MU-MISO Wireless Systems

• MU-MISO is a wireless communication paradigm in which a multi-antenna base station simultaneously serves single-antenna users, facilitating spatial multiplexing and enhanced spectral efficiency.
• Key techniques such as linear precoding, beamforming, and user scheduling manage inter-user interference while optimizing power allocation and performance.
• Emerging research integrates hybrid beamforming, metasurface technologies, and learning-based optimization to improve energy efficiency, security, and scalability in next-generation networks.

Multi-user Multiple-input Single-output (MU-MISO) communication is a fundamental paradigm in modern wireless systems, characterizing downlink scenarios where a transmitter equipped with multiple antennas serves multiple single-antenna users. MU-MISO is central to the evolution of massive MIMO, millimeter-wave (mmWave) communications, reconfigurable intelligent surfaces, energy-efficient precoding, and several other key technologies shaping beyond-5G and 6G networks. This article systematically covers the physical principles, mathematical modeling, core methodologies, performance trade-offs, and emerging architectures of MU-MISO systems from a technical research perspective.

1. System Model and Channel Representations

In the canonical MU-MISO downlink setup, a base station (BS) with $M$ antennas communicates with $K$ users, each with a single antenna. The received signal at user $k$ is typically modeled as

$y_k = \mathbf{h}_k^H \mathbf{x} + n_k$

where $\mathbf{h}_k \in \mathbb{C}^M$ represents the channel vector to user $k$, $\mathbf{x} \in \mathbb{C}^M$ is the transmitted signal vector, and $n_k$ is additive white Gaussian noise. The system operates under a sum-power constraint $\mathbb{E}[\|\mathbf{x}\|^2] \leq P$.

The channel models are critical for MU-MISO design. In mmWave regimes and highly directional propagation environments, sparse line-of-sight (LoS) models such as the Uniform Random LoS (UR-LoS) are appropriate, expressing the channel as

$h_k = \alpha_k \sqrt{M} \mathbf{a}(\theta_k)$

with steering vector $\mathbf{a}(\theta)$ and complex gain $\alpha_k$ (Lee et al., 2014). In rich scattering or sub-6GHz bands, classical i.i.d Rayleigh or Rician fading models are assumed. Reconfigurable intelligent surface (RIS)-assisted systems or hybrid beamforming architectures further modify this model by incorporating channel matrices due to the presence of programmable reflecting/transmitting surfaces (Manasa et al., 13 Apr 2024, Jayalal et al., 2022).

2. Transmit Precoding and Beamforming Techniques

Selecting the transmit signal $\mathbf{x}$ given the channel state information (CSI) is the essence of MU-MISO. Techniques include:

• Linear Precoding: Schemes such as Zero-Forcing (ZF), Maximum Ratio Transmission (MRT), and Minimum Mean Squared Error (MMSE) precoding attempt to manage inter-user interference. ZF nulls all inter-user interference but can be power-inefficient at low SNR; MRT focuses energy in users’ directions but ignores interference; MMSE provides a trade-off.
• Randomly-Directional Beamforming (RDB): In mmWave analog architectures or when CSI is limited, RDB points beams in random spatial directions and relies on multi-user scheduling to capture “angle-matched” users (Lee et al., 2014).
• Hybrid Digital–Analog Beamforming: Hybrid schemes partition beamforming into analog and digital domains. Dynamic subarrays and low-resolution phase shifters allow flexible and energy-efficient architectures, where subarrays are dynamically associated with RF chains and analog beamformers are drawn from quantized candidate codebooks (Li et al., 2019).

These methods are adapted for particular hardware (e.g., constant envelope or quantized phase constraint for PA efficiency (Noll et al., 2017)), for SWIPT objectives (Krikidis et al., 2022), or for channel-coded transmission (Nguyen et al., 30 Oct 2024).

