MIMO interference alignment in random access networks

In wireless interference networks, orthogonal medium access techniques like time division multiple access (TDMA) and frequency division multiple access (FDMA) achieve merely one degree of freedom (DoF). However, by using interference alignment (IA) the achievable DoF can be linearly scaled up with the number of users. Nevertheless, this outperformance of IA heavily depends on the availability of perfect channel state information (CSI), which is not a realistic assumption in practice. Since under imperfect CSI, the performance of IA may become severely degraded, design of enhanced IA algorithms by relying on the availability of merely imperfect CSI is of particular interest. In this paper, we propose a least squares (LS)-based IA algorithm which adaptively designs the beamformers based on the knowledge of the channel estimation error variance, which is possible to be known in advance. Then, we compare the performance of the proposed scheme with interference leakage minimization algorithms. It is shown that under both perfect and imperfect CSI, the proposed LS-based IA outperforms interference leakage minimization algorithms.

For the next generation of wireless communication network, a heterogeneous network architecture with macro cells, small cells, and relays offers numerous advantages, such as higher spectrum efficiency, better fairness in resource allocation, and energy efficient usage as well as optimal coverage. However, this approach encounters various network management challenges, including interference mitigation techniques. In this paper, we consider a multi-user half-duplex amplify-and-forward-MIMO relay system, where a macro basis station communicates with edge cell users via relays and each node has multiple antennas. In this context, we propose two interference alignment (IA) schemes, for which a hybrid approach of the problem formulation based on zero-forcing (ZF) and minimum-mean-square-error optimization criteria was developed to deal with interferences in perfect and imperfect channel state information (CSI) cases. In the case of perfect CSI, simulation results show that this approach provides a SNR gain of about 4 dB regarding BER performance in comparison to that achieved by the reference approach, where all filters are determined solely based on ZF criterion. Furthermore, the achieved capacity and effective signal-to-interference-plus-noise ratio at each edge node are improved by around 5 dB. Having CSI errors, the system performance is significantly improved using the robust design IA approach by minimizing the expected value of cost functions.

Interference alignment (IA) is an effective method that can eliminate interferences in wireless networks, and has been applied to spectrum sharing in cognitive radio (CR) networks recently. However, the availability of perfect network channel state information (CSI) is necessary for most existing IA schemes, which is not practical in general due to the realistic communication scenarios and deployment challenges. In this paper, we apply IA to cognitive relay networks under CSI mismatch where the variance of the CSI measurement error depends on signal-to-noise ratio (SNR). An adaptive Max-SINR IA algorithm has been introduced to improve the performance of the secondary network by using the knowledge of CSI error variance. Finally, we analyze the performance of the secondary network in terms of the end-to-end equivalent transmission rate and outage probability. Simulation results indicate that our proposed adaptive Max-SINR IA scheme can greatly improve the performance of the secondary network.

A fundamental problem arising in dense wireless networks is the high co-channel interference. Interference alignment (IA) was recently proposed as an effective way to combat interference in wireless networks. The concept of IA, though, is originated by the capacity study of interference channels and as such, its performance is mainly gauged under ideal assumptions, such as instantaneous and perfect channel state information (CSI) at all nodes, and homogeneous signal-to-noise ratio (SNR) users, i.e., each user has the same average SNR. Consequently, the performance of IA under realistic conditions has not been completely investigated yet. In this paper, we aim at filling this gap by providing a performance assessment of spatial IA in practical systems. Specifically, we derive a closed-form expression for the IA average sum-rate when CSI is acquired through training and users have heterogeneous SNR. A main insight from our analysis is that IA can indeed provide significant spectral efficiency gains over traditional approaches in a wide range of dense network scenarios. To demonstrate this, we consider the examples of linear, grid and random network topologies.

In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, the authors propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, the authors compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. The authors show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR.

