[Paper Review] Multiplexing Analysis of Millimeter-Wave Massive MIMO Systems

Dian‐Wu Yue, Ha H. Nguyen+1 more|arXiv (Cornell University)|Jan 7, 2018

Millimeter-Wave Propagation and Modeling30 references3 citations

TL;DR

This paper analyzes spatial multiplexing in mmWave massive MIMO systems using a distributed antenna subarray architecture, deriving an asymptotic multiplexing gain formula that achieves $ K_rK_tar{L} $ gain as subarray antenna counts grow large. The results show that distributed subarrays significantly scale multiplexing gain compared to co-located arrays, with a derived diversity-multiplexing tradeoff providing design insights for mmWave systems.

ABSTRACT

This paper is concerned with spatial multiplexing analysis for millimeter-wave (mmWave) massive MIMO systems. For a single-user mmWave system employing distributed antenna subarray architecture in which the transmitter and receiver consist of Kt and Kr subarrays, respectively, an asymptotic multiplexing gain formula is firstly derived when the numbers of antennas at subarrays go to infinity. Specifically, assuming that all subchannels have the same average number of propagation paths L, the formula implies that by employing such a distributed antenna-subarray architecture, an exact average maximum multiplexing gain of KrKtL can be achieved. This result means that compared to the co-located antenna architecture, using the distributed antenna-subarray architecture can scale up the maximum multiplexing gain proportionally to KrKt. In order to further reveal the relation between diversity gain and multiplexing gain, a simple characterization of the diversity-multiplexing tradeoff is also given. The multiplexing gain analysis is then extended to the multiuser scenario. Moreover, simulation results obtained with the hybrid analog/digital processing corroborate the analysis results.

Motivation & Objective

• To analyze spatial multiplexing performance in mmWave massive MIMO systems using a distributed antenna subarray architecture.
• To derive an asymptotic multiplexing gain formula for single-user and multiuser scenarios when subarray antenna numbers approach infinity.
• To characterize the diversity-multiplexing tradeoff (DMT) in mmWave systems under the proposed architecture.
• To extend the analysis to conventional partially-connected RF structures and validate results via simulation.
• To quantify the performance gain of distributed subarrays over co-located antenna arrays in terms of multiplexing and diversity gains.

Proposed method

• Derives an asymptotic multiplexing gain formula for a single-user mmWave system with $ K_t $ transmit and $ K_r $ receive subarrays, assuming i.i.d. subchannels with $ \bar{L} $ average paths.
• Uses large-scale array asymptotics to show that the maximum multiplexing gain scales as $ K_rK_t\bar{L} $, independent of array geometry.
• Applies the diversity-multiplexing tradeoff (DMT) framework to characterize the joint tradeoff between diversity and multiplexing gains.
• Extends analysis to multiuser downlink and uplink systems with hybrid analog/digital beamforming, modeling the effective channel matrix as a product of RF and baseband precoders/combining matrices.
• Employs a narrowband flat fading model with uniform linear arrays (ULAs) and assumes optimal RF and baseband beamformers for each user.
• Derives closed-form expressions for multiplexing gain under given diversity gain constraints, using the formula $ G_m^{(i)} = \sum_{l=1}^{L_s^{(i)}} \left(1 - \frac{d^{(i)}}{L_s^{(i)} - l + 1}\right)^+ $ for each user.

Experimental results

Research questions

• RQ1 What is the asymptotic spatial multiplexing gain of a mmWave massive MIMO system using a distributed antenna subarray architecture as subarray size increases?
• RQ2 How does the distributed subarray architecture compare to co-located antenna arrays in terms of multiplexing gain scaling?
• RQ3 What is the diversity-multiplexing tradeoff (DMT) in mmWave massive MIMO systems under the distributed subarray architecture?
• RQ4 Can the derived multiplexing gain expressions be extended to multiuser downlink and uplink scenarios with hybrid precoding?
• RQ5 What is the achievable multiplexing gain under a given diversity gain constraint in multiuser mmWave systems?

Key findings

• The asymptotic maximum spatial multiplexing gain for a single-user system with $ K_t $ transmit and $ K_r $ receive subarrays is $ K_rK_t\bar{L} $, where $ \bar{L} $ is the average number of propagation paths per subchannel.
• This result implies that distributed subarrays can statistically scale the maximum multiplexing gain proportionally to $ K_rK_t $, offering a significant advantage over co-located arrays.
• For multiuser downlink, the total multiplexing gain under diversity gain $ d $ is $ G_m = K_u \sum_{l=1}^{K_bL} \left(1 - \frac{d}{K_bL - l + 1}\right)^+ $, with $ K_b $ as the number of RF chains.
• The uplink system achieves the same multiplexing gain expression as the downlink, indicating symmetric performance under the same conditions.
• The derived DMT characterization reveals a direct tradeoff between diversity and multiplexing gains, enabling system design tradeoffs based on QoS requirements.
• Simulation results with hybrid analog/digital processing confirm the analytical predictions, validating the derived multiplexing gain formulas.