Cenk M. Yetis

On Feasibility of Interference Alignment in MIMO Interference Networks

We explore the feasibility of interference alignment in signal vector space-based only on beamforming-for K-user MIMO interference channels. Our main contribution is to relate the feasibility issue to the problem of determining the solvability of a multivariate polynomial system which is considered extensively in algebraic geometry. It is well known, e.g., from Bezouts theorem, that generic polynomial systems are solvable if and only if the number of equations does not exceed the number of variables. Following this intuition, we classify signal space interference alignment problems as either proper or improper based on the number of equations and variables. Rigorous connections between feasible and proper systems are made through Bernshteins theorem for the case where each transmitter uses only one beamforming vector. The multibeam case introduces dependencies among the coefficients of a polynomial system so that the system is no longer generic in the sense required by both theorems. In this case, we show that the connection between feasible and proper systems can be further strengthened (since the equivalency between feasible and proper systems does not always hold) by including standard information theoretic outer bounds in the feasibility analysis.

Feasibility Conditions for Interference Alignment

The degrees of freedom (DoF) of K-user MIMO interference networks with constant channel coefficients are not known in general. Determining the feasibility of a linear interference alignment is a key step toward solving this open problem. Our approach in this paper is to view the alignment problem for interference networks as a multivariate polynomial system and determine its solvability by comparing the number of equations and the number of variables. Consequently, we divide the interference networks into two classes - proper and improper, where interference alignment is and is not achievable, respectively. An interference network is called proper if the cardinality of every subset of equations in the corresponding polynomial system is less than or equal to the number of variables involved in that subset of equations. Otherwise, it is called improper. Our intuition in this paper is that for general channel matrices, proper systems are almost surely feasible and improper systems are almost surely infeasible. We prove the direct link between proper (improper) and feasible (infeasible) systems for some important cases, thus significantly strengthening our intuition. Numerical simulation results also support our intuition.

Sub-stream fairness and numerical correctness in MIMO interference channels

Signal-to-interference plus noise ratio (SINR) and rate fairness in a system are substantial quality-of-service (QoS) metrics. The acclaimed SINR maximization (max-SINR) algorithm does not achieve fairness between users streams, i.e., sub-stream fairness is not achieved. To this end, we propose a distributed power control algorithm to render sub-stream fairness in the system. Sub-stream fairness is a less restrictive design metric than stream fairness (i.e., fairness between all streams) thus sum-rate degradation is milder. Algorithmic parameters can significantly differentiate the results of numerical algorithms. A complete picture for comparison of algorithms can only be depicted by varying these parameters. For example, a predetermined iteration number or a negligible increment in the sum-rate can be the stopping criterion of an algorithm. While the distributed interference alignment (DIA) can reasonably achieve sub-stream fairness for the later, the imbalance between sub-streams increases as the preset iteration number decreases. Thus comparison of max-SINR and DIA with a low preset iteration number can only depict a part of the picture. We analyze such important parameters and their effects on SINR and rate metrics to exhibit numerical correctness in executing the benchmarks. Finally, we propose group filtering schemes that jointly design the streams of a user in contrast to max-SINR scheme that designs each stream of a user separately.

A New Training Protocol for Channel State Estimation in Wireless Relay Networks

In this correspondence, we introduce a new training protocol for channel state estimation in wireless relay networks. The distinctive feature of our protocol is that each relay forwards the imperfect channel state information (CSI) to the destination. We show that our method allows to obtain at the destination a higher effective SNR and a faster transfer of the CSI compared with the other existing training protocols.

Balancing Weighted Substreams in MIMO Interference Channels

Substreams refer to the streams of each user in a system. Substream weighting, where the weights determine the prioritization order, can be important in multiple-input multiple-output interference channels. In this letter, a distributed algorithm is proposed for the problem of power minimization subject to weighted SINR constraint. The algorithm is based on two basic features, the well-known distributed power control algorithm by Yates in 1995 and a simple linear search to find feasible SINR targets. The power control law used in the proposed algorithm is proven to linearly converge to a unique fixed point.

