An interference alignment scheme based on limited feedback with differentiation in heterogeneous networks

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.

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.

In Multi-user MIMO (MU-MIMO) downlink system, suitable user selection schemes can improve spatial diversity gain. In most of previous studies, it is always assumed that the base station (BS) knows full channel state information (CSI) of each user, which does not consider the reality. However, there are only limited feedback bits in real system. Besides, user fairness is often ignored in most of current user selection schemes. To discuss the user fairness and limited feedback, in this paper, the user selection scheme with limited feedback bits is proposed. The BS utilizes codebook precoding transmitting strategy with LTE codebook. Furthermore, this paper analyzes the influence of the number of feedback bits and the number of users on user fairness and system sum capacity. Simulation results show that in order to achieve better user fairness, we can use fewer bits for feedback CSI when the number of user is small, and more feedback bits when the number of users is large.

The provision for spectrally efficient multicast broadcast services (MBS) is one of the key functional requirements for next generation wireless communication systems. The challenge inherent to MBS is to ensure that all MBS users can be served, and one effective solution to this problem is to employ MIMO multicast transmit precoding. In previous works on MIMO multicast transmit precoding design, the authors either assumed (1) perfect transmitter-side channel state information (CSIT) or (2) special channel conditions that facilitate precoder design with imperfect CSIT. In this paper, we focus on transmit precoding design for MBS where the CSIT is obtained via limited feedback. In addition, we analyze the average minimum receive signal-noise-ratio (RxSNR) among the MBS users and study the order of growth with respect to the number of MBS users, the number of feedback bits, and the number of transmit antennas. Finally, we propose a threshold based feedback reduction scheme and study the tradeoff between feedback cost and performance loss.

We study a two-user multiple-input single-output Gaussian interference channel with limited rate feedback and transmitter cooperation. Each receiver quantizes the channel state information of the direct and cross channels, and sends the codebook indices back to the transmitters through two sum-rate-limited feedback channels. The quantization errors reduce the beamforming gain from the direct transmitter, and cause interference leakage from the cross transmitter. Under an assumption of high signal-to-noise ratio, we first approximate the average transmission rate of each link, and use the sum rate to find the optimal transmit power and corresponding feedback bit allocation. We show that the maximum sum throughput is achieved using full transmit power, and the achievable sum rate under limited feedback is bounded above by a constant. We then extend the results to the case where secrecy is desired. In contrast to the first problem, increasing the transmit power beyond a certain point decreases the secrecy performance. Additionally, we analyze the asymptotic behavior of the solutions when the total feedback bandwidth and the number of transmit antennas grow large. We derive all results in closed form. Simulations validate the theoretical analysis and demonstrate the significant performance gains that result from the use of optimal transmit power control and intelligent feedback bit allocation.

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.

We consider the uplink three-cell single-user cellular systems with limited feedback interference alignment (IA). Considering the exchange of channel state information (CSI) between base stations (BSs), IA solution can be done at BSs. Then the indices of the quantized precoding vectors are fed back to users. A joint quantization strategy, which quantizes the precoding vectors for different users jointly, is proposed. The proposed quantization scheme enlarges the codebooks and quantizes precoding vectors jointly through the exchange of codebook information between BSs. The quantized precoding vectors for different users are set to have a same index. Only one of the three BSs is appointed to broadcast the same index so that the total feedback cost would not be increased. With the proposed quantization scheme, the quantization errors are mitigated and the system sum rate is increased. A quantization criterion, which we refer to as the maximum sum rate criterion, is also proposed. Compared with the general minimum chordal distance criterion, the proposed quantization criterion can achieve a higher sum rate. Performance improvement of the proposed scheme is analyzed. Simulations also confirm its effectiveness.

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 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.

