Performance Analysis of Multistream Receive Spatial Modulation in the MIMO Broadcast Channel

In Multiple-input multiple-output (MIMO) broadcast channels (BCs), the transmitter simultaneously broadcasts signals to multiple receivers at same frequency band, resulting in that the communication capacity is affected by both interference, channel fading and random noise. Although channel fading can be mitigated by transceivers, the signal-to-noise-ratio (SNR) of the practical communication system is still dynamically changing due to the randomly changing noise. Traditional MIMO transceiver optimization algorithms can not flexibly adapt to the dynamic changes of SNR, resulting in large performance degradation. In this paper, we comprehensively consider signal power and signal space dimensions of the received signal in MIMO BCs, and propose two transceiver optimization algorithms which can dynamically adapt to the variance of SNRs. In the proposed algorithms, SNR is adopted to be an adjustment factor to cope with its variance. When SNR is low, i.e, large noise, the algorithm parameters are automatically adjusted so that the signal power is preserved as much as possible to combat the loss of communication capacity caused by large random noise. Correspondingly, under the condition of high SNR environment, the algorithm parameters are adjusted automatically to effectively compress the inter-user-interference (IUI) and intra-user-inter-stream-interference (ISI) by optimizing signal space dimensions. Simulation results show that in different SNR environments, the proposed algorithms can automatically adjust the focus of optimization, so that the optimization of signal power and signal space dimensions can automatically adapt to different SNRs. Compared with traditional transceiver optimization algorithms, the proposed algorithms can improve the communication capacity within a large dynamic range of SNR.

We study the multiuser diversity in both multiple-input multiple output (MIMO) multiple-access channel (MAC) and MIMO broadcast channel (BC). We consider multiuser scheduling with linear receivers for uplink and linear precoders for downlink. In each time slot, a group of users are selected in either transmission or reception. Based on the performance analysis, a criterion of selecting a number of active users to optimize error performance is presented. We show that the linear processing for downlink and uplink achieves the same SNR. This makes it convenient to use a single scheduling algorithm in both downlink and uplink. Furthermore, we present an analysis of the performance of the proposed scheduling algorithm. It is shown that the analysis agrees with the simulation.

In this letter, the diversity order and the coding gain of Receive Space Modulation (RSM) in the Multiple-Input Multiple-Output (MIMO) broadcast channel are derived by taking into account both small and large scale fading. The considered linear precoding method is Zero Forcing (ZF). Note that the proposed framework is directly applicable to the conventional spatially multiplexed broadcast channel. Based on the derived mathematical framework, a theoretical criterion is provided, which determines the superiority between the deployment of RSM and Spatial MultipleXing (SMX) in the shadowing MIMO broadcast channel. Finally, the provided theoretical results are validated via Monte Carlo simulation results.

This paper considers the joint optimization of the transmitter beamforming filters and receiver combining filters for the multiple-input multiple-output (MIMO) broadcast channel. A low-complexity iterative algorithm to compute the filters is proposed and then a closed-form expression of the filters for the downlink with two transmit antennas is derived, avoiding the need for iterative computation in this case. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the channel structure in the closed form solution, and is independent of the number of receive antennas. Performance is evaluated by Monte Carlo simulations as a function of the amount of feedback. With two receive antennas, the proposed method performs close to the sum capacity of the MIMO broadcast channel, without the need for multiuser diversity and with only limited feedback.

We consider the minimization of the energy per bit (or, equivalently, the maximization of the energy efficiency) in multiple-input multiple-output (MIMO) broadcast channels with rate balancing constraints for fairness between users, and we propose a framework to find the globally optimal energy-efficient solution, which relies on dirty paper coding (DPC). The main idea is to introduce a continuous, differentiable, and concave optimal rate function, which transforms the problem into a convex-concave fractional program in one scalar variable. This not only allows an efficient solution, but also an intuitive interpretation of the method as well as the possibility to extend the method to related problems. In numerical simulations, we compare the energy efficiency with and without fairness constraints.

