Paul de Kerret

Interference Alignment with Incomplete CSIT Sharing

In this work we study the impact of having only incomplete channel state information at the transmitters (CSIT) over the feasibility of interference alignment (IA) in a K-user MIMO interference channel (IC). Incompleteness of CSIT refers to the perfect knowledge at each transmitter (TX) of only a sub-matrix of the global channel matrix, where the sub-matrix is specific to each TX. This paper investigates the notion of IA feasibility for CSIT configurations being as incomplete as possible, as this leads to feedback overhead reductions in practice. We distinguish between antenna configurations where (i) removing a single antenna makes IA unfeasible, referred to as tightly-feasible settings, and (ii) cases where extra antennas are available, referred to as super-feasible settings. We show conditions for which IA is feasible in strictly incomplete CSIT scenarios, even in tightly-feasible settings. For such cases, we provide a CSIT allocation policy preserving IA feasibility while reducing significantly the amount of CSIT required. For super-feasible settings, we develop a heuristic CSIT allocation algorithm which exploits the additional antennas to further reduce the size of the CSIT allocation. As a byproduct of our approach, a simple and intuitive algorithm for testing feasibility of single stream IA is provided.

On the degrees of freedom of the K-user time correlated broadcast channel with delayed CSIT

The degrees of freedom (DoF) of a K-User MISO broadcast channel (BC) is studied when the transmitter (TX) has access to a delayed channel estimate in addition to an imperfect estimate of the current channel. The current estimate could be for example obtained from prediction applied on past estimates, in the case where feedback delay is within the coherence time. Prior results in this setting are promising, yet remain limited to the two-user case. In contrast, we consider here an arbitrary number of users. We develop a new transmission scheme, called the Kα-MAT scheme, which builds upon both the principle of the MAT alignment from Maddah-Ali and Tse and zero-forcing (ZF) to achieve a larger DoF in the channel state information (CSI) configuration previously described. We also develop a new upper bound for the DoF to compare with the DoF achieved by Kα-MAT. Although not optimal, the Kα-MAT scheme performs well when the CSIT quality is not too delayed or K is small. The Kα-MAT scheme can be seen as a robust version of ZF with respect to the delay in the CSI feedback.

Sparse precoding in multicell MIMO systems

In this work, we consider the joint precoding across K distant transmitters (TXs) towards K single-antenna receivers (RXs) and we let the TXs have access to perfect Channel State Information (CSI). Instead of considering the conventional method of clustering to allocate the users data symbols, we focus on determining the most efficient symbol sharing patterns. Consequently, we optimize directly the users data symbol allocation subject to a constraint on the total number of users data bits transmitted through the core network. We develop a novel approach whereby sparse precoders approximating the true precoders are computed. These precoders require only a fraction of the overall symbol sharing overhead while introducing only limited losses. Thereby, allocating the symbols only to their nonzero coefficients leads to very efficient symbol sharing (or routing) algorithms. Furthermore, these algorithms have a much lower complexity that conventional approaches. By simulations, we show that our approach outperforms clustering-based multicell MIMO methods from the literature and that the routing obtained is mainly dependent on the pathloss structure and can be applied using only long term CSI with reduced losses.

Robust precoding for network MIMO with hierarchical CSIT

In this work1 we consider a wireless network with K cooperating transmitters (TXs) serving jointly K receivers (RXs). Due to the practical limitations of the backhaul network, it is relevant to consider a setting where each TX receives its own imperfect estimate of the multi-user channel state, denoted as the distributed channel state information (CSI) setting. We focus in this work on a particular distributed CSI configuration called hierarchical CSI configuration in which the TXs can be ordered by increasing level of CSI. This scenario is particularly relevant for future networks with heterogeneous backhaul where the TXs connected with a weak backhaul link will receive only a coarse estimate while the TXs with a stronger backhaul will have a more accurate CSI. In that scenario, we formulate the optimal precoding as a team decision problem. Solving optimally this problem is extremely challenging such that we propose a heuristic approach allowing to obtain a simple, yet efficient and practical, precoding algorithm. The proposed precoding algorithm exploits the hierarchical structure of the CSI to make the transmission more robust to the imperfect CSI knowledge at the TXs.

Network MIMO: Transmitters with no CSI can still be very useful

In this paper1 we consider the Network MIMO channel under the so-called Distributed Channel State Information at the Transmitters (D-CSIT) configuration. In this setting, the precoder is designed in a distributed manner at each Transmitter (TX) on the basis of local versions of Channel State information (CSI) of various quality. Although the use of simple Zero-Forcing (ZF) was recently shown to reach the optimal DoF for a Broadcast Channel (BC) under noisy, yet centralized, CSI at the TX (CSIT), it can turn very inefficient when faced with D-CSIT: The number of Degrees-of-Freedom (DoF) achieved is then limited by the worst CSI accuracy across TXs. To circumvent this effect, we develop a new robust transmission scheme improving the DoF. A surprising result is uncovered by which, in the regime of so-called weak CSIT, the proposed scheme is shown to be DoF-optimal and to achieve a centralized outerbound consisting in the DoF of a genie-aided centralized setting in which the CSIT versions of all TXs are available everywhere. Building upon the insight obtained in the weak CSIT regime, we develop a general D-CSIT robust scheme for the 3-user case which improves over the DoF obtained by conventional robust approaches for any arbitrary CSIT configuration.

