Achieving zero-shot adversarial robustness without sacrificing generalization remains challenging for foundation models such as CLIP, especially under large adversarial perturbations. Through empirical analyses, we identify three critical yet overlooked issues: (1) Logit margins exhibit a stable offset between small and large adversarial perturbations, suggesting that explicitly adjusting margins could improve robustness against unseen large perturbations. (2) A significant negative correlation exists between logit margin and inter-class semantic similarity, indicating that semantic structures are insufficiently leveraged by existing methods. (3) Existing methods for adjusting text embeddings disrupt the intrinsic semantic consistency established by pre-trained models, undermining generalization capability. Motivated by these findings, we propose a novel Text-Image Mutual Awareness (TIMA) framework, including a Text-Aware Image (TAI) tuning module with an Adaptive Semantic-Aware Margin (ASAM) to explicitly calibrate logit margins, and an Image-Aware Text (IAT) tuning module with Semantic Consistent Minimum Hyperspherical Energy (SC-MHE) to preserve semantic consistency. Comprehensive experiments validate that TIMA significantly outperforms existing approaches by effectively addressing the identified limitations.

A major challenge in Fine-Grained Visual Classification (FGVC) is distinguishing various categories with high inter-class similarity by learning the feature that differentiates the details. Conventional cross-entropy trained Convolutional Neural Network (CNN) fails this challenge as they may suffer from producing inter-class invariant features in FGVC. In this work, we innovatively propose to regularize the training of CNN by enforcing the uniqueness of the features of each category from an information-theoretic perspective. To achieve this goal, we formulate a minimax loss based on a game-theoretic framework, where a Nash equilibrium is proved to be consistent with this regularization objective. Besides, to avoid getting a solution that produces redundant features, we present a Feature Redundancy Loss (FRL) based on the normalized inner product between each selected feature map pair to complement the proposed minimax loss. The proposed method is versatile, as it can be utilized as a regularizer for features in the mid-level or the penultimate layer, and can be combined with any architectures. Extensive experimental results on several influential benchmarks along with visualization show that our method obtains significant improvement over the baseline model without extra cost and achieves state-of-the-art results.

Dual-functional radar-communication (DFRC) signal design has received much attention lately. We consider the scenario of one-bit massive multi-input multi-output (MIMO) wherein one-bit DACs are employed for the sake of saving hardware costs. Specifically, a spatial Sigma-Delta$(\Sigma \Delta)$modulation scheme is proposed for one-bit MIMO-DFRC waveform design. Unlike the existing approaches which require large-scale binary optimization, the proposed scheme performs$\Sigma \Delta$modulation on a continuous-valued DFRC signal. The subsequent waveform design is formulated as a constrained least square problem, which can be efficiently solved. Moreover, we leverage quantization noise for radar probing purposes, rather than treating it as unwanted noise. Numerical results demonstrate that the proposed scheme performs well in both radar probing and downlink precoding.

Deep learning draws heavily on the latest progress in semantic communications. The present paper aims to examine the security aspect of this cutting-edge technique from a novel shuffling perspective. Our goal is to improve upon the conventional secure coding scheme to strike a desirable tradeoff between transmission rate and leakage rate. To be more specific, for a wiretap channel, we seek to maximize the transmission rate while minimizing the semantic error probability under the given leakage rate constraint. Toward this end, we devise a novel semantic security communication system wherein the random shuffling pattern plays the role of the shared secret key. Intuitively, the permutation of feature sequences via shuffling would distort the semantic essence of the target data to a sufficient extent so that eavesdroppers cannot access it anymore. The proposed random shuffling method also exhibits its flexibility in working for the existing semantic communication system as a plugin. Simulations demonstrate the significant advantage of the proposed method over the benchmark in boosting secure transmission, especially when channels are prone to strong noise and unpredictable fading.

