Stochastic Successive Convex Approximation Research Articles

Secrecy Rate Maximization of RIS-Assisted SWIPT Systems: A Two-Timescale Beamforming Design Approach

Reconfigurable intelligent surfaces (RISs) achieve high passive beamforming gains for signal enhancement or interference nulling by dynamically adjusting their reflection coefficients. Their employment is particularly appealing for improving both the wireless security and the efficiency of radio frequency (RF)-based wireless power transfer. Motivated by this, we conceive and investigate a RIS-assisted secure simultaneous wireless information and power transfer (SWIPT) system designed for information and power transfer from a base station (BS) to an information user (IU) and to multiple energy users (EUs), respectively. Moreover, the EUs are also potential eavesdroppers that may overhear the communication between the BS and IU. We adopt <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">two-timescale</i> transmission for reducing the signal processing complexity as well as channel training overhead, and aim for maximizing the average worst-case secrecy rate achieved by the IU. This is achieved by jointly optimizing the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">short-term</i> transmit beamforming vectors at the BS (including information and energy beams) as well as the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long-term</i> phase shifts at the RIS, under the energy harvesting constraints considered at the EUs and the power constraint at the BS. The stochastic optimization problem formulated is non-convex with intricately coupled variables, and is non-smooth due to the existence of multiple EUs/eavesdroppers. No standard optimization approach is available for this challenging scenario. To tackle this challenge, we propose a smooth approximation aided stochastic successive convex approximation (SA-SSCA) algorithm. Furthermore, a low-complexity heuristic algorithm is proposed for reducing the computational complexity without unduly eroding the performance. Simulation results show the efficiency of the RIS in securing SWIPT systems. The significant performance gains achieved by our proposed algorithms over the relevant benchmark schemes are also demonstrated.

Hybrid Offline-Online Design for Reconfigurable Intelligent Surface Aided UAV Communication

This letter considers the reconfigurable intelligent surface (RIS)-aided unmanned aerial vehicle (UAV) communication systems in urban areas under the general Rician fading channel. A hybrid offline-online design is proposed to improve the system performance by leveraging both the statistical channel state information (S-CSI) and instantaneous channel state information (I-CSI). For the offline phase, we aim to maximize the expected average achievable rate based on the S-CSI by jointly optimizing the RIS’s phase-shift and UAV trajectory. The formulated stochastic optimization problem is difficult to solve due to its non-convexity. To tackle this problem, we propose an efficient algorithm by leveraging the stochastic successive convex approximation (SSCA) techniques. For the online phase, the UAV adaptively adjusts the transmit beamforming and user scheduling according to the effective I-CSI. Numerical results verify that the proposed hybrid design performs better than various benchmark schemes, and also demonstrate a favorable trade-off between system performance and CSI overhead.

An Optimization Framework for General Rate Splitting for General Multicast

Immersive video, such as virtual reality (VR) and multi-view videos, is growing in popularity. Its wireless streaming is an instance of general multicast, extending conventional unicast and multicast, whose effective design is still open. This paper investigates general rate splitting for general multicast. Specifically, we consider a multi-carrier single-cell wireless network where a multi-antenna base station (BS) communicates to multiple single-antenna users via general multicast. We consider linear beamforming at the BS and joint decoding at each user in the slow fading and fast fading scenarios. In the slow fading scenario, we consider the maximization of the weighted sum average rate, which is a challenging nonconvex stochastic problem with numerous variables. To reduce computational complexity, we decouple the original nonconvex stochastic problem into multiple nonconvex deterministic problems, one for each system channel state. Then, we propose an iterative algorithm for each deterministic problem to obtain a Karush-Kuhn-Tucker (KKT) point using the concave-convex procedure (CCCP). In the fast fading scenario, we consider the maximization of the weighted sum ergodic rate. This problem is more challenging than the one for the slow fading scenario, as it is not separable. First, we propose a stochastic iterative algorithm to obtain a KKT point using stochastic successive convex approximation (SSCA) and the exact penalty method. Then, we propose two low-complexity iterative algorithms to obtain feasible points with promising performance for two cases of channel distributions using approximation and CCCP. The proposed optimization framework generalizes the existing ones for rate splitting for various types of services. Finally, we numerically show substantial gains of the proposed solutions over existing schemes in both scenarios and reveal the design insights of general rate splitting for general multicast.

