacity improvement occurs when Co-Tx antennas per cooperative BS increase from 1 to 4 with CBS = 1.The corresponding improvements are 173% with CBS = 2 and 153% with CBS = 3.
- Cooperative antennas and BSs: 80.99% capacity improvement occurs when CBS increases from 1 to 2 with one antenna per cooperative BS.The improvement from CBS = 2 to 3 is 37.88%; with four antennas per cooperative BS, the corresponding gains are 50.9% and 27.62%.
- Cooperative antennas and BSs: Capacity performance improves with more cooperative antennas or base stations, but the increment of capacity performance decreases.This establishes diminishing capacity gains as cooperation resources increase.
- Interfering-BS density: Cooperative transmission improves capacity performance, especially with high interfering-BS density, but its gain decreases as cooperative BSs increase.The density parameter can obviously decrease capacity performance in the multi-cell MISO network.
- Interfering-BS density: At density 0.5 × 10^-6m^-2, two cooperative BSs improve average capacity by 48.76% over one BS, while three improve it by 21.99% over two.At density 3.5×10^-6m^-2, the corresponding improvements are 90.98% and 43.81%, indicating stronger cooperation gains at high interfering-BS density.
V. CONCLUSIONS
The paper proposes an analytical co-channel interference model for multi-cell MIMO networks and derives exact and closed-form normalized downlink average capacities for MIMO and cell-edge MISO cooperative networks. Numerical results show that cooperative transmission improves capacity, especially with dense interfering base stations, while gains decline as cooperative antennas or base stations increase.
- It derives the exact normalized downlink average capacity for multi-cell MIMO cellular networks with co-channel interference.
- It derives a closed-form normalized downlink average capacity for cell-edge users in multi-cell MISO cooperative cellular networks with co-channel interference.
- The study proposes an analytical co-channel interference model for multi-cell MIMO cellular networks.
- Capacity gains decline as the number of cooperative base stations or antennas increases.
- Cooperative transmission improves capacity performance, especially when interfering base stations have high density.
Instantaneous Interference Power W
The figures depict aggregated-interference distribution, cooperative system and cluster structure, and capacity impacts from cooperative antennas and interfering-base-station density.
- The aggregated-interference probability density function is examined as the Nakagami shaping factor m varies.
- The cooperative system is illustrated in the presence of co-channel interference.
- A cooperative cluster structure is shown for the multi-cell MIMO cellular network.
- The number of Co-Tx antennas per cooperative base station is evaluated for its impact on normalized downlink average capacity in multi-cell MISO networks.
- The density of interfering base stations is evaluated for its impact on normalized downlink average capacity in multi-cell MISO networks.