Transmitting data using the phases on reconfigurable intelligent surfaces (RIS) is a promising solution for future energy-efficient communication systems. Recent work showed that a virtual phased massive multiuser multiple-input-multiple-out (MIMO) transmitter can be formed using only one active antenna and a large passive RIS. In this paper, we are interested in using such a system to perform MIMO downlink precoding. In this context, we may not be able to apply conventional MIMO precoding schemes, such as the simple zero-forcing (ZF) scheme, and we typically need to design the phase signals by solving optimization problems with constant modulus constraints or with discrete phase constraints, which pose challenges in terms of incurring high computational costs. In this work, we propose an alternative approach based on Sigma-Delta (Σ∆) modulation, which is classically famous for its noise-shaping ability. Specifically, first-order Σ∆ modulation is applied in the spatial domain to handle phase quantization in generating constant envelope signals. Under some mild assumptions, the proposed phased Σ∆ modulator allows us to use the ZF scheme to synthesize the RIS reflection phases in a low complexity fashion. The proposed approach is empirically shown to achieve comparable bit error rate performance to the unquantized ZF scheme.

This study addresses the challenge of inaccurate gradients in computing the empirical Fisher Information Matrix during network pruning. We introduce SWAP, a formulation of Entropic Wasserstein regression (EWR) for network pruning, capitalizing on the geometric properties of the optimal transport problem. The “swap” of the commonly used linear regression with the EWR in optimization is analytically demonstrated to offer noise mitigation effects by incorporating neighborhood interpolation across data points with only marginal additional computational cost. The unique strength of SWAP is its intrinsic ability to balance noise reduction and covariance information preservation effectively. Extensive experiments performed on various networks and datasets show comparable performance of SWAP with state-of-the-art (SoTA) network pruning algorithms. Our proposed method outperforms the SoTA when the network size or the target sparsity is large, the gain is even larger with the existence of noisy gradients, possibly from noisy data, analog memory, or adversarial attacks. Notably, our proposed method achieves a gain of 6% improvement in accuracy and 8% improvement in testing loss for MobileNetV1 with less than one-fourth of the network parameters remaining.

Fractional programming (FP) arises in various communications and signal processing problems because several key quantities in the field are fractionally structured, e.g., the Cramér-Rao bound, the Fisher information, and the signal-to-interference-plus-noise ratio (SINR). A recently proposed method called the quadratic transform has been applied to the FP problems extensively. The main contributions of the present paper are two-fold. First, we investigate how fast the quadratic transform converges. To the best of our knowledge, this is the first work that analyzes the convergence rate for the quadratic transform as well as its special case the weighted minimum mean square error (WMMSE) algorithm. Second, we accelerate the existing quadratic transform via a novel use of Nesterov's extrapolation scheme [2]. Specifically, by generalizing the minorization-maximization (MM) approach in [3], we establish a nontrivial connection between the quadratic transform and the gradient projection, thereby further incorporating the gradient extrapolation into the quadratic transform to make it converge more rapidly. Moreover, the paper showcases the practical use of the accelerated quadratic transform with two frontier wireless applications: integrated sensing and communication (ISAC) and massive multiple-input multiple-output (MIMO).

Artificial intelligence (AI) is critical in evolving 5G and developing 6G networks, running on edge devices, and solving resource management challenges. The burgeoning number of edge devices draws attention to the potential of low-earth orbit (LEO) satellite networks with their onboard computing capabilities for edge inference. This paper explores LEO scenarios where multiple remote sensing edge AI inference tasks concurrently process data from a single source. However, due to there being parts with the same functions between different AI applications, traditional monolithic edge AI architecture must be deployed repeatedly and falls short in efficiently harnessing the heterogeneous resources of LEO satellite networks. To solve this problem, we utilize the microservice architecture to decouple a single AI application into several independent microservices to reuse these same functions. However, due to the high latency caused by multiple microservices’ communication, we need to design a deployment strategy to fully utilize resources to reduce the service latency. We present a microservice deployment model to minimize the total service latency across all AI applications and meet resource constraints with the constraints of hardware, energy, and memory limitations. This latency optimization problem is rewritten as a Markov decision process (MDP) to effectively deal with the challenge posed by the time-varying transmission rate caused by satellite mobility. To increase the training data utilization, we employ a Proximal Policy Optimization (PPO) based reinforcement learning algorithm to meet the dynamic environment challenge. Finally, we obtain a sub-optimal solution with minimal accuracy loss and an acceptable solution time.