Latency Minimization for mmWave D2D Mobile Edge Computing Systems: Joint Task Allocation and Hybrid Beamforming Design

Mobile edge computing (MEC) and millimeter wave (mmWave) communications are capable of significantly reducing the network's delay and enhancing its capacity. In this paper we investigate a mmWave and device-to-device (D2D) assisted MEC system, in which user A carries out some computational tasks and shares the results with user B with the aid of a base station (BS). We assume partial offloading model and the task can be partitioned into two portions: the first part is computed locally at user A, while the second part is transmitted to the BS and computed by the MEC server. The computational results are then sent to user B through a D2D link and via the link from the BS to user B, respectively. To support computation offloading, both the users and the BS are equipped with multiple antennas and employ analog and digital (A/D) hybrid beamforming. Moreover, we propose a novel two-timescale joint hybrid beamforming and task allocation algorithm to reduce the system latency whilst cut down the required signaling overhead. Specifically, the high-dimensional analog beamforming matrices are updated in a frame-based manner based on the channel state information (CSI) samples, where each frame consists of a number of time slots, while the low-dimensional digital beamforming matrices and the offloading ratio are optimized more frequently relied on the low-dimensional effective channel matrices in each time slot. A stochastic successive convex approximation (SSCA) based algorithm is developed to design the long-term analog beamforming matrices. As for the short-term variables, the digital beamforming matrices are optimized relying on the innovative penalty-concave convex procedure (penalty-CCCP) for handling the mmWave non-linear transmit power constraint, and the offloading ratio can be obtained via the derived closed-form solution. Simulation results verify the effectiveness of the proposed algorithm by comparing the benchmarks.

Robust Beamforming for Active Reconfigurable Intelligent Omni-Surface in Vehicular Communications

Two key impediments to reconfigurable intelligent surface (RIS)-aided vehicular communications are, respectively, the double fading experienced by the signal on RIS-aided cascaded links and the high-mobility-induced intractability of acquiring channel state information (CSI). To overcome these challenges, a novel kind of RIS is presented in this paper, namely active reconfigurable intelligent omni-surface (RIOS), each element of which is supported by active loads, that concurrently transmits and reflects the incident signal amplified rather than just reflecting it as compared to the case of a passive reflecting-only RIS. We consider the use of an active RIOS to a vehicular communication system for mitigating double fading effect. Specifically, the active RIOS is mounted on the vehicle window to enhance transmission for users in the vehicle and for adjacent vehicles. We aim to jointly optimize the transmit precoding matrix at the base station (BS) and RIOS coefficient matrices to minimize the BS’s transmit power relying exclusively upon the imperfect knowledge of the large-scale CSI. To significantly relax the frequency of channel information updates, initially an efficient transmission protocol is put forward to reap the high active RIOS beamforming gain with low channel training overhead by appropriately tailoring the time-scale of CSI acquisition. Then, two algorithms, namely an alternating optimization (AO)-based algorithm and a constrained stochastic successive convex approximation (CSSCA)-based algorithm, are developed to tackle with the investigated resource allocation problem, whose pros and cons are elaborated, respectively. Simulation results substantiate the significant performance improvement of active RIOS as well as determine the validity and robustness of our proposed algorithms over various benchmark schemes.

Mixed-Timescale Deep-Unfolding for Joint Channel Estimation and Hybrid Beamforming

In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital beamforming is an essential technique for exploiting the potential array gain without using a dedicated radio frequency chain for each antenna. However, due to the large number of antennas, the conventional channel estimation and hybrid beamforming algorithms generally require high computational complexity and signaling overhead. In this work, we propose an end-to-end deep-unfolding neural network (NN) joint channel estimation and hybrid beamforming (JCEHB) algorithm to maximize the system sum rate in time-division duplex (TDD) massive MIMO. Specifically, the recursive least-squares (RLS) algorithm and stochastic successive convex approximation (SSCA) algorithm are unfolded for channel estimation and hybrid beamforming, respectively. In order to reduce the signaling overhead, we consider a mixed-timescale hybrid beamforming scheme, where the analog beamforming matrices are optimized based on the channel state information (CSI) statistics offline, while the digital beamforming matrices are designed at each time slot based on the estimated low-dimensional equivalent CSI matrices. We jointly train the analog beamformers together with the trainable parameters of the RLS and SSCA induced deep-unfolding NNs based on the CSI statistics offline. During data transmission, we estimate the low-dimensional equivalent CSI by the RLS induced deep-unfolding NN and update the digital beamformers. In addition, we propose a mixed-timescale deep-unfolding NN where the analog beamformers are optimized online, and extend the framework to frequency-division duplex (FDD) systems where channel feedback is considered. Simulation results show that the proposed algorithm can significantly outperform conventional algorithms with reduced computational complexity and signaling overhead.

