Multiple-input Single-output Broadcast Channel Research Articles

Fundamental Limits of Intelligent Reflecting Surface Aided Multiuser Broadcast Channel

Intelligent reflecting surface (IRS) has recently received significant attention in wireless networks owing to its ability to smartly control the wireless propagation through passive reflection. Although prior works have employed the IRS to enhance the system performance under various setups, the fundamental capacity limits of an IRS aided multi-antenna multi-user system have not yet been characterized. Motivated by this, we investigate an IRS aided multiple-input single-output (MISO) broadcast channel by considering the capacity-achieving dirty paper coding (DPC) scheme and dynamic beamforming configurations. We first propose a bisection based framework to characterize its capacity region by optimally solving the sum-rate maximization problem under a set of rate constraints, which is also applicable to characterize the achievable rate region with the zero-forcing (ZF) scheme. Interestingly, it is rigorously proved that dynamic beamforming is able to enlarge the achievable rate region of ZF if the IRS phase-shifts cannot achieve fully orthogonal channels, whereas the attained gains become marginal due to the reduction of the channel correlations induced by smartly adjusting the IRS phase-shifts. The result implies that employing the IRS is able to reduce the demand for implementing dynamic beamforming. Finally, we analytically prove that the sum-rate achieved by the IRS aided ZF is capable of approaching that of the IRS aided DPC with a sufficiently large IRS in practice. Simulation results shed light on the impact of the IRS on transceiver designs and validate our theoretical findings, which provide useful guidelines to practical systems by indicating that replacing sophisticated schemes with easy-implementation schemes would only result in slight performance loss.

Full Duplex Cooperative Rate Splitting Multiple Access for a MISO Broadcast Channel With Two Users

In this letter, we investigate the performance of a full-duplex (FD) cooperative rate splitting multiple access (C-RSMA) scheme in a downlink multiple-input single-output (MISO) system consisting of one base station (BS) that serves two users simultaneously. With the objective of maximizing the minimum achievable rate, we jointly optimize the BS precoding vectors, the common-stream split and the device-to-device transmit power subject to the power budget of both the BS and the relay device. As the entire problem is non-convex, we propose a low complexity algorithm based on the successive convex approximation (SCA) technique. Simulation results demonstrated that the FD C-RSMA can achieve a higher minimum achievable rate than some baseline schemes, including the FD cooperative non-orthogonal multiple access (FD C-NOMA), the half-duplex (HD) C-RSMA, RSMA and NOMA.

Cache-Aided Retrospective Interference Alignment in Wireless Broadcast Channels

In this paper, we investigate joint retrospective interference alignment (RIA) and caching schemes for multiple-input single-output (MISO) broadcast channels (BC) with delayed channel state information at the transmitter (CSIT). By exploiting the cached content, we propose one sophisticated cache-aided RIA scheme to cancel the interference. Importantly, our scheme takes the number of symbols in a packet into account, as different number of symbols in a packet result in different system configuration, which may have significant impact on the design of the transmission scheme and achievable degrees of freedom (DoF). Furthermore, we present two theorems to quantify the achievable sum DoF of the proposed cached-aided RIA scheme for different system configuration. Moreover, the system configuration of the existing cache-aided RIA scheme with mixed CSIT can be treated as a special case in our paper. And also our scheme can simultaneously support more users than the existing cache-aided RIA scheme with mixed CSIT to invoke zero forcing (ZF) precoding, which limits the number of users simultaneously supported.

Globally Optimal Spectrum- and Energy-Efficient Beamforming for Rate Splitting Multiple Access

Rate splitting multiple access (RSMA) is a promising non-orthogonal transmission strategy for next-generation wireless networks. It has been shown to outperform existing multiple access schemes in terms of spectral and energy efficiency when suboptimal beamforming schemes are employed. In this work, we fill the gap between suboptimal and truly optimal beamforming schemes and conclusively establish the superior spectral and energy efficiency of RSMA. To this end, we propose a successive incumbent transcending (SIT) branch and bound (BB) algorithm to find globally optimal beamforming solutions that maximize the weighted sum rate or energy efficiency of RSMA in Gaussian multiple-input single-output (MISO) broadcast channels. Numerical results show that RSMA exhibits an explicit globally optimal spectral and energy efficiency gain over conventional multi-user linear precoding (MU-LP) and power-domain non-orthogonal multiple access (NOMA). Compared to existing globally optimal beamforming algorithms for MU-LP, the proposed SIT BB not only improves the numerical stability but also achieves faster convergence. Moreover, for the first time, we show that the spectral/energy efficiency of RSMA achieved by suboptimal beamforming schemes (including weighted minimum mean squared error (WMMSE) and successive convex approximation) almost coincides with the corresponding globally optimal performance, making it a valid choice for performance comparisons. The globally optimal results provided in this work are imperative to the ongoing research on RSMA as they serve as benchmarks for existing suboptimal beamforming strategies and those to be developed in multi-antenna broadcast channels.