Fractional programming (FP) arises in various communications and signal processing problems because several key quantities in these fields are fractionally structured, e.g., the Cramér-Rao bound, the Fisher information, and the signal-to-interference-plus-noise ratio (SINR). A recently proposed method called the quadratic transform has been applied to the FP problems extensively. The main contributions of the present paper are two-fold. First, we investigate how fast the quadratic transform converges. To the best of our knowledge, this is the first work that analyzes the convergence rate for the quadratic transform as well as its special case the weighted minimum mean square error (WMMSE) algorithm. Second, we accelerate the existing quadratic transform via a novel use of Nesterov’s extrapolation scheme. Specifically, by generalizing the minorization-maximization (MM) approach, we establish a subtle connection between the quadratic transform and the gradient projection, thereby further incorporating the gradient extrapolation into the quadratic transform to make it converge more rapidly. Moreover, the paper showcases the practical use of the accelerated quadratic transform with two frontier wireless applications: integrated sensing and communications (ISAC) and massive multiple-input multiple-output (MIMO).

This paper investigates the information theoretic limit of a reconfigurable intelligent surface (RIS) aided communication scenario in which the RIS and the transmitter either jointly or independently send information to the receiver. The RIS is an emerging technology that uses a large number of passive reflective elements with adjustable phases to intelligently reflect the transmit signal to the intended receiver. While most previous studies of the RIS focus on its ability to beamform and to boost the received signal-to-noise ratio (SNR), this paper shows that if the information data stream is also available at the RIS and can be modulated through the adjustable phases at the RIS, significant improvement in the degree-of-freedom (DoF) of the overall channel is possible. For example, for an RIS system in which the signals are reflected from a transmitter with$M$antennas to a receiver with$K$antennas through an RIS with$N$reflective elements, assuming no direct path between the transmitter and the receiver, joint transmission of the transmitter and the RIS can achieve a DoF of$\min \left({M+\frac {N}{2}-\frac {1}{2},N,K}\right)$as compared to the DoF of$\min (M,K)$for the conventional multiple-input multiple-output (MIMO) channel. This result is obtained by establishing a connection between the RIS system and the MIMO channel with phase noise and by using results for characterizing the information dimension under projection. The result is further extended to the case with a direct path between the transmitter and the receiver, and also to the multiple access scenario, in which the transmitter and the RIS send independent information. Finally, this paper proposes a symbol-level precoding approach for modulating data through the phases of the RIS, and provides numerical simulation results to verify the theoretical DoF results.

Reconfigurable Intelligent Surfaces (RIS) have emerged as a key component in wireless communication and sensing systems, offering the potential to significantly enhance network performance. However, due to the passive nature of RIS, most existing studies focus on the cascaded channels from the transmitter (TX) through RIS to the users, leaving a gap in our understanding of the channel between the TX and RIS. This paper addresses this lacuna by proposing a novel channel estimation protocol specifically designed for the TX-RIS link. This new protocol provides a foundation for a more complete understanding and optimization of RIS-aided wireless communication and sensing systems. Our methodology deploys a least squares (LS) estimator, for which we utilize a matrix eigenvalue decomposition method. We prove that our proposed two-step approach is optimal under appropriate pilot and reflective coefficient design. Simulation results verified the viability of the proposed method.

Deep learning and natural language processing draw heavily on the recent progress in semantic communications; this paper examines the security aspect of this cutting-edge technique. Our goal is to improve upon the conventional secure coding methods to strike a superior tradeoff between transmission rate and leakage rate. Toward this end, we devise a novel semantic security communication system wherein the random shuffling pattern serves as the secret key shared. Intuitively, the permutation of words in the same text via shuffling would result in the meaning distortion of the target text to such a great extent that an eavesdropper can no longer recover the semantic truth. The proposed method can be rephrased as maximizing the transmission rate while minimizing the semantic error probability under the given leakage rate constraint. Simulations demonstrate the significant advantage of the proposed method over the benchmark in boosting secure transmission, especially when channels are prone to strong noise and unpredictable fading, can achieve up to 60% performance gain.