Preceding with block diagonalization is an attractive approach for approaching sum capacity in multiuser MIMO (multiple input multiple output) broadcast channels. This method though requires either global channel state information at every receiver or an additional training phase, which requires additional system planning. This paper proposes a lattice based multi-user precoder that uses block diagonalization combined with pre-equalization and perturbation for the multiuser MIMO broadcast channel. Achievable rates are computed and used to show that the proposed technique approaches the capacity with block diagonalization and water-filling but does not require the additional channel state information at the receiver. Monte Carlo simulations under the case of equal power allocation show that the proposed method provides better diversity and BER (bit error rate) performance than block diagonalization with a zero-forcing receiver.

We study the Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and private messages. We first obtain an outer bound for the capacity region of the two-user discrete memoryless broadcast channel with common and private messages. We next show that if jointly Gaussian random variables are sufficient to evaluate this outer bound for the Gaussian MIMO broadcast channel, the dirty-paper coding (DPC) region is the capacity region of the Gaussian MIMO broadcast channel with common and private messages. However, we can evaluate only a loosened version of this outer bound, which yields the result that extending the DPC region in the common message rate direction by a fixed amount is an outer bound for the capacity region of the Gaussian MIMO broadcast channel with common and private messages. However, this fixed amount, i.e., the gap, is not finite for all channels. We derive the necessary and sufficient conditions for this gap to be finite.

Consider a Gaussian multiple-input multiple-output (MIMO) multiple-access channel (MAC) with channel matrix $\mathbf{H}$ and a Gaussian MIMO broadcast channel (BC) with channel matrix $\mathbf{H}^{\mathsf{T}}$. For the MIMO MAC, the integer-forcing architecture consists of first decoding integer-linear combinations of the transmitted codewords, which are then solved for the original messages. For the MIMO BC, the integer-forcing architecture consists of pre-inverting the integer-linear combinations at the transmitter so that each receiver can obtain its desired codeword by decoding an integer-linear combination. In both cases, integer-forcing offers higher achievable rates than zero-forcing while maintaining a similar implementation complexity. This paper establishes an uplink-downlink duality relationship for integer-forcing, i.e., any sum rate that is achievable via integer-forcing on the MIMO MAC can be achieved via integer-forcing on the MIMO BC with the same sum power and vice versa. Using this duality relationship, it is shown that integer-forcing can operate within a constant gap of the MIMO BC sum capacity. Finally, the paper proposes a duality-based iterative algorithm for the non-convex problem of selecting optimal beamforming and equalization vectors, and establishes that it converges to a local optimum.

We provide an alternative proof for the capacity region of the degraded Gaussian multiple-input multiple-output (MIMO) broadcast channel. Our proof does not use the channel enhancement technique as opposed to the original proof of Weingertan and the alternative proof of Liu et al. Our proof starts with the single-letter description of the capacity region of the degraded broadcast channel, and by using it, obtains a tight (i.e., achievable) outer bound for the capacity region of the degraded Gaussian MIMO broadcast channel, by using two main technical tools. The first one is the generalized de Bruijn identity due to Palomar which provides a connection between the differential entropy and the Fisher information matrix. The second tool we use is an inequality due to Dembo which lower bounds the differential entropy in terms of the Fisher information matrix.

This letter investigates the secure degrees of freedom (SDoF) of reconfigurable intelligent surface (RIS) aided 2-user multiple-input multiple-output (MIMO) broadcast channel with confidential messages. In this model, transmitter sends corresponding secure messages to each receiver and ensure the other receiver cannot decode them. Compared to existing studies on broadcast channel with confidential messages, our model employs an active RIS that reduces the rank of channel matrices, enlarging the nullspace for secure transmission to increase the SDoF. In particular, our model can realize secure communication even when the SDoF of original model is zero. According to the different configurations of antennas, the problem is divided into several regimes. We present outer bound and corresponding proof for each regime by utilizing theoretical methods and RIS beamforming. Then we propose universal achievable schemes for different regimes by using zero-forcing decoding. Finally, we determine the exact SDoF of RIS-assisted MIMO broadcast channel with confidential messages and its SDoF gain compared to original model.

