Interference Alignment in Multi-user MIMO Systems

Multiple-input multiple-output (MIMO) wireless communication systems can achieve higher throughput through interference alignment. For a small number of users, determining the maximum possible degrees of freedom as well as the feasibility of interference alignment in MIMO systems is well studied. However, the issues of scheduling in systems employing interference alignment and serving a large number of users have received little attention so far. In this paper, we study the problem of joint scheduling, interference alignment, and packet admission control in MIMO wireless systems with the goal of maximizing system throughput subject to stability constraints. We formulate a stochastic network optimization problem and propose a scheduling and interference alignment (SIA) algorithm. In each time slot, SIA schedules some users among many competing ones to transmit data, and determines encoding and decoding matrices for the selected users. Packet admission control is performed in each time slot. In addition, we propose a heuristic semi-distributed algorithm (SDSIA), which has a lower computational complexity than the SIA algorithm. Via simulation, we evaluate the performance of SIA and SDSIA for different algorithm parameters and different numbers of users. We also compare the performance of SDSIA with other approaches which do not simultaneously exploit interference alignment and scheduling and find that the combination of these two techniques increases the achievable data rate dramatically.

The explosive demand for high data rates and the need ubiquitous wireless connectivity has led to the phenomenon of network densification, the deployment of large number of base station within a geographic area. Since the radio spectrum is limited, wireless transmissions need to share a common resource which results in interference. Interference in turn creates a bottleneck on the communication rate. Recently three breakthroughs have been made to increase the capacity of wireless networks while mitigating interference : multiple input multiple output (MIMO) beamforming, interference alignment (IA) and pattern reconfigurable antennas (PRA). While a great deal of progress has been made on understanding each individually, relatively little is known about how to use these techniques in combination to increase system performance. In this dissertation, we analyze and experimentally evaluate how these new technologies can be leveraged to enhance the rate performance of communication networks. Specifically, we address three problems: i) enhancing multi-user MIMO performance with PRA, ii) improving IA performance with PRA-based antenna selection, and iii) enabling practical blind IA with PRA. To understand the impact PRAs on MU-MIMO and IA, it is necessary to evaluate their performance through measurements. Simulation-based studies often reiterate over set of simplistic channel models and unrealistic assumptions. This dissertation focuses on a measurement-based evaluation approach. For each of these problems, a hardware testbed implementation and measurement methodology is developed for evaluating the performance of the aforementioned technologies through efficient and repeatable experiments. The first two major contributions of this dissertation focus on multi-user MIMO (MU-MIMO) and IA. While the theoretical rate gains of MU-MIMO and IA are substantial, the performance gains in practical systems and measured channels have been limited. One of the key limiting factors are spatially correlated user channels. In this work, we propose MU-MIMO and IA transmission schemes that leverage the pattern diversity provided by PRAs to mitigate the effects of spatial correlation in wireless channels. PRAs are capable of dynamically adjusting their radiation pattern, providing an additional degree of freedom that can be exploited to improve MU-MIMO and IA performance by treating the array configuration and radiation characteristics as additional components in the joint optimization of adaptive system parameters. We quantify the benefits of pattern diversity on the rate performance of MU-MIMO and IA systems through extensive measurements. Furthermore, we develop efficient antenna mode selection algorithms to realize those benefits without increasing the system complexity or overhead, making these techniques suitable for practical implementation. The third contribution of this dissertation focuses on a transmission technique known as blind IA. In contrast to MU-MIMO and conventional IA, blind IA is signaling scheme that suppresses interference in multi-user systems, without the knowledge of channel state information at the transmitter (CSIT). The key to performing IA without CSIT is the use of PRAs that are capable of dynamically switching among a fixed number of radiation patterns to introduce artificial fluctuations in the channel. In this dissertation, we develop a novel implementation of a blind IA system on a software defined radio platform where each of the receivers is equipped with a PRA. Our work provides the first experimental evaluation of PRA-based blind IA schemes and demonstrates significant gains in rate and reliability over traditional orthogonal transmission schemes such as TDMA.

In multi-user wireless communication system, there is huge demand for higher data rates. One promising solution to achieve it is through the amalgamation of Code Division Multiple Access (CDMA) and Orthogonal Frequency Division Multiplexing (OFDM) technologies which results in Multi Carrier-CDMA (MC-CDMA) system. In CDMA system, the multiple access interference (MAI) can be reduced through proper selection of spreading codes. Bit error rate (BER) is an effective measure to evaluate the interference performance of a multi-user communication system. In this paper the BER and Peak to Average Power Ratio (PAPR) of MC-CDMA system is analyzed for different orthogonal spreading codes such as Walsh codes, complementary Golay codes and Orthogonal Gold codes in Rayleigh multipath fading channel employing Low Density Parity Check (LDPC) channel coding technique.

