7,970 research outputs found
Real Interference Alignment and Degrees of Freedom Region of Wireless X Networks
Abstract-We consider a single hop wireless X network with K transmitters and J receivers, all with single antenna. Each transmitter conveys for each receiver an independent message. The channel is assumed to have constant coefficients. We develop interference alignment scheme for this setup and derived several achievable degrees of freedom regions. We show that in some cases, the derived region meets a previous outer bound and are hence the DoF region. For our achievability schemes, we divide each message into streams and use real interference alignment on the streams. Several previous results on the DoF region and total DoF for various special cases can be recovered from our result. Index Terms-real interference alignment, degrees of freedom region, wireless X network, stream alignmen
Degrees of Freedom Region of Wireless X Networks Based on Real Interference Alignment
We first consider a single hop wireless X network with K transmitters and J receivers, all with a single antenna. Each transmitter conveys an independent message for each receiver. The channel is assumed to have constant coefficients. We develop an interference alignment scheme for this setup and derive an achievable degrees of freedom (DoF) region. We show that in some cases, the derived region meets a previous outer bound, and hence, is the (exact) DoF region. For our achievability schemes, we divide each message into streams and use real interference alignment on the streams. Several previous results on the DoF region and total DoF for several special cases can be recovered from our result. Next, we consider a network model, such that each transmitter emits an arbitrary number of messages and each receiver can request an arbitrary subset of all emitted messages. We term this network the X network with multicast. We derive an achievability result for the DoF region of such networks, as well as an outer bound. Our achievability scheme is based on a novel extension of real interference alignment that enables us to achieve more points of the DoF region. This approach allows multiple messages from a single user to be aligned with other users\u27 messages. Finally, we discuss some points on the outer bounds that are not achievable with any of the alignment schemes that we present
Multiple-Antenna Interference Channels with Real Interference Alignment and Receive Antenna Joint Processing
In this paper, the degrees of freedom (DoF) regions of constant coefficient multiple antenna interference channels are investigated. First, we consider a K-user Gaussian interference channel with Mk antennas at transmitter k, 1≤k≤K, and Nj antennas at receiver j, 1≤j≤K, denoted as a (K,[Mk],[Nj]) channel. Relying on a result of simultaneous Diophantine approximation, a real interference alignment scheme with joint receive antenna processing is developed. The scheme is used to obtain an achievable DoF region. The proposed DoF region includes two previously known results as special cases, namely 1) the total DoF of a K-user interference channel with N antennas at each node, (K,[N],[N]) channel, is NK/2; and 2) the total DoF of a (K,[M],[N]) channel is at least KMN/(M+N). We next explore constant-coefficient interference networks with K transmitters and J receivers, all having N antennas. Each transmitter emits an independent message and each receiver requests an arbitrary subset of the messages. Employing the novel joint receive antenna processing, the DoF region for this set-up is obtained. We finally consider wireless X networks where each node is allowed to have an arbitrary number of antennas. It is shown that the joint receive antenna processing can be used to establish an achievable DoF region, which is larger than what is possible with antenna splitting. As a special case of the derived achievable DoF region for constant coefficient X network, the total DoF of wireless X networks with the same number of antennas at all nodes and with joint antenna processing is tight while the best inner bound based on antenna splitting cannot meet the outer bound. Finally, we obtain a DoF region outer bound based on the technique of transmitter grouping
Degrees of Freedom of Two-Hop Wireless Networks: "Everyone Gets the Entire Cake"
We show that fully connected two-hop wireless networks with K sources, K
relays and K destinations have K degrees of freedom both in the case of
time-varying channel coefficients and in the case of constant channel
coefficients (in which case the result holds for almost all values of constant
channel coefficients). Our main contribution is a new achievability scheme
which we call Aligned Network Diagonalization. This scheme allows the data
streams transmitted by the sources to undergo a diagonal linear transformation
from the sources to the destinations, thus being received free of interference
by their intended destination. In addition, we extend our scheme to multi-hop
networks with fully connected hops, and multi-hop networks with MIMO nodes, for
which the degrees of freedom are also fully characterized.Comment: Presented at the 2012 Allerton Conference. Submitted to IEEE
Transactions on Information Theor
Multiple Unicast Capacity of 2-Source 2-Sink Networks
We study the sum capacity of multiple unicasts in wired and wireless multihop
networks. With 2 source nodes and 2 sink nodes, there are a total of 4
independent unicast sessions (messages), one from each source to each sink node
(this setting is also known as an X network). For wired networks with arbitrary
connectivity, the sum capacity is achieved simply by routing. For wireless
networks, we explore the degrees of freedom (DoF) of multihop X networks with a
layered structure, allowing arbitrary number of hops, and arbitrary
connectivity within each hop. For the case when there are no more than two
relay nodes in each layer, the DoF can only take values 1, 4/3, 3/2 or 2, based
on the connectivity of the network, for almost all values of channel
coefficients. When there are arbitrary number of relays in each layer, the DoF
can also take the value 5/3 . Achievability schemes incorporate linear
forwarding, interference alignment and aligned interference neutralization
principles. Information theoretic converse arguments specialized for the
connectivity of the network are constructed based on the intuition from linear
dimension counting arguments.Comment: 6 pages, 7 figures, submitted to IEEE Globecom 201
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 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 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
- …