3. User Scheduling and Multiple Access Strategies

MU-MISO performance relies on both spatial and user diversity:

• Opportunistic Scheduling: In systems with many users, transmitting toward the strongest user/channel vector or best spatial alignment enables multiuser diversity gains (Lee et al., 2014, Kampeas et al., 2016).
• User Grouping: Grouping users with aligned spatial signatures and joint codeword design enables non-orthogonal multiple access and efficient superposition transmission, as realized by modulation-division (MD) schemes with uniquely decomposable constellation groups (UDCGs) (Dong et al., 2016).
• Rate Splitting Multiple Access (RSMA): RSMA divides user messages into common/super-common and private components, allowing part of user interference to be decoded and subtracted, which increases throughput especially under imperfect CSI (Amor et al., 21 Mar 2024).
• Physical-Layer Multicast with Queueing: For content-centric networks with repeated content requests, content-centric queuing and multicast beamforming optimize service delay and capacity, handled by the Simple Multicast Queue (SMQ) and its fairness-improved extensions (Raghu et al., 2021).

4. Performance Analysis and Scaling Laws

The limits of MU-MISO performance are quantified via capacity, achievable rate scaling, outage and security metrics:

• Fractional Rate Order (FRO): In highly directional mmWave RDB systems, the per-user or sum-rate scaling with the number of antennas $M$ and users $K$ is characterized by $$\gamma = \lim_{M\to\infty} \frac{\log \mathcal{R}}{\log M}$$. For RDB, a phase transition at $K \sim M^{1/2}$ is observed, with near-linear sum-rate scaling achievable when the number of users scales linearly with $M$ (Lee et al., 2014).
• Secrecy Outage and Scaling: In wiretap scenarios with many users/eavesdroppers, the net secrecy rate scales logarithmically with the ratio of the legitimate user pool to the eavesdropper pool, governed by the extremal values of chi-squared distributed channel norms (Kampeas et al., 2016). Achieving vanishing secrecy outage requires the number of users to scale according to $\Omega(n(\log n)^{t-1})$ for $t$ transmit antennas and $n$ eavesdroppers.
• Statistical SINR/OP Analysis: In RIS-aided systems, outage probability is analytically approximated using log-normal approximations for the complicated sums/products of propagation coefficients, with performance explicitly linked to physical deployment (e.g., the position and number of RIS elements) (Jayalal et al., 2022).
• Impact of Code-Aware Precoding: Channel-coded precoding (CCP) allows signal design to proactively allocate energy among symbols so as to minimize the resulting bit error rate after channel decoding. CCP can deliver up to 3 dB SNR gains, particularly in systems with low code rates or when $K \approx M$ (Nguyen et al., 30 Oct 2024).

5. Low-Complexity and Emerging Hardware Architectures

MU-MISO is evolving with new hardware and algorithmic innovations:

• Wave-Domain Signal Processing via Metasurfaces: Stacked intelligent metasurfaces (SIMs) use cascaded programmable layers to physically implement analog beamforming and precoding, reducing digital hardware complexity. Joint optimization over analog phases and transmit power allocation exploits the “over-the-air” computational capacity of SIMs (Liu et al., 14 Feb 2024, Liu et al., 9 Aug 2024).
• Reconfigurable Intelligent Metasurface Antennas (RIMSA): Contrasting conventional RIS, RIMSA directly serves as the radiating aperture with programmable phase per meta-atom, allowing phased analog combining at both the BS and the user transceivers. System sum-rate is maximized via alternating optimization over digital processing and product-manifold optimization for the unit-modulus constraints (Wei et al., 23 Jun 2025).
• Hybrid Active-Passive RIS: Inclusion of a small number of active elements in a passive RIS array (hybrid RIS) enables amplification of weak links, overcoming double-fading cascaded channels. Max–min rate optimization using alternating convex approximation yields up to 80% improvement in minimum user rate compared to passive RIS only (Nguyen et al., 2022).
• Constant Envelope and Quantized Precoding: For energy-constrained or hardware-limited scenarios, constant envelope and quantized PSK precoding with symbol-wise minimization of squared error achieves competitive BER with high energy efficiency, through gradient-based optimization and careful codebook design (Noll et al., 2017).