Channel acquisition is one of the main challenges for the deployment of reconfigurable intelligent surface (RIS) aided communication systems. This is because an RIS has a large number of reflective elements, which are passive devices with no active transmitting/receiving abilities. In this paper, we study the channel estimation problem for the RIS aided multi-user millimeter-wave (mmWave) multi-input multi-output (MIMO) system. Specifically, we propose a novel channel estimation protocol for the above system to estimate the cascaded channels, which are the products of the channels from the base station (BS) to the RIS and from the RIS to the users. Further, since the cascaded channels are typically sparse, this allows us to formulate the channel estimation problem as a sparse recovery problem using compressive sensing (CS) techniques, thereby allowing the channels to be estimated with less training overhead. Moreover, the sparse channel matrices of the cascaded channels of all users have a common block sparsity structure due to the common channel between the BS and the RIS. To take advantage of the common sparsity pattern, we propose a two-step multi-user joint channel estimation procedure. In the first step, we make use of the common column-block sparsity and project the received signals onto the common column subspace. In the second step, we make use of the row-block sparsity of the projected signals and propose a multi-user joint sparse matrix recovery algorithm that takes into account the common channel between the BS and the RIS.

This paper investigates the information theoretical limit of a reconfigurable intelligent surface (RIS) aided communication scenario in which the RIS and the transmitter jointly send information to the receiver. The RIS is an emerging technology that uses a large number of passive reflective elements with adjustable phases to intelligently reflect the transmit signal to the intended receiver. While most previous studies of the RIS focus on its ability to beamform and to boost the received signal-to-noise ratio (SNR), this paper shows that if the information data stream is available both at the transmitter and the RIS and the phases at the RIS can be used to modulate data, then the multiplexing gain of the overall channel can potentially be significantly enhanced. Specifically, we show that in a multiple-input multiple-output (MIMO) channel with$M$transmit antennas and$K$receive antennas, a RIS with$N$reflective elements can improve the multiplexing gain from min(M, K) to min(M + N/2 - 1/2,$N$, K). This result is obtained by establishing a connection between the RIS system and the MIMO channel with phase noises and using results for characterizing the information dimension under projection.

Intelligent reflecting surface (IRS), which consists of a large number of tunable reflective elements, is capable of enhancing the wireless propagation environment in a cellular network by intelligently reflecting the electromagnetic waves from the base-station (BS) toward the users. The optimal tuning of the phase shifters at the IRS is, however, a challenging problem, because due to the passive nature of reflective elements, it is difficult to directly measure the channels between the IRS, the BS, and the users. Instead of following the traditional paradigm of first estimating the channels then optimizing the system parameters, this paper advocates a machine learning approach capable of directly optimizing both the beamformers at the BS and the reflective coefficients at the IRS based on a system objective. This is achieved by using a deep neural network to parameterize the mapping from the received pilots (plus any additional information, such as the user locations) to an optimized system configuration, and by adopting a permutation invariant/equivariant graph neural network (GNN) architecture to capture the interactions among the different users in the cellular network. Simulation results show that the proposed implicit channel estimation based approach is generalizable, can be interpreted, and can efficiently learn to maximize a sum-rate or minimum-rate objective from a much fewer number of pilots than the traditional explicit channel estimation based approaches.

Intelligent reflecting surface (IRS), consisting of massive number of tunable reflective elements, is capable of boosting spectral efficiency between a base station (BS) and a user by intelligently tuning the phase shifters at the IRS according to the channel state information (CSI). However, due to the large number of passive elements which cannot transmit and receive signals, acquisition of CSI for IRS is a practically challenging task. Instead of using the received pilots to estimate the channels explicitly, this paper shows that it is possible to learn the effective IRS reflection pattern and beamforming at the BS directly based on the received pilots. This is achieved by parameterizing the mapping from the received pilots to the optimal configuration of IRS and the beamforming matrix at the BS by properly tuning a deep neural network using unsupervised training. Simulation results indicate that the proposed neural network can efficiently learn to maximize the system sum rate from much fewer received pilots as compared to the traditional channel estimation based solutions.

