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409
Real Interference Alignment with Real Numbers
, 2009
"... A novel coding scheme applicable in networks with single antenna nodes is proposed. This scheme converts a single antenna system to an equivalent Multiple Input Multiple Output (MIMO) system with fractional dimensions. Interference can be aligned along these dimensions and higher Multiplexing gains ..."
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Cited by 46 (2 self)
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A novel coding scheme applicable in networks with single antenna nodes is proposed. This scheme converts a single antenna system to an equivalent Multiple Input Multiple Output (MIMO) system with fractional dimensions. Interference can be aligned along these dimensions and higher Multiplexing gains can be achieved. Tools from the field of Diophantine approximation in number theory are used to show that the proposed coding scheme in fact mimics the traditional schemes used in MIMO systems where each data stream is sent along a direction and alignment happens when several streams arrive at the same direction. Two types of constellation are proposed for the encoding part, namely the single layer constellation and the multilayer constellation. Using the single layer constellation, the coding scheme is applied to the twouser X channel and the threeuser Gaussian Interference Channel (GIC). In case of the twouser X channel, it is proved that the total DegreesofFreedom (DOF), i.e. 4, of 3 the channel is achievable almost surely. This is the first example in which it is shown that a time invariant single antenna system does not fall short of achieving its total DOF. For the threeuser GIC, it is shown that the DOF of 4 is achievable almost surely. 3 Using the multilayer constellation, the coding scheme is applied to the symmetric threeuser GIC. Achievable DOFs are derived for all channel gains. As a function of the channel gain, it is observed that the DOF is everywhere discontinuous. In particular, it is proved that for the irrational channel gains the achievable DOF meets the upper bound 3. For the rational gains, 2 the achievable DOF has a gap to the available upper bounds. By allowing carry over from multiple layers, however, it is shown that higher DOFs can be achieved.
Providing Secrecy With Structured Codes: Tools and Applications to TwoUser Gaussian Channels
, 2009
"... Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured c ..."
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Cited by 45 (17 self)
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Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured codes are useful for providing secrecy, and show how to compute the secrecy rate when structured codes are used. In particular, we solve the problem of bounding equivocation rates with one important class of structured codes, i.e., nested lattice codes. Having established this result, we next demonstrate the use of structured codes for secrecy in twouser Gaussian channels. In particular, with structured codes, we prove that a positive secure degree of freedom is achievable for a large class of fully connected Gaussian channels as long as the channel is not degraded. By way of this, for these channels, we establish that structured codes outperform Gaussian random codes at high SNR. This class of channels include the twouser multiple access wiretap channel, the twouser interference channel with confidential messages and the twouser interference wiretap channel. A notable consequence of this result is that, unlike the case with Gaussian random codes, using structured codes for both transmission and cooperative jamming, it is possible to achieve an arbitrary large secrecy rate given enough power.
On secrecy capacity scaling in wireless networks
"... We study a random extended network, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area n. It is shown that, when the legitimate nodes have unit intensity, λ = 1, and the eavesdroppers have an intensity of λe = O ( (lo ..."
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Cited by 44 (3 self)
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We study a random extended network, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area n. It is shown that, when the legitimate nodes have unit intensity, λ = 1, and the eavesdroppers have an intensity of λe = O ( (log n) −2) , almost all of the nodes achieve a perfectly
Cellular Interference Alignment with Imperfect Channel Knowledge
"... Abstract—Interference alignment is evaluated as a technique to mitigate intercell interference in the downlink of a cellular network using OFDMA. The sum mutual information achieved by interference alignment together with a zeroforcing receiver is considered, and upper and lower bounds are derived ..."
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Cited by 39 (5 self)
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Abstract—Interference alignment is evaluated as a technique to mitigate intercell interference in the downlink of a cellular network using OFDMA. The sum mutual information achieved by interference alignment together with a zeroforcing receiver is considered, and upper and lower bounds are derived for the case of imperfect channel knowledge. The sum mutual information achieved by interference alignment when the base stations share their information about the channels is shown to compare favorably to the achievable sumrate of methods where the base stations do not cooperate, even under moderately accurate knowledge of the channel state. I.
Random Access Heterogeneous MIMO Networks
"... This paper presents the design and implementation of 802.11n +, a fully distributed random access protocol for MIMO networks. 802.11n + allows nodes that differ in the number of antennas to contend not just for time, but also for the degrees of freedom provided by multiple antennas. We show that eve ..."
