On the Capacity of the Finite Field Counterparts of Wireless Interference Networks

This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over $\mathbb{F}_{p^n}$ are analogous to n x n vector (MIMO) channels in the wireless setting, but with an important distinction -- there is additional structure due to finite field arithmetic which enforces commutativity of matrix multiplication and limits the channel diversity to n, making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity optimal solutions for their finite field counterparts. This is shown through the study of the 2-user X channel and the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over $\mathbb{F}_{p^n}$ also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between p and SNR, and n and diversity.Comment: Full version of paper accepted for presentation at ISIT 201

Elements of Cellular Blind Interference Alignment --- Aligned Frequency Reuse, Wireless Index Coding and Interference Diversity

We explore degrees of freedom (DoF) characterizations of partially connected wireless networks, especially cellular networks, with no channel state information at the transmitters. Specifically, we introduce three fundamental elements --- aligned frequency reuse, wireless index coding and interference diversity --- through a series of examples, focusing first on infinite regular arrays, then on finite clusters with arbitrary connectivity and message sets, and finally on heterogeneous settings with asymmetric multiple antenna configurations. Aligned frequency reuse refers to the optimality of orthogonal resource allocations in many cases, but according to unconventional reuse patterns that are guided by interference alignment principles. Wireless index coding highlights both the intimate connection between the index coding problem and cellular blind interference alignment, as well as the added complexity inherent to wireless settings. Interference diversity refers to the observation that in a wireless network each receiver experiences a different set of interferers, and depending on the actions of its own set of interferers, the interference-free signal space at each receiver fluctuates differently from other receivers, creating opportunities for robust applications of blind interference alignment principles

Opportunistic Interference Mitigation Achieves Optimal Degrees-of-Freedom in Wireless Multi-cell Uplink Networks

We introduce an opportunistic interference mitigation (OIM) protocol, where a user scheduling strategy is utilized in $K$-cell uplink networks with time-invariant channel coefficients and base stations (BSs) having $M$ antennas. Each BS opportunistically selects a set of users who generate the minimum interference to the other BSs. Two OIM protocols are shown according to the number $S$ of simultaneously transmitting users per cell: opportunistic interference nulling (OIN) and opportunistic interference alignment (OIA). Then, their performance is analyzed in terms of degrees-of-freedom (DoFs). As our main result, it is shown that $KM$ DoFs are achievable under the OIN protocol with $M$ selected users per cell, if the total number $N$ of users in a cell scales at least as $\text{SNR}^{(K-1)M}$. Similarly, it turns out that the OIA scheme with $S$($<M$) selected users achieves $KS$ DoFs, if $N$ scales faster than $\text{SNR}^{(K-1)S}$. These results indicate that there exists a trade-off between the achievable DoFs and the minimum required $N$. By deriving the corresponding upper bound on the DoFs, it is shown that the OIN scheme is DoF optimal. Finally, numerical evaluation, a two-step scheduling method, and the extension to multi-carrier scenarios are shown.Comment: 18 pages, 3 figures, Submitted to IEEE Transactions on Communication

Demo: Non-classic Interference Alignment for Downlink Cellular Networks

Our demo aims at proving the concept of a recent proposed interference management scheme that reduces the inter-cell interference in downlink without complex coordination, known as non-classic interference alignment (IA) scheme. We assume a case where one main Base Station (BS) needs to serve three users equipments (UE) while another BS is causing interference. The primary goal is to construct the alignment scheme ; i.e. each UE estimates the main and interfered channel coefficients, calculates the optimal interference free directions dropped by the interfering BS and feeds them back to the main BS which in turn applies a scheduling to select the best free inter-cell interference directions. Once the scheme is build, we are able to measure the total capacity of the downlink interference channel. We run the scheme in CorteXlab ; a controlled hardware facility located in Lyon, France with remotely programmable radios and multi-node processing capabilities, and we illustrate the achievable capacity gain for different channel realizations.Comment: Joint NEWCOM/COST Workshop on Wireless Communications JNCW 2015, Oct 2015, Barcelone, Spain. 201

A Distributed Approach to Interference Alignment in OFDM-based Two-tiered Networks

In this contribution, we consider a two-tiered network and focus on the coexistence between the two tiers at physical layer. We target our efforts on a long term evolution advanced (LTE-A) orthogonal frequency division multiple access (OFDMA) macro-cell sharing the spectrum with a randomly deployed second tier of small-cells. In such networks, high levels of co-channel interference between the macro and small base stations (MBS/SBS) may largely limit the potential spectral efficiency gains provided by the frequency reuse 1. To address this issue, we propose a novel cognitive interference alignment based scheme to protect the macro-cell from the cross-tier interference, while mitigating the co-tier interference in the second tier. Remarkably, only local channel state information (CSI) and autonomous operations are required in the second tier, resulting in a completely self-organizing approach for the SBSs. The optimal precoder that maximizes the spectral efficiency of the link between each SBS and its served user equipment is found by means of a distributed one-shot strategy. Numerical findings reveal non-negligible spectral efficiency enhancements with respect to traditional time division multiple access approaches at any signal to noise (SNR) regime. Additionally, the proposed technique exhibits significant robustness to channel estimation errors, achieving remarkable results for the imperfect CSI case and yielding consistent performance enhancements to the network.Comment: 15 pages, 10 figures, accepted and to appear in IEEE Transactions on Vehicular Technology Special Section: Self-Organizing Radio Networks, 2013. Authors' final version. Copyright transferred to IEE