This paper proposes an autoencoder-based symbol-level precoding (SLP) scheme for a massive multiple-input multiple-output (MIMO) system operating in a limited-scattering environment. By recognizing that only imperfect channel state information (CSI) is available in practice, the goal of the proposed approach is to design the down-link SLP system robust to such imperfect CSI. Toward this goal, this paper leverages the concept of autoencoder wherein the end-to-end communications system is modeled by a deep neural network. By end-to-end training the proposed autoencoder, this paper shows that the downlink symbol-level precoder as well as the receivers' decision rule can be jointly designed in ways that are robust to channel uncertainty. Moreover, this paper introduces a novel two-step training procedure to design a robust precoding scheme for conventional modulations such as quadrature amplitude modulation (QAM) and phase shift keying (PSK). Numerical results indicate that the proposed autoencoder-based framework, either trained by the end-to-end approach in which the receive constellation is a design variable or by the proposed two-step training approach with QAM constellation, can efficiently design a SLP scheme for massive MIMO system which is robust to channel uncertainty.

Symbiotic radio (SR) is emerging as a spectrum-and energy-efficient communication paradigm for future passive Internet of Things (IoT), where some single-antenna backscatter devices, referred to as Tags, are parasitic in an active primary transmission. The primary transceiver is designed to assist both direct-link (DL) and backscatter-link (BL) communication. In multi-Tags SR systems, the transceiver designs become much more complicated due to the presence of DL and inter-Tag interference, which further poses new challenges to the availability and reliability of DL and BL transmission. To overcome these challenges, we formulate the stochastic optimization of transceiver design as the general network utility maximization problem (GUMP). The resultant problem is a stochastic multiple-ratio fractional nonconvex problem, and consequently challenging to solve. By leveraging some fractional programming techniques, we tailor a surrogate function with the specific structure and subsequently develop a batch stochastic parallel decomposition (BSPD) algorithm, which is shown to converge to stationary solutions of the GNUMP. The simulation results verify the effectiveness of the proposed algorithm by numerical examples in terms of the achieved system throughput.

This paper studies the transmit power optimization in multi-cell Massive multiple-input multiple-output (MIMO) systems. Network-wide max-min fairness (NW-MMF) and network-wide proportional fairness (NW-PF) are two well-known power control schemes in the literature. The NW-MMF focus on maximizing the fairness among users at the cost of penalizing users with good channel conditions. On the other hand, the NW-PF focuses on maximizing the sum SE, thereby ignoring fairness, but gives some extra attention to the weakest users. However, both of these schemes suffer from a scalability issue which means that for large networks, it is highly probable that one user has a very poor channel condition, pushing the spectral efficiency (SE) of all users towards zero. To overcome the scalability issue of NW-MMF and NW-PF, we propose a novel power control scheme that is provably scalable. This scheme maximizes the geometric mean (GM) of the per-cell max-min SE. To solve this new optimization problem, we prove that it can be rewritten in a convex optimization form and then solved using standard tools. The simulation results highlight the benefits of our model which is balancing between NW-PF and NW-MMF.

Pilot contamination is a limiting factor in multicell massive multiple-input multiple-output (MIMO) systems because it can severely impair channel estimation. Prior works have suggested coordinating pilot design across cells in order to reduce the channel estimation error caused by pilot contamination. In this paper, we propose a method for coordinated pilot design using fractional programming to minimize the weighted mean squared-error (MSE) in channel estimation. In particular, we apply the recently proposed quadratic transform to the MSE expression which allows the effect of pilot contamination to be decoupled. The resulting problem reformulation enables the pilots to be optimized in closed form if they can be designed arbitrarily. When the pilots are restricted to a given set of orthogonal sequences, pilot optimization reduces to an assignment problem which can be solved by weighted bipartite matching. Furthermore, we consider the max-min fairness of data rates with orthogonal pilots and obtain an extension of the proposed method to correlated Rayleigh fading. Finally, simulations demonstrate the advantage of the proposed (orthogonal and nonorthogonal) pilot designs as compared with state-of-the-art methods in combating pilot contamination.