Cellular Networks With Finite Precision CSIT: GDoF Optimality of Multi-Cell TIN and Extremal Gains of Multi-Cell Cooperation

We study the generalized degrees-of-freedom (GDoF) of cellular networks under finite precision channel state information at the transmitters (CSIT). We consider downlink settings modeled by the interfering broadcast channel (IBC) under no multi-cell cooperation, and the overloaded multiple-input-single-output broadcast channel (MISO-BC) under full multi-cell cooperation. We focus on three regimes of interest: the mc-TIN regime, where a scheme based on treating inter-cell interference as noise (mc-TIN) was shown to be GDoF optimal for the IBC; the mc-CTIN regime, where the GDoF region achievable by mc-TIN is convex without the need for time-sharing; and the mc-SLS regime which extends a previously identified regime, where a simple layered superposition (SLS) scheme is optimal for the 3-transmitter-3-user MISO-BC, to overloaded cellular-type networks with more users than transmitters. We first show that the optimality of mc-TIN for the IBC extends to the entire mc-CTIN regime when CSIT is limited to finite precision. The converse proof of this result relies on a new application of aligned images bounds. We then extend the IBC converse proof to the counterpart overloaded MISO-BC, obtained by enabling full transmitter cooperation. This, in turn, is utilized to show that a multi-cell variant of the SLS scheme is optimal in the mc-SLS regime under full multi-cell cooperation, albeit only for 2-cell networks. The overwhelming combinatorial complexity of the GDoF region stands in the way of extending this result to larger networks. Alternatively, we appeal to extremal network analysis, recently introduced by Chan et al., and study the GDoF gain of multi-cell cooperation over mc-TIN in the three regimes of interest. We show that this extremal GDoF gain is bounded by small constants in the mc-TIN and mc-CTIN regimes, yet scales logarithmically with the number of cells in the mc-SLS regime.

Random Beam-Based Non-Orthogonal Multiple Access for Low Latency K-User MISO Broadcast Channels.

In this paper, we propose random beam-based non-orthogonal multiple access (NOMA) for low latency multiple-input single-output (MISO) broadcast channels, where there is a target signal-to-interference-plus-noise power ratio (SINR) for each user. In our system model, there is a multi-antenna transmitter with its own single antenna users, and the transmitter selects and serves some of them. For low latency, the transmitter exploits random beams, which can reduce the feedback overhead for the channel acquisition, and each beam can support more than a single user with NOMA. In our proposed random beam-based NOMA, each user feeds a selected beam index, the corresponding SINR, and the channel gain, so it feeds one more scalar value compared to the conventional random beamforming. By allocating the same powers across the beams, the transmitter independently selects NOMA users for each beam, so it can also reduce the computational complexity. We optimize our proposed scheme finding the optimal user grouping and the optimal power allocation. The numerical results show that our proposed scheme outperforms the conventional random beamforming by supporting more users for each beam.

Intelligent Reflecting Surface Enabled Random Rotations Scheme for the MISO Broadcast Channel

The current literature on intelligent reflecting surface (IRS) focuses on optimizing the IRS phase shifts to yield coherent beamforming gains, under the assumption of perfect channel state information (CSI) of individual IRS-assisted links, which is highly impractical. This work, instead, considers the random rotations scheme at the IRS in which the reflecting elements only employ random phase rotations without requiring any CSI. The only CSI then needed is at the base station (BS) of the overall channel to implement the beamforming transmission scheme. Under this framework, we derive the sum-rate scaling laws in the large number of users regime for the IRS-assisted multiple-input single-output (MISO) broadcast channel, with optimal dirty paper coding (DPC) scheme and the lower-complexity random beamforming (RBF) and deterministic beamforming (DBF) schemes at the BS. The random rotations scheme increases the sum-rate by exploiting multi-user diversity, but also compromises the gain to some extent due to correlation. Finally, energy efficiency maximization problems in terms of the number of BS antennas, IRS elements and transmit power are solved using the derived scaling laws. Simulation results show the proposed scheme to improve the sum-rate, with performance becoming close to that under coherent beamforming for a large number of users.