Spectrum Sharing Among Multiple-Seller and Multiple-Buyer Operators of a Mobile Network: A Stochastic Geometry Approach

Sharing the spectrum among mobile network operators (MNOs) is a promising approach to improve the spectrum utilization and to increase the monetary income of MNOs. In this paper, we model a nonorthogonal spectrum sharing system for a large-scale cellular network where multiple seller MNOs lease their licensed sub-bands to several buyer MNOs. We first analyze the per-user expected rate and the per-MNO expected profit using stochastic geometry. Then, we formulate the joint problem of power control and licensed sub-band sharing to maximize the expected profit of all MNOs as a multiobjective optimization problem (MOOP) under the users' quality of service requirement and the nonnegative return on investment constraints. To transform the MOOP into a single objective form, we use a combination of the $\epsilon$-constraint and weighted sum methods. However, the transformed problem is nonconvex because of the presence of binary variables and nonconvex rate functions in the objective function and constraints. We address this problem by using a penalty function and approximating the nonconvex rate functions by a constrained stochastic successive convex approximation method. Finally, the numerical results show the correctness and performance of the proposed algorithm under various conditions.

Deep-Unfolding Beamforming for Intelligent Reflecting Surface Assisted Full-Duplex Systems

In this paper, we investigate an intelligent reflecting surface (IRS) assisted multi-user multiple-input multiple-output (MIMO) full-duplex (FD) system. We jointly optimize the active beamforming matrices at the access point (AP) and uplink users, and the passive beamforming matrix at the IRS to maximize the weighted sum-rate of the system. Since it is practically difficult to acquire the channel state information (CSI) for IRS-related links due to its passive operation and large number of elements, we conceive a mixed-timescale beamforming scheme. Specifically, the high-dimensional passive beamforming matrix at the IRS is updated based on the channel statistics while the active beamforming matrices are optimized relied on the low-dimensional real-time effective CSI at each time slot. We propose an efficient stochastic successive convex approximation (SSCA)-based algorithm for jointly designing the active and passive beamforming matrices. Moreover, due to the high computational complexity caused by the matrix inversion computation in the SSCA-based optimization algorithm, we further develop a deep-unfolding neural network (NN) to address this issue. The proposed deep-unfolding NN maintains the structure of the SSCA-based algorithm but introduces a novel non-linear activation function and some learnable parameters induced by the first-order Taylor expansion to approximate the matrix inversion. In addition, we develop a black-box NN as a benchmark. Simulation results show that the proposed mixed-timescale algorithm outperforms the existing single-timescale algorithm and the proposed deep-unfolding NN approaches the performance of the SSCA-based algorithm with much reduced computational complexity when deployed online.

Sample-Based and Feature-Based Federated Learning for Unconstrained and Constrained Nonconvex Optimization via Mini-batch SSCA

Federated learning (FL) has become a hot research area in enabling the collaborative training of machine learning models among multiple clients that hold sensitive local data. Nevertheless, unconstrained federated optimization has been studied mainly using stochastic gradient descent (SGD), which may converge slowly, and constrained federated optimization, which is more challenging, has not been investigated so far. This paper investigates sample-based and feature-based federated optimization, respectively, and considers both unconstrained and constrained nonconvex problems for each of them. First, we propose FL algorithms using stochastic successive convex approximation (SSCA) and mini-batch techniques. These algorithms can adequately exploit the structures of the objective and constraint functions and incrementally utilize samples. We show that the proposed FL algorithms converge to stationary points and Karush-Kuhn-Tucker (KKT) points of the respective unconstrained and constrained nonconvex problems, respectively. Next, we provide algorithm examples with appealing computational complexity and communication load per communication round. We show that the proposed algorithm examples for unconstrained federated optimization are identical to FL algorithms via momentum SGD and provide an analytical connection between SSCA and momentum SGD. Finally, numerical experiments demonstrate the inherent advantages of the proposed algorithms in convergence speeds, communication and computation costs, and model specifications.

