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Achievable DoF Bounds for Cache-Aided Asymmetric MIMO Communications

Mohammad NaseriTehrani, MohammadJavad Salehi, Antti Tölli

Abstract

This is an extended journal version of the conference paper published in ISIT 2025; submitted to IEEE Transactions on Communications (TCOM). Integrating coded caching (CC) into multiple-input multiple-output (MIMO) communications significantly enhances the achievable degrees of freedom (DoF). This paper investigates a practical cache-aided asymmetric MIMO configuration with cache ratio $γ$, where a server with $L$ transmit antennas communicates with $K$ users. The users are partitioned into $J$ groups, and each user in group $j$ has $G_j$ receive antennas. We propose four content-aware MIMO-CC strategies: \emph{min-$G$} enforces symmetry using the smallest antenna count among users; \emph{Grouping} maximizes intra-subset spatial multiplexing gain at the expense of some global caching gain; \emph{Super-grouping} aggregates users into optimized \emph{min-$G$}-based super-sets with identical effective receive multiplexing gains before applying \emph{Grouping} across them; and \emph{Phantom} redistributes spatial resources assuming ``phantom'' antennas at the users to bridge the performance gains of \emph{min-$G$} and \emph{Grouping}. We develop these asymmetric strategies under three reference symmetric CC placement-delivery policies with guaranteed linear decodability: a DoF-optimal policy achieving the optimal single-shot DoF, and two closed-form policies, namely combinatorial and linear cyclic low-complexity constructions, with the cyclic policy attaining DoF performance close to the others in many operating regimes. Analytical and numerical results demonstrate significant DoF improvements across various system configurations, and that policy-strategy combinations offer flexible trade-offs between DoF and subpacketization complexity.

Achievable DoF Bounds for Cache-Aided Asymmetric MIMO Communications

Abstract

This is an extended journal version of the conference paper published in ISIT 2025; submitted to IEEE Transactions on Communications (TCOM). Integrating coded caching (CC) into multiple-input multiple-output (MIMO) communications significantly enhances the achievable degrees of freedom (DoF). This paper investigates a practical cache-aided asymmetric MIMO configuration with cache ratio , where a server with transmit antennas communicates with users. The users are partitioned into groups, and each user in group has receive antennas. We propose four content-aware MIMO-CC strategies: \emph{min-} enforces symmetry using the smallest antenna count among users; \emph{Grouping} maximizes intra-subset spatial multiplexing gain at the expense of some global caching gain; \emph{Super-grouping} aggregates users into optimized \emph{min-}-based super-sets with identical effective receive multiplexing gains before applying \emph{Grouping} across them; and \emph{Phantom} redistributes spatial resources assuming ``phantom'' antennas at the users to bridge the performance gains of \emph{min-} and \emph{Grouping}. We develop these asymmetric strategies under three reference symmetric CC placement-delivery policies with guaranteed linear decodability: a DoF-optimal policy achieving the optimal single-shot DoF, and two closed-form policies, namely combinatorial and linear cyclic low-complexity constructions, with the cyclic policy attaining DoF performance close to the others in many operating regimes. Analytical and numerical results demonstrate significant DoF improvements across various system configurations, and that policy-strategy combinations offer flexible trade-offs between DoF and subpacketization complexity.
Paper Structure (20 sections, 4 theorems, 47 equations, 9 figures, 8 tables)

This paper contains 20 sections, 4 theorems, 47 equations, 9 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Asymmetric SISO-CC Networks
  4. Asymmetric MISO-CC Networks
  5. Symmetric MIMO-CC
  6. Subpacketization bottleneck
  7. Main Contributions
  8. System Model
  9. Reference Symmetric MIMO-CC Policies
  10. The DoF-optimized policy $(\mathrm{opt})$
  11. The combinatorial parallel links policy $(\mathrm{cmb})$
  12. The cyclic parallel links policy $(\mathrm{lin})$
  13. Primary asymmetric solutions
  14. The min-$G$ strategy
  15. The Grouping strategy
  16. ...and 5 more sections

Key Result

Lemma 1

The DoF of the Grouping strategy with the $\mathrm{opt}$ policy, denoted by $\mathrm{DoF}_{\mathrm{opt},{\mathcal{J}}}^*$, can be written as eq:total_DoF_grouping in Table tab:grouping-table.

Figures (9)

  • Figure 1: Asymmetric MIMO-CC downlink serving a target UE set ${\mathcal{K}}$ of size $K$, where all UEs has the same cache size $MF$ bits but heterogeneous Rx spatial multiplexing gains ${\mathsf{G}}_{k}$.
  • Figure 2: The min-$G$ delivery strategy. Spatial multiplexing capacity is fixed to with $\check{G}$ for all $k\in [K]$
  • Figure 3: The Grouping strategy with the spatial multiplexing capacity of $G_{j}$ and $K_{j}$ users in group $j\in{\mathcal{J}}$
  • Figure 4: User heterogeneity impact on DoF scaling under different strategies and policies. $L=14$, $\gamma = 0.2$, and $K_1 = 35-K_2$.
  • Figure 5: DoF comparison, hybrid vs primary strategies.
  • ...and 4 more figures

Theorems & Definitions (12)

  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 1
  • proof
  • Remark 2
  • ...and 2 more