Mixed Quality of Service in Cell-Free Massive MIMO

Cell-free massive multiple-input multiple-output (MIMO) is a potential key technology for fifth generation wireless communication networks. A mixed quality-of-service (QoS) problem is investigated in the uplink of a cell-free massive MIMO system where the minimum rate of non-real time users is maximized with per user power constraints whilst the rate of the real-time users (RTUs) meet their target rates. First an approximated uplink user rate is derived based on available channel statistics. Next, the original mixed QoS problem is formulated in terms of receiver filter coefficients and user power allocations which can iteratively be solved through two sub-problems, namely, receiver filter coefficient design and power allocation, which are dealt with using a generalized eigenvalue problem and geometric programming, respectively. Numerical results show that with the proposed scheme, while the rates of RTUs meet the QoS constraints, the $90%$-likely throughput improves significantly, compared to a simple benchmark scheme.

💡 Research Summary

This paper addresses the mixed quality‑of‑service (QoS) problem in the uplink of a cell‑free massive multiple‑input multiple‑output (MIMO) system, a promising architecture for fifth‑generation (5G) wireless networks. In a cell‑free deployment, a large number of access points (APs) equipped with multiple antennas are distributed over a coverage area and are connected to a central processing unit (CPU) via high‑capacity backhaul links. The authors consider two classes of users: real‑time users (RTUs) that require a predefined signal‑to‑interference‑plus‑noise ratio (SINR) to support latency‑sensitive services, and non‑real‑time users (NRTUs) for which fairness is expressed as maximizing the minimum achievable rate (or equivalently the minimum SINR).

The system model assumes K single‑antenna users, of which K₁ are RTUs, and M APs each with N antennas. Large‑scale fading coefficients βₘₖ capture path loss and shadowing, while small‑scale fading is modeled as independent complex Gaussian. During the pilot phase, each user transmits a τ‑symbol pilot sequence with power pₚ; the CPU obtains minimum‑mean‑square‑error (MMSE) channel estimates ˆgₘₖ that incorporate both the true channel and estimation noise.

For data transmission, each AP applies maximal‑ratio combining (MRC) to its N‑antenna received vector and forwards a weighted sum to the CPU. The CPU further combines the contributions from all APs using receiver filter coefficients uₘₖ. By taking expectations over the channel statistics, the authors derive a closed‑form approximate uplink SINR expression (equations (4)–(5)). This expression is a rational function of the user transmit powers qₖ and the filter coefficients uₘₖ, with a quadratic numerator (desired signal power) and a denominator that aggregates beamforming uncertainty, inter‑user interference, and thermal noise.

The mixed QoS optimization problem is then formulated: (i) each RTU must achieve SINR ≥ SINRₜₖ, (ii) each user’s transmit power is bounded by 0 ≤ qₖ ≤ pₘₐₓₖ, and (iii) the minimum SINR among NRTUs is maximized. The resulting problem, denoted P₁, is non‑convex because the variables uₘₖ and qₖ appear jointly in both numerator and denominator.

To overcome this difficulty, the authors decompose P₁ into two sub‑problems that are solved iteratively:

1. Receiver filter design (P₂). With the powers qₖ fixed, the SINR maximization with respect to uₘₖ reduces to a generalized eigenvalue problem of the form
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