Massive connectivity is regarded as a key requirement for future networks to support new communication paradigms, where the human-type communications coexist with machine-type communications. Owing to the limited coherence time but the huge number of potential devices, it is impossible to allocate mutually orthogonal pilot sequence for all potential devices, which may impose severe interference on the device activity detection and channel estimation. Existing nonorthogonal pilot design methods for conventional cellular network are not suitable for the massive connectivity regime. To overcome this challenge, we first formulate the pilot sequences design as an optimization problem to minimize the average mean square error (MSE) of channel estimation under the individual power constraint. The proposed optimization problem is nonconvex and highly coupled. By exploiting some approximation techniques, we convert the problem into a more tractable form and subsequently develop a distributed algorithm based on the matrix fractional programming (FP) and the alternating direction method of multipliers (ADMM) methods. Simulations validates that the proposed scheme not only achieves significant gains in channel estimation over state-of-the-art baseline schemes, but also improves the device activity detection performance.

This paper studies the transmit power optimization in a multi-cell massive multiple-input multiple-output (MIMO) system. To over-come the scalability issue of network-wide max-min fairness (NW-MMF), we propose a novel power control (PC) scheme. This scheme maximizes the geometric mean (GM) of the per-cell max-min spectral efficiency (SE). To solve this new optimization problem, we prove that it can be rewritten in a convex form and then solved using standard tools. To provide a fair comparison with the available utility functions in the literature, we solve the network-wide proportional fairness (NW-PF) PC as well. The NW-PF focuses on maximizing the sum SE, thereby ignoring fairness, but gives some extra attention to the weakest users. The simulation results highlight the benefits of our model which is balancing between NW-PF and NW-MMF.

Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity patterns for improving performance. In this letter, we propose a data-driven approach to jointly design the measurement matrix and support recovery method for complex sparse signals, using auto-encoder in deep learning. The proposed architecture includes two components, an auto-encoder and a hard thresholding module. The proposed auto-encoder successfully handles complex signals using standard auto-encoder for real numbers. The proposed approach can effectively exploit properties of sparsity patterns, and is especially useful when these underlying properties do not have analytic models. In addition, the proposed approach can achieve sparse support recovery with low computational complexity. Experiments are conducted on an application example, device activity detection in grant-free massive access for massive machine type communications (mMTC). Numerical results show that the proposed approach achieves significantly better performance with much less computation time than classic methods, in the presence of extra structures in sparsity patterns.

The capacity of the MIMO channel taking into account both a limitation on total consumed power, and per-antenna radiated power constraints is considered. The total consumed power takes into account the traditionally used sum radiated power, and also the power dissipation in the amplifiers. For a fixed channel with full CSI at both the transmitter and the receiver, maximization of the mutual information is formulated as an optimization problem. Lower and upper bounds on the capacity are provided by numerical algorithms based on partitioning of the feasible region. Both bounds are shown to converge and give the exact capacity when number of regions increases. The bounds are also used to construct a monotonic optimization algorithm based on the branch-and-bound approach. An efficient suboptimal algorithm based on successive convex approximation performing close to the capacity is also presented. Numerical results show that the performance of the solution obtained from the suboptimal algorithm is close to that of the global optimal solution. Simulation results also show that in the low SNR regime, antenna selection provides performance that is close to the optimal scheme while at high SNR, uniform power allocation performs close to the optimal scheme.