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.

Recent results establish the optimality of interference alignment to approach the Shannon capacity of interference networks at high SNR. However, the extent to which interference can be aligned over a finite number of signalling dimensions remains unknown. Another important concern for interference alignment schemes is the requirement of global channel knowledge. In this work, we provide examples of iterative algorithms that utilize the reciprocity of wireless networks to achieve interference alignment with only local channel knowledge at each node. These algorithms also provide numerical insights into the feasibility of interference alignment that are not yet available in theory.

We show that the three-user M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> × M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> Multiple-Input Multiple-Output (MIMO) interference channel where each transmitter is equipped with M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> antennas and each receiver is equipped with M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> antennas has (M) d(M, N) = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> min (M/2-1/κ, N/2+1/κ) degrees of freedom (DoF) normalized by time, frequency, and space dimensions, where = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> min(M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> ), N = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> max(M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> ), κ = <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Δ</sup> ⌈M/N-M⌉. While the DoF outer bound of d(M, N) is established for every M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> value, the achievability of d(M, N) DoF is established in general subject to a normalization with respect to spatial extensions, i.e., the scaling of the number of antennas at all nodes. In particular, we show that qd(M, N) DoF are achievable for the three-user qMT × qMR MIMO interference channel, for some positive integer q, which may be seen as a spatial extension factor. q is the scaling factor needed to make the value qd(M, N) an integer. Given spatial extensions, the achievability relies only on linear beamforming based interference alignment schemes and requires neither channel extensions nor channel variations in time or frequency. In the absence of spatial extensions, it is shown through examples how essentially the same interference alignment scheme may be applied over time-extensions over either constant or time-varying channels. The central new insight to emerge from this paper is the notion of subspace alignment chains as the DoF bottlenecks. The subspace alignment chains are instrumental both in identifying the extra dimensions to be provided by a genie to a receiver for the DoF outer bound, as well as in the construction of the optimal interference alignment schemes. The DoF value d(M, N) is a piecewise linear function of M, N, with either M or N being the bottleneck within each linear segment, whereas the other value contains some redundancy, i.e., it can be reduced without reducing the DoF. The corner points of these piecewise linear segments correspond to two sets, A={1/2, 2/3, 3/4, ...}and B={1/3, 3/5, 5/7, ...}. The set A contains all those values of M/N and only those values of M/N for which there is redundancy in both M and N, i.e., either can be reduced without reducing the DoF. The set B contains all those values of M/N and only those values of M/N for which there is no redundancy in either M or N, i.e., neither can be reduced without reducing the DoF. Because A and B represent settings with maximum and minimum redundancy, essentially they are the basis for the DoF outer bounds and inner bounds, respectively. Our results settle the question of feasibility of linear interference alignment, introduced previously by Cenk et al., for the three-user M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> × M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> MIMO interference channel, completely for all values of M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> . In particular, we show that the linear interference alignment problem (M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> × M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> , d) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> (as defined in previous paper by Cenk et al.) is feasible if and only if d ≤ d(M, N). With the exception of the values M/N ∈ B, and only with that exception, we show that for every M/N value there are proper systems (as defined by Cenk et al.) that are not feasible. Evidently the redundancy contained in all other values of M/N manifests itself as superfluous variables that are not discounted in the definition of proper systems, thus creating a discrepancy between proper and feasible systems. Our results show that M/N ∈ A are the only values for which there is no DoF benefit of joint processing among co-located antennas at the transmitters or receivers. This may also be seen as a consequence of the maximum redundancy in the M/N ∈ A settings.

We consider the application of interference alignment (IA) to the cellular case with constant MIMO channel coefficients. Neglecting the weakest interferers in the network, we introduce an algorithm to obtain a partially connected (in particular, L-interfering) network, over which the feasibility of IA can be analyzed simply. We consider the application of IA over the obtained L-interfering network, while the rest of the interference is treated as noise. We benchmark this technique through extensive Monte-Carlo simulations, and introduce an approximate, compact expression for the ergodic mutual information achievable in the considered network setting.

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.