Interference alignment (IA) in heterogeneous networks (HetNet) is a promising technology that can achieve a significant increase of network capacity. However, there are some issues on IA in HetNet. One of them is that each pico base station (BS) requires a large number of transmit antennas, because it tries to align all inter-pico interference. In actual environments, the strength of inter-pico interference varies depending on the distance between pico cells, i.e., inter-pico interference from the remote pico cell is much smaller than that from the close one, so that aligning all interference is not necessarily the best. In addition, the residual interference from macro BS that is not eliminated by IA may decrease the capacity. In this paper, we propose 1) to reduce the required number of transmit antennas at pico BS by clustering pico cells based on the strength of inter-pico interference and 2) to apply combined weight, that comprises ZF (zero forcing) weight and MMSE (minimum mean square error) weight, to pico user equipment (UE) so as to mitigate the residual interference that is not eliminated perfectly by IA. Simulation results show that by applying combined weight to pico UEs, the capacity increases compared to the case of applying only ZF weight, and that the average rate per pico cell normalized by the required number of transmit antennas at each pico BS, that is, the rate per transmit antenna can be increased with pico cell clustering, which indicates that each pico BS can utilize its transmit antennas more efficiently.

Assuming perfect channel state information, the existing interference alignment (IA) algorithm proposed in [2] suppresses inter-cell interference (ICI) by aligning ICI to a randomly selected reference vector. However, IA in practice relies on limited feedback, resulting in residual ICI. In this letter, we propose the optimization of the reference vector for regulating the residual ICI. Specifically, it is shown that the reference vector that minimizes an upper bound on the residual ICI power is the eigenvector corresponding to the largest eigenvalue of the sum of the interference-channel matrices multiplied by their corresponding Hermitian matrices. Moreover, the performance gain of the proposed IA algorithm compared with the existing one in [2] is analyzed and demonstrated by simulation to be significant.

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.

Multicell cooperative transmit strategies typically require full channel state information (CSI) at the base stations. In this paper, a more practical limited feedback scenario is considered for a recently proposed multicell beamforming approach that approximately maximizes the sum-rates in a two-cell two-user network. In the limited feedback system presented, the desired and interfering CSI is quantized by the users and fed back to the base stations over a finite-bandwidth link. Each receiver is assumed to use two separate codebooks to quantize the desired and interfering channels. It is proposed to vary the codebook sizes adaptively as a function of the relative strength of the channels to minimize the loss in sum-rate. To this end, the mean loss in sum-rate due to random vector quantization is quantified. Closed-form expressions are derived to partition the available feedback bits adaptively between the desired and interfering channels to minimize the mean loss in sum-rate. Finally, simulations are used to verify the results presented in the paper.

Downlink multi-user transmission techniques that allow several users to be served simultaneously in frequency and time have been recognized as a promising means to increase system capacity. However they require accurate channel state information (CSI) at the base station (BS) such that appropriate signal processing can be performed to separate multiple users in the space domain. In practice however, CSI cannot be perfectly known to the BS due to the capacity-limited feedback channel in FDD systems for instance. In this letter we investigate multiuser multiple-input single-output (MU-MISO) transmission with limited feedback. In particular we identify the useful information that the BS needs to deal with inter-user interference and a codebook design is derived accordingly. In addition, an adaptive threshold-based feedback approach is proposed, where only users with good feedback quality are allowed to do feedback. It is shown that the adaptive scheme can effectively improve the system performance given a fixed number of feedback bits.

To maintain a specific degree of multiplexing gain with limited feedback in multiple-input/multiple-output broadcast channels, the number of feedback bits has been increased linearly with the signal-to-noise ratio (SNR) measured in decibel, and conditions for the slope of this increase have been derived in previous studies. However, previous studies mostly focused on the chordal distance (ChD) for channel quantization, although it is not an optimally designed distance measure. Thus, the possibility exists that the same degree of multiplexing gain can be obtained by using fewer feedback bits than the existing method requires. In this paper, we propose an optimal distance measure that can maximize the multiplexing gain achieved by limited-feedback-based block diagonalization over broadcast channels. Then, we provide a sufficient condition for the number of feedback bits to achieve a specific degree of multiplexing gain with the proposed method. The sufficient number of feedback bits is given by a linear function of the SNR (decibel) as in previous studies, but the slope of the linear increase can be much less than that obtained in previous studies. As a consequence, the proposed method achieves higher multiplexing gain and corresponding throughput than the existing methods with the same number of feedback bits.