Utilizing Interference by Network Coding for Simultaneous Wireless Information and Power Transfer

This letter puts forth a novel way to manage interference in simultaneous wireless information and power transfer (SWIPT) systems by utilizing physical-layer network coding (PNC). We consider multi-user multiple-input single-output (MU-MISO) broadcast channels. Unlike the conventional zero-forcing scheme, the PNC-SWIPT scheme introduced in this letter does not eliminate the interfering signals at the receivers. The PNC-SWIPT scheme cancels out the undesired messages over a finite field during PNC demodulation for information decoding (ID). It preserves the interfering signals which are beneficial energy sources for energy harvesting (EH). Simulation results show that the PNC-SWIPT scheme achieves superior EH performance than conventional interference mitigation schemes, such as zero-forcing (ZF) and maximizing EH precoding (Max EH), while maintaining the same ID performance. The performance improvement of the PNC-SWIPT scheme mainly comes from canceling out the interference at the receivers from the aspect of data by PNC, without eliminating the interfering signals which are beneficial energy sources.

Rate-Splitting Multiple Access for Overloaded Cellular Internet of Things

In the near future, it is envisioned that cellular networks will have to cope with extensive internet of things (IoT) devices. Therefore, a required feature of cellular IoT will be the capability to serve simultaneously a large number of devices with heterogeneous demands and qualities of channel state information at the transmitter (CSIT). In this paper, we focus on an overloaded multiple-input single-output (MISO) broadcast channel (BC) with two groups of CSIT qualities, namely, one group of users (representative of high-end devices) for which the transmitter has partial knowledge of the CSI, the other group of users (representative of IoT devices) for which the transmitter only has knowledge of the statistical CSI (i.e., the distribution information of the user channels). We introduce rate-splitting multiple access (RSMA), a new multiple access based on multi-antenna rate-splitting (RS) technique for cellular IoT. Two strategies are proposed, namely, time partitioning-RSMA (TP-RSMA) and power partitioning-RSMA (PP-RSMA). The former independently serves the two groups of users over orthogonal time slots while the latter jointly serves the two groups of users within the same time slot in a non-orthogonal manner. We first show at high signal-to-noise ratio (SNR) that PP-RSMA achieves the optimal degrees-of-freedom (DoF) in an overloaded MISO BC with heterogeneous CSIT qualities. We then show at finite SNR that PP-RSMA achieves explicit sum rate gain over TP-RSMA and all baseline schemes by marrying the benefits of PP and RSMA. Furthermore, PP-RSMA is robust to CSIT inaccuracy and flexible to cope with quality of service (QoS) rate constraints of all users. The DoF and rate analysis helps us in drawing the conclusion that PP-RSMA is a powerful framework for cellular IoT with a large number of devices.

Joint Beamforming and Power Allocation for Multiuser MISO Broadcast Channel SWIPT Employing OFDM

Resource allocation strategies for simultaneous wireless information and power transfer (SWIPT) employing orthogonal frequency division multiplexing (OFDM) typically rely on subcarrier assignment for multiple access. For information transfer, however, subcarrier assignment is only sum-rate optimal when the network is interference limited; otherwise, it is optimal to reuse subcarriers. Beamforming-based space-division multiple access (SDMA) is a multiple access technique that enables subcarrier reuse by managing interference. Although beamforming is considered a key SWIPT component, OFDM-based SWIPT has yet to utilize beamforming for SDMA. As such, this paper seeks to develop a low-complexity resource allocation strategy to jointly allocate power and design beamforming vectors for an OFDM-based multiuser (MU) multiple-input single-output (MISO) broadcast channel (BC) SWIPT system capable of utilizing SDMA. To this end, a non-convex optimization problem is formulated in which a weighted sum of user data rates is maximized subject to meeting receive and transmit power constraints. The time-sharing property of multicarrier systems is observed to justify utilizing Lagrangian decomposition despite the non-convexity. Whereas previous SWIPT research used Lagrangian decomposition to simplify subcarrier assignment, this paper instead uses it to enable SDMA through beamforming. Beamforming is achieved via a medium access channel (MAC)-BC duality, which enables a closed-form solution for the beamforming vectors given the dual MAC power allocation. The dual MAC power allocation is approximated using a successive convex approximation (SCA) technique. The result is a resource allocation algorithm that provides close-to-optimal performance with low computational complexity.