MIMO researches penetrate the network community due to recent advances in MIMO degree-of-freedom (DoF) frameworks. Independent from MIMO, Successive Interference Cancellation (SIC) is a powerful multi-user detection technology in physical layer, and Interference Alignment (IA) is a powerful technique for handling interference. Based on the understanding of the strengths and weaknesses of SIC and DoF, we propose mutual assistance by joint IA, SIC and DoF-based Interference Cancellation (DoF IC) to (i) conserve precious DoF resources through IA and SIC; (ii) meet strict SINR threshold criteria through IC and IA. In this paper, we develop the mathematical model to achieve the two ideas in a multi-hop MIMO network. Combined with scheduling and routing constraints, we developed a cross-layer optimization framework to the throughput maximization problem with joint IA and SIC for MIMO networks. Simulation results show that the join of IA and SIC can significantly conserve DoFs for IC and thereby improve the throughput.

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 (IA) has attracted great attention in the last few years for its breakthrough performance in interference networks. However, despite the numerous works dedicated to IA, the feasibility conditions of IA remains unclear for most network topologies. The IA feasibility analysis is challenging as the IA constraints are sets of high-degree polynomials, for which no systematic tool to analyze the solvability conditions exists. In this work, by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first-order terms, we propose a sufficient condition that applies to MIMO interference networks with general configurations. We have further proved that this sufficient condition matches with the necessary conditions under a wide range of configurations. These results further consolidate the theoretical basis of IA.

Interference alignment is a novel technique that aligns interference in each receiver using half of the signal space and leaving the other half for the desired signal, independent of the number of users that share the channel. Most of the research focuses on the channel’s capacity, degrees of freedom or throughput. In this paper we work with the error probability. For this purpose, we consider the pairwise error probability using a particle swarm optimization to optimize the precoders of a three-user interference channel with interference alignment. Simulations show that using this technique improves the performance of the three users when optimized jointly by at least 15dB SNR at a 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> BER for the first user compared to the one proposed by Cadambe and Jafar, and at least 5dB SNR at a 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> BER when optimizing the precoder for user one only compared to user one when the three users are optimized jointly.

Many works considered the CSI uncertainty effect on interference alignment (IA) in MIMO narrow-band interference channel (IC). However, much less attention has been paid to CSI uncertainty effect on IA in SISO frequency-selective IC. This is partially due to the impractical requirement of infinitely large number of subcarriers to implement IA in such channel. Recently, a new approach was proposed to alleviate this limitation through applying IA in time domain while utilizing the guard interval [1]. In this paper, we investigate the performance of this approach under CSI imperfection. We also propose robust transceiver design algorithm that maximizes the received SINR accounting for the CSI imperfection in SISO frequency selective IC. In addition, the average sum stream rate under CSI imperfection is derived.

Interference alignment (IA) with symbol extensions in the quasi-static flat-fading K-user multipleinput multiple-output (MIMO) interference channel (IC) is considered in this paper. In general, long symbol extensions are required to achieve the optimal fractional degrees of freedom (DOF). However, long symbol extensions over orthogonal dimensions produce structured (diagonal or block diagonal) channel matrices from transmitters to receivers. Most of existing approaches are limited in cases where the channels have some special structures, because they align the interference without preserving the dimensionality of the desired signal explicitly. To overcome this common drawback of most existing IA algorithms, two novel iterative algorithms for IA with symbol extensions are proposed. The first algorithm designs transceivers for IA based on the mean square error (MSE) criterion which minimizes the total MSE of the system while preserving the dimensionality of the desired signal. The novel IA algorithm is a constrained optimization problem which can be solved by Lagrangian method. Its convergence is proven as well. Utilizing the reciprocity of alignment, the second algorithm is proposed based on the maximization of the multidimensional case of the generalized Rayleigh Quotient. It maximizes each receiver’s signal to interference plus noise ratio (SINR) while preserving the dimensionality of the desired signal. In simulation results, we show the superiority of the proposed algorithms in terms of four aspects, i.e., average sum rate, the fraction of the interfering signal power in the desired signal subspace, bit error rate (BER) and the relative power of the weakest desired data stream.

In this paper, we present uplink interference alignment (IA) schemes for two-cell multiple-input–multiple-output (MIMO) channels. Assuming that each cell has $K$ interfering users, we propose an IA scheme for the full interference channel (FIC) and derive the achievable degrees of freedom (DOFs). The proposed scheme is extended to a two-cell Z-interference channel (ZIC), where only one of the two cells is subject to interference. The achievable DOF for the two-cell ZIC channel is also derived, and it is compared with that of the FIC with the IA and that of the conventional orthogonal scheme based on numerical results.