Optimal packet length for throughput maximization in correlated multi-user channels

In this paper, a multi-user uplink channel with correlated Rayleigh fading coefficients is considered. Optimal data packet length is derived for throughput maximization of the system with stop and wait automatic repeat request (SW-ARQ). For the throughput formulation of the SW-ARQ system, the packet error rate (PER) is analytically derived using a two-state Markov chain modelling of the signal-to-interference ratio (SIR) of the time-varying channel. For the PER formulation, second-order channel statistics including average level crossing rate (LCR) and average outage duration (AOD) are derived. Numerical results indicate the accuracy of the obtained theoretical results. The effect of increasing the number of interferers on the throughput is investigated w.r.t given SIR threshold.

Finite-SNR Precoder Designs for the Interference Relay Channel Without CSI at the transmitters

Recently, a transmission strategy was designed for the K-user interference channel (IC) without CSI at the transmitters (CSIT) but aided by a relay which knows the global CSI, where it was shown that K - 1 relay antennas are required to attain the maximum network DoF. In this paper, we derive general IA feasibility conditions for a single relay-aided IC with CSI at both the relay and the transmitters. Our result shows that except for the special case of K = 3 users, providing CSI to the transmitters still requires K - 1 relay antennas to achieve the maximum network DoF. Next, we design the minimum-sum-mean-squareerror (MSMSE) and weighted-sum-rate (WSR) maximizing precoders for the relay-aided IC network without CSIT which show higher sum-rate in the finite-SNR region compared to the IA precoding. Further, a so-called scaled-IA initialization is proposed for the MSMSE and the WSR algorithms which not only preserves the network DoF but also saves the power at the relay considerably compared to the MSMSE and the WSR schemes with random initializations. Extensive simulation results in both symmetric and asymmetric networks show that the MSMSE precoder shows better BER performance than both the IA and the WSR algorithms for low-to-moderate data rates.

Precoder design for the interference relay channel with blind transmitters

In this paper, for the K-user interference relay channel (IRC) with transmitters and relays having no and global channel state information (CSI), respectively, a minimum sum mean squared error (MSMSE) based relay precoder is proposed. It is shown that MSMSE outperforms interference alignment (IA) relay precoder in sum rate at low to mid signal-to-noise ratio (SNR) regions as well as in bit error rate (BER) at all SNR regions for small and moderate sizes of Gray encoded constellations.

Improper Gaussian signaling for the K-user SISO interference channel

This paper studies the transmit optimization for the K-user Gaussian single-input single-output interference channel (SISO-IC), with the interference treated as Gaussian noise and by applying improper or circularly asymmetric complex Gaussian signaling. The transmit optimization with improper Gaussian signaling involves not only the signal covariance as in the conventional proper or circularly symmetric complex Gaussian signaling, but also the signal pseudo-covariance, which is conventionally set to zero in proper Gaussian signaling. By utilizing the rate-profile method, the achievable rate region of the K-user SISO-IC is characterized by solving a sequence of minimum-weighted-rate maximization (MinWR-Max) problems, which are non-convex and thus difficult to be solved globally optimally. By applying the semidefinite relaxation (SDR) technique, we propose an efficient approximate solution, which jointly optimizes the covariance and pseudo-covariance of the transmitted signals. Simulation results demonstrate the effectiveness of the proposed algorithm for the K-user SISO-IC with improper Gaussian signaling.

Implementation aspects for interference alignment

Several interference alignment (IA) testbeds have been reported by research groups that validate the theoretical findings thus demonstrating the feasibility of IA. The design complexity of the IA testbed is significant since many simultaneous wireless links have to be established to observe the benefits of IA. Therefore, the already enormous efforts needed for the development of multiple-input multiple-output (MIMO) testbeds are folded multiple times in IA testbeds. In general, testbeds can be categorized into three groups depending on the hardware platform, generic, specific and the hybrid of two. Clearly, developing on generic, hybrid and application specific platforms in turn are the safe steps towards real life prototyping. There are many research groups that have been developing IA on generic platforms [1]-[17]. To the best of our knowledge, there is only one research group that has developed on a hybrid platform [18], and none on the application specific platform. In this paper, we review the experimental IA evaluations in the literature, include important aspects from well-known prototyping principles in the picture, and give comparative discussion with the state-of-art wireless communications testbeds.