Fairness-Oriented Multiple RIS-Aided mmWave Transmission: Stochastic Optimization Methods

In millimeter wave (mmWave) systems, it is challenging to ensure reliable communication links due to the high sensitivity to the presence of blockages. In order to improve the robustness of mmWave systems in the presence of random blockages, we consider the deployment of multiple reconfigurable intelligent surfaces (RISs) to enhance the spatial diversity gain, and the design of robust beamforming schemes based on stochastic optimization methods that minimize the maximum outage probability among multiple users so as to ensure fairness. Under the stochastic optimization framework, we adopt the stochastic majorization–minimization (SMM) method and the stochastic successive convex approximation (SSCA) method to construct deterministic surrogate problems at each iteration, and to obtain closed-form solutions of the precoding matrix at the base station (BS) and the beamforming vectors at the RISs. Both stochastic optimization methods are proved to converge to the set of stationary points of the original stochastic problems. Simulation results show that the proposed robust beamforming for RIS-aided systems can effectively compensate for the performance loss caused by the presence of random blockages, especially when the blockage probability is high.

Latency Minimization in Intelligent Reflecting Surface Assisted D2D Offloading Systems

In this letter, we investigate an intelligent reflecting surface (IRS) aided device-to-device (D2D) offloading system, where an IRS is employed to assist in computation offloading from a group of users with intensive tasks to another group of idle users. To minimize the system latency while cutting down the heavy overhead in exchange of channel state information (CSI), we study the joint design of beamforming and resource allocation on mixed timescales. Specifically, the high-dimensional passive beamforming vector at the IRS is updated in a frame-based manner based on the channel statistics, where each frame consists of a number of time slots, while the offloading ratio and user matching strategy are optimized relied on the low-dimensional real-time effective channel coefficients in each time slot. A novel mixed-integer stochastic successive convex approximation (MISSCA) algorithm is proposed to tackle the challenging problem. The convergence property and the computational complexity of the proposed algorithm are then examined. Simulation results show that our proposed algorithm significantly outperforms the conventional benchmarks.

On Spectral Efficiency for Multiuser MISO Systems Under Imperfect Channel Information

We consider downlink transmission whereby a multiantenna base station simultaneously transmits data to multiple single-antenna users. We focus on slow flat fading channel where the channel state information is imperfect, the channel estimation error is unbounded and its statistics are known. The aim is to design beamforming vectors such that the sum rate is maximized under the constraints on probability of successful transmission for each user and maximum transmit power. The optimization problem is intractable due to the chance constraints. To this end, we propose an efficient solution drawn upon stochastic optimization. In particular, we first use the step function and its smooth approximation to get an approximate nonconvex stochastic program of the considered problem. We then develop an iterative procedure to solve the stochastic program based on the stochastic successive convex approximation framework. The numerical results show that the proposed solution can achieve remarkable sum rate gains compared to the conventional one.

Outage-Constrained Robust Beamforming for Intelligent Reflecting Surface Aided Wireless Communication

In intelligent reflecting surface (IRS) aided wireless communication systems, channel state information (CSI) is crucial to achieve its promising passive beamforming gains. However, CSI errors are inevitable in practice and generally correlated over the IRS reflecting elements due to the limited training with discrete phase shifts, which degrade the data transmission rate and reliability. In this paper, we focus on investigating the effect of CSI errors to the outage performance in an IRS-aided multiuser downlink communication system. Specifically, we aim to jointly optimize the active transmit precoding vectors at the access point (AP) and passive discrete phase shifts at the IRS to minimize the AP's transmit power, subject to the constraints on the maximum CSI-error induced outage probability for the users. First, we consider the single-user case and derive the user's outage probability in terms of the mean signal power (MSP) and variance of the received signal at the user. Since there is a trade-off in tuning these two parameters to minimize the outage probability, we propose to maximize their weighted sum with the optimal weight found by one-dimensional search. Then, for the general multiuser case, since the users' outage probabilities are difficult to obtain in closed-form due to the inter-user interference, we propose a novel constrained stochastic successive convex approximation (CSSCA) algorithm, which replaces the non-convex outage probability constraints with properly designed convex surrogate approximations. Simulation results verify the effectiveness of the proposed robust beamfoming algorithms and show their significant performance improvement over various benchmark schemes.

