# Resource-Efficient Multicast URLLC Service in 5G Systems
## 2 System Model and Problem Statement  
Consider a gNB providing the multicast URLLC service for \(N\) UEs (see Figure 1). We suppose that all UEs are connected to the gNB. Thus, the gNB allocates uplink resources for transmission of uplink control information (e.g., UE feedback) and Sounding Reference Signals (SRSs) (tspecifications introduce both multicast and broadcast modes. In contrast to multicast mode, broadcast mode allows transmitting to UEs not connected to the gNB. In broadcast mode, UEs do not send any feedback, and the gNB cannot guarantee strict URLLC requirements [8]). The QoS requirements of an mURLLC stream are as follows: (i) the latency for each packet (i.e., the time interval between packet arrival at the gNB and \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Problem** & **Multicast eMBB** & **Multicast URLLC** & **Unicast URLLC** \\ \hline The maximum number of transmission attempts (TXs) & One TX attempt & Two TX attempts (if the delay budget allows, use HARQ retransmissions) & Two TX attempts (if the delay budget allows, use HARQ retransmissions) & Two TX attempts (if the delay budget allows, use HARQ retransmissions) \\ \hline Feedback Scheme & No feedback & X & NACK-only feedback & X & ACK/NACK feedback \\ \hline Sounding period & The optimal period is scenario-dependent & X & Optimization of the sounding period is for low-mobility scenarios & The optimal period is scenario-dependent \\ \hline Precoder selection & QR, SBFC, IU, MU, SCA-ADMM, FF-C2,RC-C2. & QR, SBFC, IU, FF-C2,RC-C2. & MRT, ZF, MMSE \\ \hline Scheduler & FS PF and its modifications. & Multicast adaptation of (non-)FS EDF & FS EDF \\ \hline MCS selection & Fixed subtraction (eOLLA) & Multicast adaptation of OLLA with two target BLERs & OLLA \\ \hline \end{tabular}
\end{table} 
Table 1: Inheritance of Multicast URLLC Solutions from Multicast eMBB and Unicast URLLC Solutions. its delivery to all UEs in the multicast group) shall not exceed \(D^{QoS}\) and (ii) the Packet Loss Ratio (PLR) shall be lower than \(PLR^{QoS}\). A multicast packet is considered lost if it is not delivered within a given latency budget to at least one UE. The typical values of \(D^{QoS}\) and reliability (i.e., \(1-PLR^{QoS}\)) for mURLLC traffic are provided at the beginning of Section 1. We consider an M-MIMO system: the gNB is equipped with a large number \(M\) of antennas. To simplify the description, we consider single antenna UEs. However, the results can be easily extended for multi-antenna UEs. To provide efficient M-MIMO operation, the gNB uses a Time Division Duplex (TDD) scheme with a periodic structure of downlink (DL) and uplink (UL) time slots, which have equal duration \(T_{slot}\). Specifically, \(k_{dl}\) DL slots used for data transmission are followed by \(k_{ul}\) UL slots used for UE feedback and/or Sounding Reference Signals (SRSs). SRSs are transmitted by UEs with the period \(T_{SRS}\). Thanks to channel reciprocity in the case of TDD, the gNB can use SRSs to estimate both DL and UL channel quality. In a frequency domain, each slot is divided into \(B\) Resource Blocks (RBs), where \(B\) depends on the bandwidth and the used numerology. For each multicast stream, the gNB solves the following problems, see Table 2. First, in the long-term timescale, the gNB configures the maximum number of transmission attempts (including HARQ retransmissions) and selects the feedback scheme and the sounding period \(T_{SRS}\). Second, in the short-term timescale, i.e., for each transmission attempt, the gNB dynamically: (i) constructs a precoder in each RB, (ii) allocates RBs taking into account their quality and the current buffer size, and (iii) selects an MCS. Since the 3 GPP does not describe how to address these problems, in the following sections, we consider various solutions and evaluate which of them can provide resource-efficient mURLLC service, i.e., provide low overall (DL + UL) channel resource consumption while satisfying strict mURLLC requirements.