The Degree-of-Freedom Regions of MIMO Broadcast, Interference, and Cognitive Radio Channels With No CSIT

Abstract

The degrees of freedom (DoF) regions are characterized for the multiple-input multiple-output (MIMO) broadcast channel (BC), interference channels (IC) (including X and multi-hop interference channels) 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 K-user MIMO BC, the exact characterization of the DoF region is obtained, which shows that a simple time-division-based transmission scheme is DoF-region optimal. Using the techniques developed for the MIMO BC, the corresponding problems for the two-user MIMO IC and the two-user MIMO CRC with an arbitrary number of antennas at each of the four terminals are addressed. For both of these channels, inner and outer bounds to the DoF region are obtained and are seen to coincide for a vast majority of the relative numbers of antennas at the four terminals, thereby characterizing DoF regions for all but a few cases.Finally, the DoF regions of the K-user MIMO IC, the CRC, and X networks are derived for certain classes of these networks, including the one where all transmitters have an equal number of antennas and so do all receivers. The results of this paper are derived for distributions of fading channel matrices and additive noises that are more general than those considered in other simultaneous related works. The DoF regions with and without CSIT are compared and conditions on the relative numbers of antennas at the terminals under which a lack of CSIT does, or does not, result in the loss of DoF are identified, thereby providing, on the one hand, simple and robust communication schemes that don't require CSIT but have the same DoF performance as their previously found CSIT counterparts, and on the other hand, identifying situations where CSI feedback to transmitters would provide gains that are significant enough that even the DoF performance could be improved. ).The material in this paper was presented in part at the IEEE Intl. Symp. of Inform. Th., Austin, TX, Jun. 2010. 1 Broadcast channel, cognitive radio channel, degrees of freedom region, interference channel, multihop interference network, multiple-input multiple-output systems, X network. I. INTRODUCTIONM Ultiple-input multiple-output (MIMO) systems are of great interest because they can provide a significantly higher capacity as compared to their single-input single-output (SISO) counterparts by exploiting the spatial dimension. One way of measuring this benefit at high signal-to-noise ratio (SNR) is via the spatial multiplexing gain or the degrees of freedom (DoF), which is defined as the limit of the ratio of the capacity to the logarithm of the SNR. For example, the point-to-point MIMO channel with M transmit and N receive antennas has min(M, N) DoF whereas its SISO counterpart has only 1 DoF [1]. Interestingly, min(M, N) DoF are achievable over the MIMO channel even if there is perfect channel state information (CSI) just at the receiver (CSIR). In other words, the presence or absence...

Achievable DoF for 2-User MIMO Relay Interference Channels with Outdated Channel State Information

“…While the sum rate performance has the slowest increasing speed when R = 3. In [8], the optimal sum-DoF for a K-user M × N MIMO interference channel with no CSIT is…”

Relays can provide alignment for the K-user interference channel without channel state information at the transmitters

“…This is still a significant improvement compared to the DoF with no relays for the Rayleigh fading channel [5].…”

“…Remark 2: If we assume that the channel coefficients are drawn from the Rayleigh distribution, then it is shown in [5] that the DoF for the K-user interference channel without CSIT and relays is upper bounded by 1. It is thus clear that relays can provide DoF gain for the K-user interference channel without CSIT.…”

“…In a practical system, however, obtaining full CSIT is difficult. Consequently, references [4], [5] have studied the DoF of various channel models with the assumption that no CSIT is available, and loss of DoF is observed for many scenarios. Without CSIT, the transmitters cannot steer the signals to the exact desired directions to guarantee that the interference is aligned together at the receivers, which causes the performance degradation in terms of DoF.…”

Cognitive Interference Alignment for Spectral Coexistence

“…The DoF regions are characterized for several wireless channels such as MIMO BC, interference channels (ICs), including X and multihop ICs, and the CR channels [68]. The DoF metric has been extensively used for interference mitigation and alignment objectives in various wireless networks such as interference mitigation in multicell networks [10,31], interference mitigation in two-cell MIMO interfering BCs [63], IA in CR networks [14,34,57].…”