Two-Stage Stochastic Optimization Via Primal-Dual Decomposition and Deep Unrolling

We consider a two-stage stochastic optimization problem, in which a long-term optimization variable is coupled with a set of short-term optimization variables in both objective and constraint functions. Despite that two-stage stochastic optimization plays a critical role in various engineering and scientific applications, there still lack efficient algorithms, especially when the long-term and short-term variables are coupled in the constraints. To overcome the challenge caused by tightly coupled stochastic constraints, we first establish a two-stage primal-dual decomposition (PDD) method to decompose the two-stage problem into a long-term problem and a family of short-term subproblems. Then we propose a PDD-based stochastic successive convex approximation (PDD-SSCA) algorithmic framework to find KKT solutions for two-stage stochastic optimization problems. At each iteration, PDD-SSCA first runs a short-term sub-algorithm to find stationary points of the short-term subproblems associated with a mini-batch of the state samples. Then it constructs a convex surrogate for the long-term problem based on the deep unrolling of the short-term sub-algorithm and the back propagation method. Finally, the optimal solution of the convex surrogate problem is solved to generate the next iterate. We establish the almost sure convergence of PDD-SSCA and customize the algorithmic framework to solve two important application problems. Simulations show that PDD-SSCA can achieve superior performance over existing solutions.

Power Minimization for Massive MIMO Over-the-Air Computation With Two-Timescale Hybrid Beamforming

This letter studies the massive multiple-input multiple-output (MIMO) analog uncoded over-the-air computation (AirComp), which is a promising solution in Internet-of-Things (IoT) networks for fusion centers (FCs) to compute functions of data distributed in a large number of wireless devices (WDs). To avoid the heavy overhead of the perfect real-time channel state information (CSI) estimation, we develop a two-timescale hybrid beamforming (THB) scheme in AirComp. Under this setup, we aim to minimize the transmit power over time, while ensuring a minimum required computation distortion in terms of the mean-squared error (MSE). We propose a constrained stochastic successive convex approximation (CSSCA) based algorithm to solve the formulated stochastic non-convex optimization problem for the THB design. Specifically, the short-timescale receive digital beamforming matrix at the FC is optimized at each time slot based on the real-time effective low-dimensional CSI matrices by a sum-minimization-mean-squared-error (sum-MMSE) receiver, which can better deal with the signal misalignment. By contrast, the long-timescale transmit beamforming matrix at WDs and the receive analog beamforming matrix at the FC are designed based on the available channel statistics and updated in a frame-based manner, where a frame contains a fixed number of time slots. Numerical results show that the proposed THB design algorithm achieves similar transmit power performance as that achieved by the design when the perfect real-time CSI is available.

Stochastic Hybrid Combining Design for Quantized Massive MIMO Systems

Both the power-dissipation and cost of massive multiple-input multiple-output (mMIMO) systems may be substantially reduced by using low-resolution analog-to-digital converters (LADCs) at the receivers. However, both the coarse quantization of LADCs and the inaccurate instantaneous channel state information (ICSI) degrade the performance of quantized mMIMO systems. To overcome these challenges, we propose a novel stochastic hybrid analog-digital combiner (SHC) scheme for adapting the hybrid combiner to the long-term statistics of the channel state information (SCSI). We seek to minimize the transmit power by jointly optimizing the SHC subject to average rate constraints. For the sake of solving the resultant nonconvex stochastic optimization problem, we develop a relaxed stochastic successive convex approximation (RSSCA) algorithm. Simulations are carried out to confirm the benefits of our proposed scheme over the benchmarkers.

High-Mobility Multi-Modal Sensing for IoT Network via MIMO AirComp: A Mixed-Timescale Optimization Approach

Multiple-input-multiple-output (MIMO) over-the-air Computation (AirComp) is a promising technique for implementing high-mobility multi-modal sensing (HMS) to compute multiple target functions of distributed data by leveraging the superposition property of wireless multi-access channel, thereby significantly improving the computation efficiency as compared to the traditional orthogonal multi-access scheme. However, two obstacles constraining the potential gain of MIMO AirComp are high hardware cost and power consumption, and huge channel state information (CSI) signaling overhead. To overcome these challenges, we propose a novel mixed-timescale hybrid combining (MHC) scheme to minimize the average mean-square error (MSE) under some practical constraints in the uplink of a IoT network. Specifically, the radio frequency (RF) combiner is adapted to the long-term statistical CSI, while the baseband combiner is adapted to the real-time effective CSI. In order to tackle the resulting stochastic nonconvex optimization problem, we devise a mixed-timescale stochastic successive convex approximation (MSCA) algorithm. Simulation results are presented to verify the effectiveness of our proposed scheme over the state-of-the-art baselines.

