The Wideband Slope of Interference Channels: The Small Bandwidth Case

This paper studies the low-SNR regime performance of a scalar complex <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-user interference channel with the Gaussian noise. The finite bandwidth case is considered, where the low-SNR regime is approached by letting the input power go to zero, while the bandwidth is small and fixed. We show that for all <inline-formula> <tex-math notation="LaTeX">$\delta >0$ </tex-math></inline-formula>, there exists a set of channel coefficients with non-zero measure (probability), in which the wideband slope per user satisfies <inline-formula> <tex-math notation="LaTeX">$ \mathcal {S}_{0}< {\scriptstyle {}^{\scriptstyle 2}}\hspace{-0.224em}/\hspace{-0.112em}{\scriptstyle K}+\delta $ </tex-math></inline-formula>. This is quite contrary to the large bandwidth case, where a slope of 1 per user is achievable with probability 1. We also develop an interference alignment scheme for the finite bandwidth case that shows some gain in wideband slope.

[1]  Te Sun Han,et al.  A new achievable rate region for the interference channel , 1981, IEEE Trans. Inf. Theory.

[2]  Hiroshi Sato,et al.  The capacity of the Gaussian interference channel under strong interference , 1981, IEEE Trans. Inf. Theory.

[3]  Aydano B. Carleial,et al.  Interference channels , 1978, IEEE Trans. Inf. Theory.

[4]  Anders Høst-Madsen,et al.  The Wideband Slope of Interference Channels: The Large Bandwidth Case , 2010, IEEE Transactions on Information Theory.

[5]  Moritz Wiese,et al.  The performance of QPSK in low-SNR interference channels , 2010, 2010 International Symposium On Information Theory & Its Applications.

[6]  Venugopal V. Veeravalli,et al.  Gaussian interference networks: sum capacity in the low-interference regime and new outer bounds on the capacity region , 2009, IEEE Trans. Inf. Theory.

[7]  Erik Ordentlich,et al.  The Degrees-of-Freedom of the $K$-User Gaussian Interference Channel Is Discontinuous at Rational Channel Coefficients , 2009, IEEE Transactions on Information Theory.

[8]  Syed Ali Jafar,et al.  Interference Alignment and Degrees of Freedom of the $K$-User Interference Channel , 2008, IEEE Transactions on Information Theory.

[9]  Svante Janson,et al.  Random graphs , 2000, Wiley-Interscience series in discrete mathematics and optimization.

[10]  H. Vincent Poor,et al.  Capacity Regions and Sum-Rate Capacities of Vector Gaussian Interference Channels , 2009, IEEE Transactions on Information Theory.

[11]  Syed Ali Jafar,et al.  Parallel Gaussian Interference Channels Are Not Always Separable , 2009, IEEE Transactions on Information Theory.

[12]  Syed Ali Jafar,et al.  Approaching the Capacity of Wireless Networks through Distributed Interference Alignment , 2008, IEEE GLOBECOM 2008 - 2008 IEEE Global Telecommunications Conference.

[13]  Hua Wang,et al.  Gaussian Interference Channel Capacity to Within One Bit , 2007, IEEE Transactions on Information Theory.

[14]  Shlomo Shamai,et al.  Degrees of freedom of the interference channel: A general formula , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[15]  R. Mathar,et al.  On spatial patterns of transmitter-receiver pairs that allow for interference alignment by delay , 2009, 2009 3rd International Conference on Signal Processing and Communication Systems.

[16]  Sergio Verdú,et al.  Spectral efficiency in the wideband regime , 2002, IEEE Trans. Inf. Theory.

[17]  Anders Høst-Madsen,et al.  Wideband slope of interference channel: Finite bandwidth case , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[18]  Antonia Maria Tulino,et al.  Multiple-antenna capacity in the low-power regime , 2003, IEEE Trans. Inf. Theory.

[19]  T. Apostol.  Modular Functions and Dirichlet Series in Number Theory , 1976 .

[20]  Béla Bollobás,et al.  Random Graphs: Notation , 2001 .

[21]  Mehul Motani,et al.  On The Han–Kobayashi Region for theInterference Channel , 2008, IEEE Transactions on Information Theory.

[22]  Syed Ali Jafar,et al.  Interference Alignment With Asymmetric Complex Signaling—Settling the Høst-Madsen–Nosratinia Conjecture , 2009, IEEE Transactions on Information Theory.

[23]  Roy D. Yates,et al.  Interference Alignment for Line-of-Sight Channels , 2008, IEEE Transactions on Information Theory.

[24]  Shlomo Shamai,et al.  Interference alignment on the deterministic channel and application to fully connected AWGN interference networks , 2008, 2008 IEEE Information Theory Workshop.

[25]  Gerhard Kramer,et al.  Outer bounds on the capacity of Gaussian interference channels , 2004, IEEE Transactions on Information Theory.

[26]  Svante Janson,et al.  Random graphs , 2000, ZOR Methods Model. Oper. Res..

[27]  Amir K. Khandani,et al.  Signaling over MIMO Multi-Base Systems: Combination of Multi-Access and Broadcast Schemes , 2006, 2006 IEEE International Symposium on Information Theory.

[28]  Béla Bollobás,et al.  Random Graphs , 1985 .

[29]  Aria Nosratinia,et al.  The multiplexing gain of wireless networks , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[30]  Max H. M. Costa,et al.  On the Gaussian interference channel , 1985, IEEE Trans. Inf. Theory.

[31]  Giuseppe Caire,et al.  Suboptimality of TDMA in the low-power regime , 2004, IEEE Transactions on Information Theory.

[32]  Patrick P. Bergmans,et al.  A simple converse for broadcast channels with additive white Gaussian noise (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[33]  H. Vincent Poor,et al.  On the capacity of MIMO interference channels , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[34]  S.A. Jafar,et al.  Degrees of Freedom of Wireless Networks - What a Difference Delay Makes , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

[35]  Gerhard Kramer,et al.  A New Outer Bound and the Noisy-Interference Sum–Rate Capacity for Gaussian Interference Channels , 2007, IEEE Transactions on Information Theory.

[36]  Daniela Tuninetti.  K-user interference channels: General outer bound and sum-capacity for certain Gaussian channels , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[37]  Amir K. Khandani,et al.  Interference alignment for the K user MIMO interference channel , 2009, 2010 IEEE International Symposium on Information Theory.

[38]  Sergio Verdú,et al.  On channel capacity per unit cost , 1990, IEEE Trans. Inf. Theory.

[39]  Amir K. Khandani,et al.  Capacity bounds for the Gaussian Interference Channel , 2008, 2008 IEEE International Symposium on Information Theory.

[40]  Venugopal V. Veeravalli,et al.  Sum capacity of the Gaussian interference channel in the low interference regime , 2008, 2008 Information Theory and Applications Workshop.

[41]  Amir K. Khandani,et al.  Real Interference Alignment with Real Numbers , 2009, ArXiv.