Full Coded Caching Gains for Cache-Less Users

Within the context of coded caching, the work reveals the interesting connection between having multiple transmitters and having heterogeneity in the cache sizes of the receivers. Our work effectively shows that having multiple transmit antennas – while providing full multiplexing gains – can also simultaneously completely remove the performance penalties that are typically associated to cache-size unevenness. Focusing on the multiple-input single-output Broadcast Channel, the work first identifies the performance limits of the extreme case where cache-aided users coincide with users that do not have caches, and then expands the analysis to the case where both user groups are cache-aided but with heterogeneous cache-sizes. In the first case, the main contribution is a new algorithm that employs perfect matchings on a bipartite graph to offer full multiplexing as well as full coded-caching gains to both cache-aided as well as cache-less users. An interesting conclusion is that, starting from a single-stream centralized coded caching setting with normalized cache size $\gamma $ , then adding $L$ antennas allows for the addition of up to approximately $L/\gamma $ extra cache-less users, at no added delay costs. Similarly surprising is the finding that, beginning with a single-antenna hybrid system (with both cache-less and cache-aided users), then adding $L-1$ antennas to the transmitter, as well as endowing the cache-less users with a cumulative normalized cache size $\Gamma _{2}$ , increases the Degrees of Freedom by a multiplicative factor of up to $\Gamma _{2}+L$ .

Max-Min Fairness of K-User Cooperative Rate-Splitting in MISO Broadcast Channel With User Relaying

Cooperative Rate-Splitting (CRS) strategy, relying on linearly precoded rate-splitting at the transmitter and opportunistic transmission of the common message by the relaying user, has recently been shown to outperform typical Non-cooperative Rate-Splitting (NRS), Cooperative Non-Orthogonal Multiple Access (C-NOMA) and Space Division Multiple Access (SDMA) in a two-user Multiple Input Single Output (MISO) Broadcast Channel (BC) with user relaying. In this work, the existing two-user CRS transmission strategy is generalized to the K-user case. We study the problem of jointly optimizing the precoders, message split, time slot allocation, and relaying user scheduling with the objective of maximizing the minimum rate among users. An efficient self-organizing relaying protocol is first proposed followed by a Successive Convex Approximation (SCA)-based algorithm to jointly optimize time slot, precoders and message split. Numerical results show that the worst-case achievable rate achieved by CRS is significantly increased over that of NRS and SDMA in a wide range of network loads and user deployments. Importantly, the proposed SCA-based algorithm dramatically reduces the computational complexity without any rate loss compared with the conventional algorithm in the literature of CRS. Therefore, we conclude that the proposed K-user CRS is more powerful than the existing transmission schemes.

On the Separability of Parallel MISO Broadcast Channels Under Partial CSIT: A Degrees of Freedom Region Perspective

We study the K-user, M-subchannel parallel multiple-input-single-output (MISO) broadcast channel (BC) under arbitrary levels of partial channel state information at the transmitter (CSIT). We show that the parallel subchannels constituting this setting are separable from a degrees-of-freedom (DoF) region perspective if and only if the partial CSIT pattern is totally ordered. This total order condition corresponds to users abiding by the same order, with respect to their CSIT quality levels, in each of the parallel subchannels. For instance, let α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[l]</sup> and α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[l]</sup> be the CSIT quality parameters for users k and j over subchannel l. Under total order, having α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[l]</sup> ≥ α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[l]</sup> implies that α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[m]</sup> ≥ α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[m]</sup> holds for every subchannel m. In this case, the entire DoF region is achievable using simple separate coding, where a single-subchannel-type transmission scheme is employed in each subchannel. To show this separability result, we first derive an outer bound for the DoF region by extending the aligned image sets approach of Davoodi and Jafar to the considered setting. We then show that this outer bound coincides with the inner bound achieved through separate coding, given by the Minkowski sum of M single-subchannel DoF regions, under the total order condition, hence settling the if part of the main theorem. To prove the only if part of the theorem, we identify a set of DoF tuples achievable through joint coding across subchannels, yet not achievable through separate coding whenever the total order condition is violated. Moreover, we also highlight the implications of our main result on the design of CSIT feedback schemes for multi-carrier multi-antenna wireless networks.