CSI feedback allocation in multicell MIMO channels

In this work1, we consider the joint precoding across K transmitters (TXs), sharing the knowledge of the users data symbols being transmitted to K single-antenna receivers (RXs). We consider a distributed channel state information (DCSI) configuration where each TX has its own local estimate of the overall multiuser MIMO channel. Our focus is on the optimization of the allocation of the CSI feedback subject to a constraint on the total amount of feedback. As a starting point, we consider the Wyner model where we derive a distance-based CSI allocation achieving close to the optimal performance using only a small percentage of the total feedback. The approach relies on the exploitation of the attenuation to restrict the cooperation at a local scale. Indeed, the CSI and the users data symbols are then shared to only a finite number of neighbors such that our approach appears as an improved alternative to clustering.

The multiplexing gain of a two-cell MIMO channel with unequal CSI

In this work1, the joint precoding across two distant transmitters (TXs), sharing the knowledge of the data symbols to be transmitted, to two receivers (RXs), each equipped with one antenna, is discussed. We consider a distributed channel state information (CSI) configuration where each TX has its own local estimate of the channel and no communication is possible between the TXs. Based on the distributed CSI configuration, we introduce a concept of distributed MIMO precoding. We focus on the high signal-to-noise ratio (SNR) regime such that the two TXs aim at designing a precoding matrix to cancel the interference. Building on the study of the multiple antenna broadcast channel, we obtain the following key results: We derive the multiplexing gain (MG) as a function of the scaling in the SNR of the number of bits quantizing at each TX the channel to a given RX. Particularly, we show that the conventional Zero Forcing precoder is not MG maximizing, and we provide a precoding scheme optimal in terms of MG. Beyond the established MG optimality, simulations show that the proposed precoding schemes achieve better performances at intermediate SNR than known linear precoders.

Best-response team power control for the interference channel with local CSI

We study in this paper the problem of binary power control in interference channels with single-antenna nodes. In many practical scenarios, letting transmitters (TXs) exchange the locally available channel state information (CSI) is unpractical. In such cases, coordinating the power allocation is a difficult problem and we propose in this work a novel binary power control policy for maximizing the ergodic sum-rate when each TX has only access to the instantaneous channel realization of the direct channel to its own user. We prove rigorously the intuitive result that the optimal binary power control policy consists in letting each TX transmits with full power if and only if the realization of this direct channel is above a threshold. The power control policy obtained with the algorithm is a “best-response” power control policy and allows to achieve benefits of coordinated power allocation at a low cost in terms of backhaul resources and complexity.

Robust regularized ZF in decentralized Broadcast Channel with correlated CSI noise

We consider in this work the Distributed Channel State Information (DCSI) Broadcast Channel (BC) setting, in which the various Transmitters (TXs) compute elements of the precoder based on their individual estimates of the global multiuser channel matrix. Previous works relative to the DCSI setting assume the estimation errors at different TXs to be uncorrelated, while we consider in contrast in this work that the CSI noises can be correlated. This generalization bridges the gap between the fully distributed and the centralized setting, and offers an avenue to analyze partially centralized networks. In addition, we generalize the regularized Zero Forcing (ZF) precoding by letting each TX use a different regularization coefficient. Building upon random matrix theory tools, we obtain a deterministic equivalent for the rate achieved in the large system limit from which we can optimize the regularization coefficients at different TXs. This extended precoding scheme in which each TX applies the optimal regularization coefficient is denoted as “DCSI Regularized ZF” and we show by numerical simulations that it allows to significantly reduce the negative impact of the distributed CSI configuration and is robust to the distribution of CSI quality level across all TXs.

Statistically coordinated precoding for the MISO cognitive radio channel

In this work1, we study a cognitive radio setting consisting of a primary multiple-antenna transmitter (TX) serving a single-antenna primary user (PU) and a secondary multiple-antenna TX serving a secondary user (SU). The main specificity of this work is that we let the primary TX coordinate its transmit strategy with the secondary TX, while considering a realistic channel state information (CSI) scenario where each TX has solely access to the instantaneous knowledge of its direct channel and the statistics of the multi-user channel. This setting gives rise to a Team Decision problem where the TXs aim at cooperating on the basis of individual information. We develop a novel coordination scheme where the TXs coordinate without any exchange of information or any iteration to guarantee the fulfillment of the primary constraint while maximizing the rate of the SU. The coordination is done on the basis of statistical information such that the coordination can be optimized offline. The proposed scheme outperforms conventional schemes from the literature and has low complexity. It can thus be used in settings with low signal processing capabilities and a weak backhaul infrastructure.