Degrees of Freedom for the MIMO Interference Channel

Jafar, Syed A.; Fakhereddin, M.J.

doi:10.1109/isit.2006.262087

Cited by 75 publications

(128 citation statements)

References 11 publications

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“…According to (1) this is a proper system, and according to [9] it is infeasible because the information theoretic DoF outer bound value for this channel is only 8/3 per user. The DoF outer bound is easily found by allowing two of the users to cooperate fully, so that the resulting 2-user MIMO interference channel with (M 1 , N 1 , M 2 , N 2 ) = (8,16,4,8) has a total DoF value of 8 according to [11]. Since cooperation does not hurt, and linear schemes (or any other scheme for that matter) cannot beat an information-theoretic outer bound, it is clear that the (4 × 8, d) 3 linear interference alignment problem is infeasible for d ≥ 8/3, and in particular for d = 3. The observation that some proper systems are not feasible is also made by Cenk et al in [12] who suggest including known information theoretic DoF outer bounds to further expand the set of infeasible systems.…”

Section: Feasibility Of Linear Interference Alignment Without Time/frmentioning

confidence: 99%

“…Since cooperation does not hurt, and linear schemes (or any other scheme for that matter) cannot beat an information-theoretic outer bound, it is clear that the (4 × 8, d) 3 linear interference alignment problem is infeasible for d ≥ 8/3, and in particular for d = 3. The observation that some proper systems are not feasible is also made by Cenk et al in [12] who suggest including known information theoretic DoF outer bounds to further expand the set of infeasible systems. Interestingly, so far, all known DoF outer bounds for K user MIMO interference channels come directly from the DoF result for the 2-user MIMO interference channel [11], applied after allowing various subsets of users to cooperate, while eliminating other users to create a 2-user interference channel (as also illustrated by the preceding example). As we show in this work, these DoF outer bounds do not suffice, even for the symmetric 3-user MIMO interference channel for all M T , M R values.…”

Section: Feasibility Of Linear Interference Alignment Without Time/frmentioning

confidence: 99%

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Subspace alignment chains and the degrees of freedom of the three-user MIMO interference channel

Wang

Gou

Jafar

2012

2012 IEEE International Symposium on Information Theory Proceedings

260

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We show that the 3-user M T × M R MIMO interference channel where each transmitter is equipped with M T antennas and each receiver is equipped with M R antennas has d(M, N ) = min M 2−1/κ , N 2+1/κ degrees of freedom (DoF) normalized by time, frequency, and space dimensions, whereWhile the DoF outer bound of d(M, N ) is established for every M T , M R value, the achievability of d(M, N ) DoF is established in general subject to a normalization with respect to spatial-extensions, i.e., the scaling of the number of antennas at all nodes. Specifically, we show that qd(M, N ) DoF are achievable for the 3-user qM T × qM R MIMO interference channel, for some positive integer q which may be seen as a spatial-extension factor. q is the scaling factor needed to make the value qd(M, N ) an integer. Given spatial-extensions, the achievability relies only on linear beamforming based interference alignment schemes and requires neither channel extensions nor channel variations in time or frequency. In the absence of spatial extensions, it is shown through examples how essentially the same interference alignment scheme may be applied over time-extensions over either constant or time-varying channels. The central new insight to emerge from this work is the notion of subspace alignment chains as DoF bottlenecks. The subspace alignment chains are instrumental both in identifying the extra dimensions to be provided by a genie to a receiver for the DoF outer bound, as well as in the construction of the optimal interference alignment schemes.The DoF value d(M, N ) is a piecewise linear function of M, N , with either M or N being the bottleneck within each linear segment while the other value contains some redundancy, i.e., it can be reduced without reducing the DoF. The corner points of these piecewise linear segments correspond to two sets, A = {1/2, 2/3, 3/4, · · · } and B = {1/3, 3/5, 5/7, · · · }. The set A contains all those values of M/N and only those values of M/N for which there is redundancy in both M and N , i.e., either can be reduced without reducing DoF. The set B contains all those values of M/N and only those values of M/N for which there is no redundancy in either M or N , i.e., neither can be reduced without reducing DoF. Because A and B represent settings with maximum and minimum redundancy, essentially they are the basis for the DoF outer bounds and inner bounds, respectively.Our Our results show that M/N ∈ A are the only values for which there is no DoF benefit of joint processing among co-located antennas at the transmitters or receivers. This may also be seen as a consequence of the maximum redundancy in the M/N ∈ A settings.

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Section: Feasibility Of Linear Interference Alignment Without Time/frmentioning

confidence: 99%

Section: Feasibility Of Linear Interference Alignment Without Time/frmentioning

confidence: 99%

Subspace alignment chains and the degrees of freedom of the three-user MIMO interference channel

Wang

Gou

Jafar

2012

2012 IEEE International Symposium on Information Theory Proceedings

260

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“…Thus, the MIMO interference channel of Figure 2(b) has a capacity region that contains the capacity region of the 3 user interference channel of Figure 1. Reference [17] has shown that the MIMO interference channel of Figure 2(b) has 1 degree of freedom meaning that its capacity is of the form log(SNR)+o(log(SNR)). Therefore, we have shown that…”

Section: The Gaussian 3 User Interference Channelmentioning

confidence: 99%

Multiple Access Outerbounds and the Inseparability of Parallel Interference Channels

Cadambe

Jafar

2008

IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference

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Abstract-It is known that the capacity of parallel (multi-carrier) Gaussian point-to-point, multiple access and broadcast channels can be achieved by separate encoding for each subchannel (carrier) subject to a power allocation across carriers. In this paper we show that such a separation does not apply to parallel Gaussian interference channels in general. A counter-example is provided in the form of a 3 user interference channel where separate encoding can only achieve a sum capacity of log(SNR)+o(log(SNR)) per carrier while the actual capacity, achieved only by jointencoding across carriers, is 3/2 log(SNR)) + o(log(SNR)) per carrier. As a byproduct of our analysis, we propose a class of multiple-access-outerbounds on the capacity of the 3 user interference channel.

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“…In a study of MIMO interference channels [3], the number of spatial degrees of freedom is defined as…”

Section: B Capacity Based Metricsmentioning

confidence: 99%

“…Clearly this is not what is required here, where it is exactly the effects of correlation on the channels that is of interest. Hence we propose the nonlimiting versions of DOF in [3] and [5] as…”

Section: B Capacity Based Metricsmentioning

confidence: 99%

On the Number of Independent Channels in a Diversity System

Smith

Dmochowski

Chiani

et al. 2010

2010 IEEE Wireless Communication and Networking Conference

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Abstract-In a receive diversity system the use of multiple antennas at one end of the link produces multiple channels. A useful, although ill-defined, metric for such a link is the number of independent channels provided. In this letter we discuss several candidate metrics and compare their utility. We show that most of the metrics available in the literature have limitations and can exhibit non-physical behaviour. In order to improve on their performance, we develop two novel measures for the number of independent channels based on the statistical construction of the channel and channel capacity.

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Degrees of Freedom for the MIMO Interference Channel

Cited by 75 publications

References 11 publications

Subspace alignment chains and the degrees of freedom of the three-user MIMO interference channel

Subspace alignment chains and the degrees of freedom of the three-user MIMO interference channel

Multiple Access Outerbounds and the Inseparability of Parallel Interference Channels

On the Number of Independent Channels in a Diversity System

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