Two-Timescale Hybrid Analog-Digital Beamforming for mmWave Full-Duplex MIMO Multiple-Relay Aided Systems

Due to the severe pathloss experienced by electromagnetic waves in the millimeter wave (mmWave) band, a substantial challenge in their design is to have an adequate coverage area. With the objective of improving the coverage area and the sum rate attained, we conceive new full-duplex (FD) mmWave multiple-input multiple-output (MIMO) multiple-relay systems. Specifically, we propose a novel two-timescale analog-digital hybrid beamforming scheme for maximizing the sum rate, while reducing the system's complexity and the channel state information (CSI) signalling overhead, as well as mitigating both the effects of self-interference and that of outdated CSIs caused by the associated delays. In the proposed scheme, the long-timescale analog beamforming matrices are designed based on the available channel statistics and updated in a frame-based manner, where a frame contains a fixed number of time slots. By contrast, the short-timescale digital beamforming matrices are optimized more frequently - namely for each time slot - based on the low-dimensional effective CSI matrices available on a real-time basis. We develop both an efficient analog beamforming algorithm based on the cut-set bound as well as on stochastic successive convex approximation (SSCA) and an innovative digital beamforming algorithm that relies on the theory of penalty dual decomposition (PDD), where our design objective is to maximize the system's sum rate. Both the convergence properties and the computational complexity of the proposed algorithms are also examined. Our simulation results show that the proposed two-timescale hybrid beamforming design significantly outperforms the conventional beamformers both in terms of requiring a lower CSI-signalling overhead and a higher sum rate in the face of realistic outdated CSIs.

A Deep Reinforcement Learning-Based Transcoder Selection Framework for Blockchain-Enabled Wireless D2D Transcoding

The boom of video streaming industry has resulted in the increasing demands for transcoding services from heterogeneous users. Recent advances of blockchain technology allow some startups to realize decentralized collaborative transcoding through device-to-device (D2D) networks, where a group of transcoders are selected to perform transcoding cooperatively. For the blockchain-enabled D2D transcoding systems, it's imperative to jointly design transcoder selection, task scheduling and resource allocation schemes in order to provide efficient and trustworthy transcoding services. In this paper, viewing the involved multi-dimensional complex factors and channel fluctuation, we propose a novel deep reinforcement learning (DRL) based transcoder selection framework for blockchain enabled D2D transcoding systems where both the platform dynamics and channel statistics are captured. To reduce the action space size, we adopt a two-stage decision approach to first select the transcoders through a normal DRL based framework and then obtain the optimal task scheduling, power control, and resource allocation scheme by solving a stochastic optimization problem with the constrained stochastic successive convex approximation (CSSCA) approach. Simulation results show that our proposed framework can achieve high transcoding revenue while meeting the quality of service (QoS) requirements, and it can well handle dynamic cases.

Randomized Channel Sparsifying Hybrid Precoding for FDD Massive MIMO Systems

We propose a novel randomized channel sparsifying hybrid precoding (RCSHP) design to reduce the signaling overhead of channel estimation and the hardware cost and power consumption at the base station (BS), in order to fully harvest benefits of frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. RCSHP allows time-sharing among multiple analog precoders, each serving a compatible user group. The analog precoder is adapted to the channel statistics to properly sparsify the channel for the associated user group, such that the resulting effective channel (product of channel and analog precoder) not only has enough spatial degrees of freedom (DoF) to serve this group of users, but also can be accurately estimated under the limited pilot budget. The digital precoder is adapted to the effective channel based on the duality theory to facilitate the power allocation and exploit the spatial multiplexing gain. We formulate the joint optimization of the time-sharing factors and the associated sets of analog precoders and power allocations as a general utility optimization problem, which considers the impact of effective channel estimation error on the system performance. Then we propose an efficient stochastic successive convex approximation algorithm to provably obtain Karush-Kuhn-Tucker (KKT) points of this problem.