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Register a new userGeneralized Degrees of Freedom of the Symmetric Gaussian $K$ User Interference Channel
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Syed Jafar
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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We characterize the generalized degrees of freedom of the $K$ user symmetric Gaussian interference channel where all desired links have the same signal-to-noise ratio (SNR) and all undesired links carrying interference have the same interference-to-noise ratio, ${INR}={SNR}^alpha$. We find that the number of generalized degrees of freedom per user, $d(alpha)$, does not depend on the number of users, so that the characterization is identical to the 2 user interference channel with the exception of a singularity at $alpha=1$ where $d(1)=frac{1}{K}$. The achievable schemes use multilevel coding with a nested lattice structure that opens the possibility that the sum of interfering signals can be decoded at a receiver even though the messages carried by the interfering signals are not decodable.
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We study the Han-Kobayashi (HK) achievable sum rate for the two-user symmetric Gaussian interference channel. We find the optimal power split ratio between the common and private messages (assuming no time-sharing), and derive a closed form expression for the corresponding sum rate. This provides a finer understanding of the achievable HK sum rate, and allows for precise comparisons between this sum rate and that of orthogonal signaling. One surprising finding is that despite the fact that the channel is symmetric, allowing for asymmetric power split ratio at both users (i.e., asymmetric rates) can improve the sum rate significantly. Considering the high SNR regime, we specify the interference channel value above which the sum rate achieved using asymmetric power splitting outperforms the symmetric case.
This paper studies a symmetric K user Gaussian interference channel with K transmitters and K receivers. A very strong interference regime is derived for this channel setup. A very strong interference regime is one where the capacity region of the interference channel is the same as the capacity region of the channel with no interference. In this regime, the interference can be perfectly canceled by all the receivers without incurring any rate penalties. A very strong interference condition for an example symmetric K user deterministic interference channel is also presented.
In this paper, we explore the benefits, in the sense of total (sum rate) degrees of freedom (DOF), of cooperation and cognitive message sharing for a two-user multiple-input-multiple-output (MIMO) Gaussian interference channel with $M_1$, $M_2$ antennas at transmitters and $N_1$, $N_2$ antennas at receivers. For the case of cooperation (including cooperation at transmitters only, at receivers only, and at transmitters as well as receivers), the DOF is $min {M_1+M_2, N_1+N_2, max(M_1, N_2)), max(M_2, N_1)}$, which is the same as the DOF of the channel without cooperation. For the case of cognitive message sharing, the DOF is $min {M_1+M_2, N_1+N_2, (1-1_{T2})((1-1_{R2}) max(M_1, N_2) + 1_{R2} (M_1+N_2)), (1-1_{T1})((1-1_{R1}) max(M_2, N_1) + 1_{R1} (M_2+N_1)) }$ where $1_{Ti} = 1$ $(0)$ when transmitter $i$ is (is not) a cognitive transmitter and $1_{Ri}$ is defined in the same fashion. Our results show that while both techniques may increase the sum rate capacity of the MIMO interference channel, only cognitive message sharing can increase the DOF. We also find that it may be more beneficial for a user to have a cognitive transmitter than to have a cognitive receiver.
We explore the capacity and generalized degrees of freedom of the two-user Gaussian X channel, i.e. a generalization of the 2 user interference channel where there is an independent message from each transmitter to each receiver. There are three main results in this paper. First, we characterize the sum capacity of the deterministic X channel model under a symmetric setting. Second, we characterize the generalized degrees of freedom of the Gaussian X channel under a similar symmetric model. Third, we extend the noisy interference capacity characterization previously obtained for the interference channel to the X channel. Specifically, we show that the X channel associated with noisy (very weak) interference channel has the same sum capacity as the noisy interference channel.
The Maddah-Ali and Tse (MAT) scheme is a linear precoding strategy that exploits Interference Alignment and perfect, but delayed, channel state information at the transmitters (delayed CSIT), improving the degrees of freedom (DoF) that can be achieved for the broadcast channel (BC). Since its appearance, many works have extended the concept of Retrospective Interference Alignment (RIA) to other multi-user channel configurations. However, little is known about the broadcast channel with multiple cells, i.e. the interference broadcast channel (IBC). In this work, the DoF are studied for the $K$-user $C$-cell multiple-input single-output (MISO) IBC with delayed CSIT (with $K/C$ users per cell). We show that the straightforward application of the MAT scheme over the IBC fails because it requires all interference to be received from the same source. Hence, in this case not all the interference can be cancelled, thus blocking the decoding of the received messages. We call this phenomenon as textit{interference coupling}, forcing to use the MAT scheme by serving just one cell at a time. In this work, we propose an extension, namely the uncoupled MAT scheme (uMAT), exploiting multiple cells, uncoupling the interference, and achieving the best known DoF inner bound for almost all settings.
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