This work introduces a new approach to solve the joint precoding and power allocation for sum rate maximization problem in the downlink multiuser MIMO by a combination of random matrix theory and optimization theory. The new approach results in a simplified problem that, though non-convex, obeys a simple separable structure. The sum rate maximization problem is decomposed into different single-variable optimization problems that can be solved in parallel. A water-filling-like solution is found, which can be applied under some mild conditions on the SNRs of the users. The proposed scheme provides large gains over heuristic solutions when the number of users in the cell is large, which suggests the applicability in massive MIMO systems.

This paper considers the use of non-orthogonal-multiple-access (NOMA) in multiuser MIMO systems in practical scenarios where channel state information (CSI) is acquired through pilot signaling. A new NOMA scheme that uses shared pilots is proposed. Achievable rate analysis is carried out for different pilot signaling schemes, including both uplink and downlink pilots. The achievable rate performance of the proposed NOMA scheme with shared pilot within each group is compared with the traditional orthogonal access scheme with orthogonal pilots. Our proposed scheme is a generalization of the orthogonal scheme, and can be reduced to the orthogonal scheme when appropriate power allocation parameters are chosen. Numerical results show that when downlink CSI is available at the users, our proposed NOMA scheme outperforms orthogonal schemes. However with more groups of users present in the cell, it is preferable to use multi-user beamforming instead of NOMA.

For both maximum ratio transmission (MRT) and zero forcing (ZF) precoding schemes and given any specific rate requirement the optimal transmit power, number of antennas to be used, number of users to be served and number of pilots spent on channel training are found with the objective to minimize the total consumed power at the base station. The optimization problem is solved by finding closed form expressions of the optimal transmit power and then search over the remaining discrete variables. The analysis consists of two parts, the first part investigates the situation when only power consumed in the RF amplifiers is considered. The second part includes both the power consumed in the RF amplifiers and in other transceiver circuits. In the former case having all antennas active while reducing the transmit power is optimal. Adaptive scheme to switch off some of the antennas at the base stations is found to be optimal in the latter case.

This paper investigates linear precoding over nonsingular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is subject to an energy constraint. It is shown that the optimal precoder only produces a finite number of different lattices, namely perfect lattices, at the receiver. The well-known densest lattice packings are instances of perfect lattices, but are not always the solution. This is a counter-intuitive result as previous work in the area showed a tight connection between densest lattices and minimum distance. Since there are only finite many different perfect lattices, they can theoretically be enumerated offline. A new upper bound on the optimal minimum distance is derived, which significantly improves upon a previously reported bound, and is useful when actually constructing the precoders.

Consider the communication system model y = HFx + n, where H and F are the channel and precoder matrices, x is a vector of data symbols drawn from some lattice-type constellation, such as M-QAM, n is an additive white Gaussian noise vector and y is the received vector. It is assumed that both the transmitter and the receiver have perfect knowledge of the channel matrix H and that the transmitted signal Fx is subject to an average energy constraint. The columns of the matrix HF can be viewed as the basis vectors that span a lattice, and we are interested in the precoder F that maximizes the minimum distance of this lattice. This particular problem remains open within the theory of lattices and the communication theory. This paper provides the complete solution for any nonsingular M × 2 channel matrix H. For real-valued matrices and vectors, the solution is that HF spans the hexagonal lattice. For complex-valued matrices and vectors, the solution is that HF, when viewed in four-dimensional real-valued space, spans the Schlafli lattice D4.

Consider the communication model ȳ = HF x̄ + n̄, where H; F are real-valued matrices, x̄ is a data vector drawn from some real-valued lattice (e.g. M-PAM), n̄ is additive white Gaussian noise and ȳ is the received vector. It is assumed that the transmitter and the receiver have perfect knowledge of the channel matrix H (perfect CSI) and that the transmitted signal F x̄ is subject to an average energy constraint. The columns of the matrix HF can be viewed as basis vectors that span a lattice, and we are interested in the minimum distance of this lattice. More precisely, for a given H, which F under an average energy constraint will maximize the minimum distance of the lattice HF? This particular question remains open within the theory of lattices. This work provides the solution for 2×2 matrices H; F. The answer is an F such that HF is a hexagonal lattice.