Interference alignment (IA) is a multi-user wireless communication strategy that enables several transmitters simultaneous communicate with their paired receivers without interfering each other. IA is a multiplexing gain optimal strategy at the expense of requiring the global channel state information (CSI) at the transmitters. Most previous works assume the availability of perfect CSI which is not possible in practice. The performance of IA algorithms based on perfect CSI drop dramatically in circumstance where CSI errors exist. In this paper we propose a robust minimum mean square error (MMSE) IA algorithm with imperfect CSI. Based on a Gaussian statistic channel error model, we give the mean square error objective function with per transmitter power constraint. The objective function is not joint convex in precoders and decoders, but convex in precoders with fixed decoders and vice versa. We convert the problem to two convex sub problems and iteratively find the solutions. Numerical results are presented to validate the effectiveness of proposed algorithm when CSI errors exist.

This paper studies the impact of channel error on the achievable rate of symmetrical K-user multiple-input multiple-output linear interference alignment (IA) networks. The upper and lower bounds of the achievable sum rate are derived analytically with the assumption of orthonormal transmit precoders and receive filters designed from imperfect channel state information (CSI) over both the uncorrelated and correlated channels. For uncorrelated channels, quite tight lower and upper bounds are obtained. The impact of channel error on the degrees of freedom (DoF) and the DoF persistence conditions are also investigated. Results show that the DoF of IA networks persists only if the channel error decreases in an order higher than the signal-to-noise ratio. For correlated channel, the lower and upper bounds for one realization of IA are derived. The derived upper bound can be used to characterize the achievable rate approximately. Simulation results indicate that the achievable rate of IA network is influenced significantly by CSI uncertainty. The obtained analytical bounds provide an intuitive way to show the impact of channel error on the achievable rate and thus can help practical systems deign.

A novel interference alignment (IA) scheme based on the errors-in-variables (EIV) mathematic model has been proposed to overcome the channel state information (CSI) estimation error for the MIMO interference channels. By solving an equivalently unconstrained optimization problem, the proposed IA scheme employing a weighted total least squares (WTLS) algorithm can obtain the solution to a constrained optimization problem for transmit precoding (TPC) matrices and minimizes the distortion caused by imperfect CSI according to the EIV model. It is shown that the design of TPC matrices can be realized through an efficient iterative algorithm. The convergence of the proposed scheme is presented as well. Simulation results show that the proposed IA scheme is robust over MIMO interference channels with imperfect CSI, which yields significantly better sum rate performance than the existing IA schemes such as distributed iterative IA, maximum signal-to-interference-plus-noise ratio (Max SINR), and minimum mean square error (MMSE) schemes.

It is very important that the radar sensor network has autonomous capabilities such as self-managing, etc. Quite often, MIMO interference channels are applied to radar sensor networks, and for self-managing purpose, interference management in MIMO interference channels is critical. Interference alignment (IA) has the potential to dramatically improve system throughput by effectively mitigating interference in multi-user networks at high signal-to-noise (SNR). However, the implementation of IA predominantly relays on perfect and global channel state information (CSI) at all transceivers. A large amount of CSI has to be fed back to all transmitters, resulting in a proliferation of feedback bits. Thus, IA with limited feedback has been introduced to reduce the sum feedback overhead. In this paper, by exploiting the advantage of heterogeneous path loss, we first investigate the throughput of IA with limited feedback in interference channels while each user transmits multi-streams simultaneously, then we get the upper bound of sum rate in terms of the transmit power and feedback bits. Moreover, we propose a dynamic feedback scheme via bit allocation to reduce the throughput loss due to limited feedback. Simulation results demonstrate that the dynamic feedback scheme achieves better performance in terms of sum rate.