Achievable Secure Degrees of Freedom of ${K}$ -User MISO Broadcast Channel With Imperfect CSIT

In this letter, we derive the achievable secure degrees of freedom (SDoF) of ${K}$ -user multiple-input single-output broadcast channel with imperfect channel state information (CSI) at the transmitter. With the help of an $N_{j}$ -antenna external jammer, we propose a jamming rate splitting (J-RS) scheme to ensure the security of two wiretap models: 1) broadcast channel with confidential messages and 2) broadcast channel with an $N_{e}$ -antenna external eavesdropper, where each legal node has no CSI of wiretap channels. Our converse is based on the degrees of freedom (DoF) of the network with secrecy constraints, and the achievability is based on J-RS. By numerical analysis, it indicates that the proposed scheme can achieve more SDoF than the traditional rate splitting scheme, zero forcing scheme, and jamming scheme, which can reach to the DoF of the network.

A High-Diversity Transceiver Design for MISO Broadcast Channels

In this paper, the outage behavior and diversity order of the mixture transceiver architecture for multiple-input single-output broadcast channels are analyzed. The mixture scheme groups users with closely-aligned channels and applies superposition coding and successive interference cancellation decoding to each group composed of users with closely-aligned channels, while applying zero-forcing beamforming across semi-orthogonal user groups. In order to enable such analysis, closed-form lower bounds on the achievable rates of a general multiple-input single-output broadcast channel with superposition coding and successive interference cancellation are newly derived. By employing channel-adaptive user grouping and proper power allocation, which ensures that the channel subspaces of user groups have angle larger than a certain threshold, it is shown that the mixture transceiver architecture achieves full diversity order in multiple-input single-output broadcast channels and opportunistically increases the multiplexing gain while achieving full diversity order. Furthermore, the achieved full diversity order is the same as that of the single-user maximum ratio transmit beamforming. Hence, the mixture scheme can provide reliable communication under channel fading for ultra-reliable low latency communication. Numerical results validate our analysis and show the outage superiority of the mixture scheme over conventional transceiver designs for multiple-input single-output broadcast channels.

Blind Interference Alignment for the &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$K$&lt;/tex-math&gt; &lt;/inline-formula&gt;-User MISO BC Under Limited Symbol Extension

In this paper, we study the achievable degrees of freedom (DoFs) for $K$ -user multiple-input single-output broadcast channel (BC) in the absence of channel state information at the transmitter under the finite channel coherent time. For the considered $K$ -user BC, a transmitter is equipped with multiple conventional antennas, and receivers are equipped with a reconfigurable antenna that is capable of dynamically modifying the receiving beam radiation pattern. In this system, we propose a blind interference alignment scheme that is able to allocate an asymmetric number of information symbols to each user, which is essentially required to improve DoFs under limited symbol extension. A generalized systematic construction method of transmit beamforming vectors and receiving mode selection patterns to deal with such asymmetric allocation is established. As a consequence, for a broad class of network configurations and symbol extension constraints, the proposed scheme attains an improved sum DoF compared to the previous works, allowing only for the same number of information symbols for all users.

Rate-splitting multiple access for downlink communication systems: bridging, generalizing, and outperforming SDMA and NOMA