6. Advanced Optimization, Learning, and Implementation Techniques

The combinatorially large design space in MU-MISO—especially with discrete/analog constraints or large user/device numbers—motivates specialized algorithmic approaches:

• Fractional Programming (FP) and Block Coordinate Ascent: FP and auxiliary variable techniques allow nonconvex, coupled SINR-maximization objectives to be handled via tractable subproblems with closed-form updates, particularly for RIS and dual-functional RIS-aided systems (Ma et al., 2021, Wei et al., 23 Jun 2025).
• Manifold and ADMM-based Algorithms: Product-manifold optimization (PMO) is applied for optimizing unit-modulus (analog phase) variables (Wei et al., 23 Jun 2025); Alternating Direction Method of Multipliers (ADMM) and quadratic programming (QP) schemes enable scalable constructive interference-based block-level precoding (Wang et al., 2023).
• Learning-Driven Control: Deep reinforcement learning (DRL)—notably, DDPG for continuous parameter spaces and deep contextual bandit approaches—optimizes phase shifts and power allocation in real time with minimal overhead, outperforming AO in sum-rate for SIM-equipped systems under dynamic channel conditions (Liu et al., 14 Feb 2024, Liu et al., 9 Aug 2024, Stylianopoulos et al., 2022, Abdalla et al., 2022).
• Environment-Aware Codebooks: In RIS-assisted scenarios, off-line codebook generation (using statistical CSI and alternating optimization for both precoding and RIS configuration) followed by lightweight on-line adaptation (via codeword selection) achieves robust rate performance with controlled training overhead (Yu et al., 30 Mar 2024).

7. Application Contexts and Practical Implications

MU-MISO serves as the core enabler for diverse applications and system requirements:

• Millimeter-Wave Networks: Highly directional propagation and sparse scattering render RDB and multiuser scheduling schemes effective, eliminating the need for per-user CSI acquisition except for lightweight user feedback (Lee et al., 2014, Li et al., 2019).
• Smart Radio Environments with RIS and SIM: Large-scale passive or active RIS arrays, as well as stacked metasurfaces, allow programmable manipulation of the radio environment, substantially improving coverage, link reliability, and network energy efficiency. Robustness to estimation errors and deployment constraints is maintained via statistical codebooks and hybrid architectures (Ma et al., 2021, Liu et al., 9 Aug 2024, Manasa et al., 13 Apr 2024).
• Secure and Fair Content Delivery: Security and fairness are practical concerns in MU-MISO multicasting and content-centric delivery. Leveraging multiuser diversity, rate splitting, fairness-based queuing, and robust design mitigates effects of eavesdroppers or user heterogeneity (Kampeas et al., 2016, Raghu et al., 2021, Amor et al., 21 Mar 2024).
• Energy Harvesting and SWIPT: Vector perturbation, modulation-division, and carefully structured symbol shaping facilitate simultaneous wireless information and power transfer, balancing information throughput and energy delivery (Krikidis et al., 2022).

Summary Table: Key MU-MISO Directions

Theme	Representative Technique	Papers
Analog/hybrid beamforming	Dynamic subarrays, RIS/SIM configuration	(Li et al., 2019, Ma et al., 2021, Liu et al., 9 Aug 2024)
Multiuser Diversity	RDB, opportunistic scheduling, grouping	(Lee et al., 2014, Dong et al., 2016)
Precoding for special goals	Constant envelope, VP, CCP	(Noll et al., 2017, Krikidis et al., 2022, Nguyen et al., 30 Oct 2024)
Learning-based optimization	DRL (DDPG, bandit), environment codebook	(Liu et al., 14 Feb 2024, Stylianopoulos et al., 2022, Yu et al., 30 Mar 2024)
Security and fairness	Secrecy outage scaling, DSMQ, RSMA	(Kampeas et al., 2016, Raghu et al., 2021, Amor et al., 21 Mar 2024)

MU-MISO wireless systems constitute a core area at the intersection of information theory, signal processing, hardware architecture, optimization, and learning. State-of-the-art research leverages sophisticated beamforming, hybrid analog-digital designs, interpretable and learning-based adaptation, and application-aware optimization under practical constraints, providing robust and scalable physical-layer solutions for current and future wireless networks.