Interference alignment (IA) is a suggested technique for multiple input multiple output (MIMO) based multipath interference channels to achieve large multiplexed gain. CSI (Channel state information) is required by IA schemes to design precoding vectors at the transmitter side. There will be significant capacity overhead in feedback link. This paper concentrates on the MIMO channels which are having overtime-correlated differential CSI feedback employed by IA design. Utmost multiplexing gain is obtained by the lowest amount of differential feedback. Because of restricted differential feedback, the interference in the upper bound is avoided by using IA system through differential CSI feedback. The analytical performance of the proposed algorithm is done using simulation results and achieved better Sum rate by using normal differential feedback and by using differential feedback through the Lloyd's algorithm.

Interference alignment (IA) is a novel technique to manage interference for multiuser wireless communications. The basic idea of IA in managing interference is based on the subspace separation. Since this property can be easily damaged, one might image that IA is sensitive to errors appeared in channel state information (CSI), which is needed at the transmitter side of each user. In this work, we will show some comparison results between IA and direct transmission (DT). In the DT scheme, the maximum likelihood (ML) receiver is used at each user. The simulation results show that IA systems are indeed very sensitive to CSI errors compared with the DT-ML system, while the complexity of the IA systems in implementation is comparable with the DT-ML systems if the constellation of transmitted symbols is of moderate cardinality.

Interference alignment (IA) is a linear precoding strategy that can achieve optimal capacity scaling at high SNR in interference networks. Most of the existing IA designs require full channel state information (CSI) at the transmitters, which induces a huge CSI signaling cost. Hence it is desirable to improve the feedback efficiency for IA and in this paper, we propose a novel IA scheme with a significantly reduced CSI feedback. To quantify the CSI feedback cost, we introduce a novel metric, namely the feedback dimension. This metric serves as a first-order measurement of CSI feedback overhead. Due to the partial CSI feedback constraint, conventional IA schemes can not be applied and hence, we develop a novel IA precoder/decorrelator design and establish new IA feasibility conditions. Via dynamic feedback profile design, the proposed IA scheme can also achieve a flexible tradeoff between the degree of freedom (DoF) requirements for data streams, the antenna resources and the CSI feedback cost. We show by analysis and simulations that the proposed scheme achieves substantial reductions of CSI feedback overhead under the same DoF requirement in MIMO interference networks.

In wideband multi-pair two-way relay networks, the performance of beamforming at a relay station (RS) is intimately related to the accuracy of the channel state information (CSI) available. The accuracy of CSI is determined by Doppler spread, delay between beamforming and channel estimation, and density of pilot symbols, including transmit power of pilot symbols. The coefficient of the Gaussian-Markov CSI error model is modeled as a function of CSI delay, Doppler spread, and signal-to-noise ratio, and can be estimated in real time. In accordance with the real-time estimated coefficients of the error model, an adaptive robust maximum signal-to-interferenceand- noise ratio (Max-SINR) plus maximum signal-to-leakage-and-noise ratio (Max-SLNR) beamformer at an RS is proposed to track the variation of the CSI error. From simulation results and analysis, it is shown that: compared to existing non-adaptive beamformers, the proposed adaptive beamformer is more robust and performs much better in the sense of bit error rate (BER); with increase in the density of transmit pilot symbols, its BER and sum-rate performances tend to those of the beamformer of Max-SINR plus Max-SLNR with ideal CSI.

We consider the effective degrees of freedom (DoF) achieved by interference alignment when channel state information (CSI) is acquired by training and feedback. For a flat block- fading K × K interference channel with power P per transmitter and M antennas per node, we show that interference alignment achieves higher DoF than orthogonal transmission (e.g., TDMA) only if the channel coherence time is large and the capacity of feedback link is at least as Θ(log P). Under this condition, to maximize the effective DoF, each receiver needs to feed back CSI via (M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -1)log P bits per coherence interval; smaller growth rate of feedback bits will decrease the effective DoF. We also show that in the presence of training and feedback cost, K = 3 achieves the optimal DoF for a broad range of channel characteristics; with larger number of user pairs, the DoF falls short of its optimum and beyond a certain point becomes a decreasing function of K.

Interference Alignment in Multi-user MIMO Systems