The capacity-achieving coding scheme for the multiple-input multiple-output (MIMO) broadcast channel is dirty-paper coding. With this type of transmission scheme the optimal number of active users that receive data and the optimal power allocation strategy are highly dependent on the structure of the channel matrix and on the total transmit power available. In the context of packet-data access with adaptive transmission where mobile users are equipped with a single receive antenna and the base station has multiple transmit antennas, we study the optimal number of active users and the optimal power allocation. In the particular case of two transmit antennas, we prove that the optimal number of active users can be a non-monotonic function of the total transmit power. Thus not only the number of users that should optimally be served simultaneously depends on the user channel vectors but also on the power available at the base station transmitter. The expected complexity of optimal scheduling algorithms is thus very high. Yet we then prove that at most as many users as the number of transmit antennas are allocated a large amount of power asymptotically in the high-power region in order to achieve the sum-capacity. Simulations confirm that constraining the number of active users to be no more than the number of transmit antennas incurs only a marginal loss in spectral efficiency. Based on these observations, we propose low-complexity scheduling algorithms with sub-optimal transmission schemes that can approach the sum-capacity of the MIMO broadcast channel by taking advantage of multiuser diversity. The suitability of known antenna selection algorithms is also demonstrated. We consider the cases of complete and partial channel knowledge at the transmitter. We provide simulation results to illustrate our conclusions.

In this paper, we present a game-theoretic approach for the purpose of deriving the problem of joint beamforming and power control in cognitive radio (CR) multiple-input multiple-output (MIMO) broadcast channels (CR MIMO-BCs), where the primary users (PUs) coexist with the secondary users (SUs) and they share the same spectrum. The cognitive base station (CBS), which is equipped with multiple antennas, is capable of transmitting data to the SU’s multiple-antenna receiver by employing the technology of beamforming. The proposed approach is an application of separable games, which are formally stated by the subgames of beamforming and power control. Furthermore, based on the model of noncooperative separate games, separable cost functions for the parameters of beamforming and power control are also proposed, showing that these cost functions are convex. Therefore, the convex theory of a noncooperative game can be employed to investigate the best response strategies as well as existence of Nash equilibrium solutions. Finally, we propose an iterative algorithm to achieve the optimal Nash equilibrium of the proposed joint beamforming subgame and power control subgame. Numerical results verify both the convergence and the tracking properties of the proposed algorithm for variant scenarios.

This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for given feedback delay and channel quantization error. The proposed transmission strategy can be easily combined with round-robin scheduling to serve a large number of users. As instantaneous channel information is not exploited, the proposed algorithm cannot provide multiuser diversity gain, but it is still able to provide throughput gain over single-user MIMO at moderate signal-to-noise ratio. In addition, it has a light feedback overhead and only requires feedback of instantaneous channel state information from a small number of users. In the system with a feedback load constraint, it is shown that the proposed algorithm provides performance close to that achieved by opportunistic scheduling with instantaneous feedback from a large number of users.

The multiple-input multiple-output (MIMO) broadcast channel uses multiple antennas at the transmitter to concurrently deliver information to multiple receivers. Despite the theoretical capacity gains over single user MIMO, the actual throughput of the system with limited feedback on channel state information suffers due to interspatial stream interference. On top of the orthogonal beamforming with limited feedback , this paper introduces two novel stream schedulers to mitigate the interference. By the proposed adaptive spatial stream schedulers, an adaptive number of spatial streams are scheduled and thus, reduces the interference, which also achieves power gains by concentrating power into fewer streams. The two proposed algorithms are evaluated and shown to effectively mitigate the interference.

In this paper, a new proof for the degrees of freedom (DoF) region of the K-user multiple-input multiple-output (MIMO) broadcast channel (BC) with no channel state information at the transmitter (CSIT) and perfect channel state information at the receivers (CSIR) is provided. Based on this proof, the capacity region of a certain class of MIMO BC with channel distribution information at the transmitter (CDIT) and perfect CSIR is derived. Finally, an outer bound for the DoF region of the K-user MIMO interference channel (IC) with no CSIT is provided.