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Cited by 36 (6 self)
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This paper presents the design and implementation of 802.11n +, a fully distributed random access protocol for MIMO networks. 802.11n + allows nodes that differ in the number of antennas to contend not just for time, but also for the degrees of freedom provided by multiple antennas. We show that even when the medium is already occupied by some nodes, nodes with more antennas can transmit concurrently without harming the ongoing transmissions. Furthermore, such nodes can contend for the medium in a fully distributed way. Our testbed evaluation shows that even for a small network with three competing node pairs, the resulting system about doubles the average network throughput. It also maintains the random access nature of today’s 802.11n networks.
The Degrees of Freedom Regions of MIMO Broadcast, Interference, and Cognitive Radio Channels with No CSIT
, 2009
"... The degrees of freedom (dof) regions are characterized for the multipleinput multipleoutput (MIMO) broadcast channel (BC), the interference channel (IC), and the cognitive radio channel (CRC) when there is perfect and no channel state information at the receivers and the transmitter(s) (CSIR and CS ..."
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Cited by 35 (8 self)
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The degrees of freedom (dof) regions are characterized for the multipleinput multipleoutput (MIMO) broadcast channel (BC), the interference channel (IC), and the cognitive radio channel (CRC) when there is perfect and no channel state information at the receivers and the transmitter(s) (CSIR and CSIT), respectively. For the Kuser MIMO BC, the exact characterization of the dof region is obtained, which shows that simple timedivisionbased transmission is dofregion optimal. Using the techniques developed during the analysis of the dof region of the twouser BC, the corresponding problems for the twouser MIMO IC and the twouser MIMO CRC are addressed. For both of these channels, the exact characterization of the dof region is provided, except in a few antenna configurations. In these cases, an outerbound on the dof region is obtained. All these results are derived for a class of distributions of the fading channel matrices and the additive noises that is more general than those considered in the earlier works such as isotropic fading or Rayleigh fading with white Gaussian noise. Furthermore, using the dof region of the Kuser MIMO BC, the dof regions of the Kuser MIMO IC and the Kuser MIMO CRC are derived in some special cases.
On the achievability of interference alignment in the Kuser constant MIMO interference channel
 In Proc. IEEE Workshop on Statistical Signal Processing (SSP
, 2009
"... Interference alignment in the Kuser MIMO interference channel with constant channel coefficients is considered. A novel constructive method for finding the interference alignment solution is proposed for the case where the number of transmit antennas equals the number of receive antennas (NT = NR = ..."
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Cited by 33 (6 self)
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Interference alignment in the Kuser MIMO interference channel with constant channel coefficients is considered. A novel constructive method for finding the interference alignment solution is proposed for the case where the number of transmit antennas equals the number of receive antennas (NT = NR = N), the number of transmitterreceiver pairs equals K = N + 1, and all interference alignment multiplexing gains are one. The core of the method consists of solving an eigenvalue problem that incorporates the channel matrices of all interfering links. This procedure provides insight into the feasibility of signal vector spaces alignment schemes in finite dimensional MIMO interference channels.
Degrees of Freedom of the K User M × N MIMO Interference Channel
, 809
"... We provide innerbound and outerbound for the total number of degrees of freedom of the K user multiple input multiple output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver if the channel coefficients are timevarying and drawn from a continuo ..."
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Cited by 32 (4 self)
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We provide innerbound and outerbound for the total number of degrees of freedom of the K user multiple input multiple output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver if the channel coefficients are timevarying and drawn from a continuous distribution. The bounds are tight when the ratio max(M,N) min(M,N) = R is equal to an integer. For this case, we show that the total number of degrees of freedom is equal to min(M, N)K if K ≤ R and min(M, N) R R+1K if K> R. Achievability is based on interference alignment. We also provide examples where using interference alignment combined with zero forcing can achieve more degrees of freedom than merely zero forcing for some MIMO interference channels with constant channel coefficients. 2 I.
Interference Alignment for the K User MIMO Interference Channel
, 2009
"... The K user multiple input multiple output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver is considered. We assume that channel coefficients are fixed and are available at all transmitters and receivers. The main objective of this paper is to ..."
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Cited by 31 (0 self)
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The K user multiple input multiple output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver is considered. We assume that channel coefficients are fixed and are available at all transmitters and receivers. The main objective of this paper is to characterize the total number of degrees of freedom (DoF) for this channel. We show that for fixed channel coefficients MN M+N K degrees of freedom can be achieved. The achivability method is based on a new technique for interference alignment recently advised by Motahari et al. [17]. Also we provide a new upperbound on the total number of DoF for this channel. This upperbound coincide with our achievable DoF for K ≥ M+N gcd(M,N) where gcd(M, N) denotes the greatest common divisor of M and N. Because there is no cooperation among transmit and/or receive antennas of each user in our approach, our results are applicable to cellular systems in which a base station with multiple antennas communicates with several users each with single antenna. For this case, as the number of users in each cell increases, the total number of DoF also increases and approaches to the interference free DoF.