Space-division multiple access (SDMA) utilizes linear precoding to separate users in the spatial domain and relies on fully treating any residual multi-user interference as noise. Non-orthogonal multiple access (NOMA) uses linearly precoded superposition coding with successive interference cancellation (SIC) to superpose users in the power domain and relies on user grouping and ordering to enforce some users to fully decode and cancel interference created by other users.In this paper, we argue that to efficiently cope with the high throughput, heterogeneity of quality of service (QoS), and massive connectivity requirements of future multi-antenna wireless networks, multiple access design needs to depart from those two extreme interference management strategies, namely fully treat interference as noise (as in SDMA) and fully decode interference (as in NOMA).Considering a multiple-input single-output broadcast channel, we develop a novel multiple access framework, called rate-splitting multiple access (RSMA). RSMA is a more general and more powerful multiple access for downlink multi-antenna systems that contains SDMA and NOMA as special cases. RSMA relies on linearly precoded rate-splitting with SIC to decode part of the interference and treat the remaining part of the interference as noise. This capability of RSMA to partially decode interference and partially treat interference as noise enables to softly bridge the two extremes of fully decoding interference and treating interference as noise and provides room for rate and QoS enhancements and complexity reduction.The three multiple access schemes are compared, and extensive numerical results show that RSMA provides a smooth transition between SDMA and NOMA and outperforms them both in a wide range of network loads (underloaded and overloaded regimes) and user deployments (with a diversity of channel directions, channel strengths, and qualities of channel state information at the transmitter). Moreover, RSMA provides rate and QoS enhancements over NOMA at a lower computational complexity for the transmit scheduler and the receivers (number of SIC layers).

Optimality of Simple Layered Superposition Coding in the 3 User MISO BC With Finite Precision CSIT

We study the $K=3$ user multiple input single output (MISO) broadcast channel (BC) with $M=3$ antennas at the transmitter and 1 antenna at each receiver, from the generalized degrees of freedom (GDoF) perspective, under the assumption that the channel state information at the transmitter (CSIT) is limited to the finite precision. In particular, our goal is to identify a parameter regime where a simple layered superposition (SLS) coding scheme achieves the entire GDoF region. With $\alpha _{ij}$ representing the channel strength parameter for the link from the $j^{th}$ antenna of the transmitter to the $i^{th}$ receiver, we prove that the SLS is GDoF optimal without the need for time-sharing if $\max (\alpha _{ki},\alpha _{im})\leq \alpha _{ii}$ and $\alpha _{ki}+\alpha _{im}\le \alpha _{ii}+\alpha _{km}$ for all $i,k\in [{3}],m\in [M]$ . The GDoF region under this condition is a convex polyhedron. The result generalizes to arbitrary $M\geq 3$ .

On Linear Precoding for the Two-User MISO Broadcast Channel With Confidential Messages and Per-Antenna Constraints

We study the design of linear precoders for secure transmission in the two-user multiple-input single-output (MISO) broadcast channel with confidential messages (BC-CM). The transmitter has multiple antennas, and each user has a single receive antenna. Two independent messages are simultaneously transmitted, one intended for each user, and each message should be kept confidential from the other user. Assuming real-valued transmitted signals, we design the linear precoders subject to total and per-antenna average power constraints, and also subject to amplitude constraints. In both cases, we tackle the design problem via weighted secrecy sum rate maximization. The resulting problem, however, involves a fractional objective, making it nonconvex and difficult to solve. Nevertheless, we show that this difficult problem can be transformed into a more tractable problem, for which a solution can be obtained by an iterative search algorithm. In addition, we characterize a condition under which the obtained solution is guaranteed to be optimal. Furthermore, we show that the problem formulation and solution approach can be easily extended to handle the robust version of the design problem with uncertain channel information. We provide numerical examples to demonstrate the performance of the proposed precoder in terms of the achievable secrecy rate regions subject to the aforementioned constraints. We also demonstrate the performance of the robust precoder under different channel uncertainty levels.

Secure Degrees of Freedom Region of the Two-User MISO Broadcast Channel With Alternating CSIT

The two user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied, in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form $I_{i}$ , $i=1,2$ where $I_{1}, I_{2}\in \{\mathsf {P}, \mathsf {D}, \mathsf {N}\}$ , and the forms $\mathsf {P}$ , $\mathsf {D}$ , and $\mathsf {N}$ correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between nine possible states corresponding to all possible values of $I_{1}I_{2}$ , with each state occurring for $\lambda _{I_{1}I_{2}}$ fraction of the total duration. We assume that perfect and instantaneous CSI is available at the all receivers. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where $\lambda _{I_{1} I_{2}}=\lambda _{I_{2}I_{1}}$ . The main technical contributions include developing 1) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints, which also highlight the synergistic benefits of inter-state coding for secrecy; 2) new converse proofs via local statistical equivalence and channel enhancement; and 3) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f.