Interference aligned space-time transmission with diversity for the 2 × 2 X-Network

Abstract

The sum degrees of freedom (DoF) of the two-transmitter, two-receiver multiple-input multipleoutput (MIMO) X-Network (2 × 2 MIMO X-Network) with M antennas at each node is known to be 4M 3 . Transmission schemes which couple local channel-state-information-at-the-transmitter (CSIT) based precoding with space-time block coding to achieve the sum-DoF of this network are known specifically for M = 2, 4. These schemes have been proven to guarantee a diversity gain of M when a finite-sized input constellation is employed. In this paper, an explicit transmission scheme that achieves the 4M 3 sum-DoF of the 2 × 2 X-Network for arbitrary M is presented. The proposed scheme needs only local CSIT unlike the Jafar-Shamai scheme which requires the availability of global CSIT in order to achieve the 4M 3 sum-DoF. Further, it is shown analytically that the proposed scheme guarantees a diversity gain of M + 1 when finite-sized input constellations are employed.Freedom.that cell edge users are susceptible to interference from the neighbouring base stations and vice-versa.These issues have instigated research on better transmission techniques in interference networks, with information-theoretic rate tuples often used as the metric for designing better schemes. Since the capacity of interference networks is unknown in general, degrees of freedom (DoF) [1] is the widely targeted metric due to its relative ease of characterization. The sum-DoF of a Gaussian network is said to be d if its sum-capacity (in bits per channel use) can be approximated as C(SNR) = d log 2 SNR + o(log 2 SNR).Availability of channel-state-information at the transmitters (CSIT) is an important assumption in the characterization of the approximate capacity of Gaussian interference networks. Availability of perfect global CSIT 1 often enables one to design precoders that cast interference onto subspaces independent of the desired signal space at the receivers. This technique, termed interference alignment (IA), was first used implicitly in [2], [3], and explicitly appeared in [4], [5] in the context of 2 × 2 multiple-input multiple-output (MIMO) X-Networks. A K × J X-Network is a Gaussian interference network with K transmitters and J receivers and a total of KJ independent messages meant to be sent over the network, one from every transmitter to every receiver. A 2×2 X-Network with M antennas at each node is referred to as the (2 × 2, M ) X-Network. A lower bound on the sum-DoF was shown to be 4M 3 for such a network in [3], and it was proven in [5] that the sum-DoF equals 4M 3 , achieved using an IA scheme. All the aforementioned works assume the availability of perfect global CSIT.The concept of DoF assumes the use of a codebook with unconstrained alphabet size as well as unlimited peak power, but with an average power constraint. The channel is assumed to be static during the transmission of an entire codeword. Further, information-theoretic rate definitions also assume the usage of unlimited coding length. Clearly, all these assumptions are infeasible in p...

On-off Switched Interference Alignment for Diversity Multiplexing Tradeoff Improvement in the 2-User X-Network With Two Antennas

“…Each transmitter transmits an independent packet consisting of a codeword obtained from random Gaussian codebook. We assume fixed data rate for input as in [8]- [11] so that we exclude adaptive modulation/transmission according to channel conditions, which is not viable under local CSIT.…”

“…Y.-b. Kim rate maximization in terms of sum DoF, recent works [6]- [11] focused on improving diversity gain in interference channels. Linear transmission schemes were proposed in [6], [7] to achieve full diversity gain in the two X-channel equipped with arbitrary numbers of antennas at the transmitters and receivers.…”

“…However, they could not achieve the sum DoF that scales with the number of antennas at the transmitters and receivers. In [8]- [11], IA schemes combined with Alamouti code [12], space time block coding (STBC) [13] or Srinath-Rajan STBC [14], were developed. Specifically, in the 2-user X-channel with two antennas at every node, the authors of [8] proposed an IA scheme that combines Alamouti coding and transmit beamforming over extended symbol times.…”

“…With the devised scheme, maximal diversity gains of 3 and 4 were shown to be achievable, respectively, while maximal sum DoF of 4×3 3 and 4×4 3 were achievable, respectively. Recently, the work was generalized for an arbitrary number of antennas in [11].…”

“…In the aforementioned works [8]- [11], the analyzed diversity gain and DoF correspond to the point (d, 0) and (0, r) in the DMT domain. However, the DMT curve obtained by a linear function connecting the two points is not optimal in 2user X-channel with two antennas.…”