Outdated Channel State Information At The Transmitter Research Articles

Retrospective Interference Alignment for the $K$ -User $M\times N$ MIMO Interference Channel

In this paper, we consider a $K$ -user $M\times N$ MIMO interference channel, with outdated channel state information at the transmitters (CSIT). Based on the technique introduced by Cadambe and Jafar, for the IC with perfect and up-to-date CSIT, we propose and analyze a scheme that guarantees interference alignment with outdated CSIT. The interference is aligned by the transmitters, and removed by the receivers using zero-forcing by Cadambe and Jafar. However, this is not feasible for the IC with outdated CSIT, since there is no up-to-date CSIT to compute the interference alignment precoders. To overcome this limitation, we propose that the interference should be aligned by the receivers instead. With this approach, the interference caused by a transmitter spans the same subspace at all receivers, i.e., the interference at receiver $k \neq m$ may be obtained through a linear map from the interference at receiver $m$ . Therefore, one interference retransmission per transmitter is enough to cancel all the interference. This reduces the overhead required for interference removal from $K(K-1)$ to $K$ interference terms.

Capacity Results for Binary Fading Interference Channels With Delayed CSIT

To study the effect of lack of up-to-date channel state information at the transmitters (CSITs), we consider two-user binary fading interference channels with Delayed-CSIT. We characterize the capacity region for such channels under homogeneous assumption, where channel gains have identical and independent distributions across time and space, eliminating the possibility of exploiting time/space correlation. We introduce and discuss several novel coding opportunities created by outdated CSIT that can enlarge the achievable rate region. The capacity-achieving scheme relies on accurate combination, concatenation, and merging of these opportunities, depending on the channel statistics. The outer-bounds are based on an extremal inequality we develop for a binary broadcast channel with delayed-CSIT. We further extend the results and characterize the capacity region when output feedback links are available from the receivers to the transmitters in addition to the delayed knowledge of the channel state information. We also discuss the extension of our results to the nonhomogeneous setting.

Achieving Full Sum DoF in the SISO Interference Channel With Feedback Delay

Channel state information at the transmitter (CSIT) is of utmost importance to manage interference in multi-user wireless networks, in which transmission rates at a high signal-to-noise ratio are characterized by (sum) degrees of freedom (DoF). Ingenious techniques have been proposed to deal with delayed CSIT, notably a scheme by Maddah-Ali and Tse, providing significant DoF with outdated CSIT. However, with most techniques, any delay in the CSIT feedback still results in a DoF loss. A notable exception is the work by Lee and Heath, allowing one to preserve the optimal DoF in the underdetermined MISO BC and IC, but for feedback delays T fb decreasing with the number of users K, up to a fraction 1/K of the channel coherence time T c . In this work, an ergodic interference alignment scheme that preserves the K/2 sum DoF of the K-user IC is proposed for T fb ≤ T c /2. It is also proven that T fb = T c /2 is the longest for which the optimal K/2 DoF can still be obtained for all K.

Optimal Use of Current and Outdated Channel State Information: Degrees of Freedom of the MISO BC with Mixed CSIT

We consider a multiple-input-single-output (MISO) broadcast channel with mixed channel state information at the transmitter (CSIT) that consists of imperfect current CSIT and perfect outdated CSIT. Recent work by Kobayashi et al. presented a scheme that exploits both imperfect current CSIT and perfect outdated CSIT and achieves higher degrees of freedom (DoF) than possible with only imperfect current CSIT or only outdated CSIT individually. In this work, we further improve the achievable DoF in this setting by incorporating additional private messages, and provide a tight information theoretic DoF outer bound, thereby identifying the DoF optimal use of mixed CSIT. The new result is stronger even in the original setting of only delayed CSIT, because it allows us to remove the restricting assumption of statistically equivalent fading for all users.

The Degrees of Freedom Region and Interference Alignment for the MIMO Interference Channel With Delayed CSIT

The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel (IC) is studied under the assumptions of fast fading and delayed channel state information (CSI) at the transmitters (CSIT). Under our fast fading assumption, the channel matrices vary independently across time, so that delayed CSIT is equivalent to outdated CSIT. In particular, the DoF region under delayed CSIT is established for the general MIMO IC with an arbitrary numbers of antennas at each of the four terminals. Toward this end, a set of outer bounds to the DoF region of the general MIMO IC is derived. These bounds are then shown to be tight by developing DoF-region-optimal interference alignment schemes. A comparison of the DoF region of the MIMO IC under the delayed CSIT assumption with those under the two extremes of instantaneous CSIT and no CSIT assumptions is made. This comparison reveals that there are nonempty classes of MIMO ICs, defined by certain relationships between the numbers of antennas at the four terminals, that correspond to each of the following four scenarios: the no CSIT DoF region is strictly contained by, or is equal to, the delayed CSIT DoF region, which in turn is strictly contained by, or is equal to, the instantaneous CSIT DoF region. It is notable that within the class of MIMO ICs for which the delayed CSIT DoF region is strictly larger than the no CSIT DoF region, there is a subclass for which the interference alignment scheme which uses just delayed CSIT achieves the entire DoF region previously known to be achievable only with instantaneous CSIT.

Capacity analysis of transmit beamforming with variable feedback delay

The feedback delay can severely affect the quality of the channel state information at the transmitter (CSIT) which is fed back from the receiver. The outdated CSIT will cause large performance loss in the transmit beamforming systems. The effect of varia

On the Capacity of MIMO Channels with Outdated Channel State Information

A Multiple-input multiple-output (MIMO) time-varying flat fading channel is considered. The transmitter obtained the channel state information (CSI) relying on the reciprocity principle or by the feedback from the receiver. Thus, channel state information at the transmitter (CSIT) is outdated due to the delay between the estimation of the channel and the transmission of the data. In order to achieve the maximum channel capacity, the transmitter linearly precoded the signal before transmission based on the outdated CSIT. Under the assumptions of wide-sense stationary uncorrelated scattering Rayleigh fading channels and Jake’s model, the instantaneous mutual information and ergodic capacity is derived for MIMO channels with outdated CSIT. The information outage probability of MIMO channel with outdated CSIT is also presented.

Design and Analysis of Delay-Sensitive Cross-Layer OFDMA Systems with Outdated CSIT

It is well known that cross-layer scheduling can boost the spectral efficiency of multi-user OFDMA systems through multi-user selection diversity but existing designs usually have two important assumptions - users are delay-insensitive and channel state information at the transmitter (CSIT) is perfect. In practice, users have heterogeneous delay requirements and CSIT usually becomes outdated in time varying channel, which in turns leads to systematic packet errors and hence results in significant degradation on the throughput and delay performance in the OFDMA systems. In this paper, a novel cross-layer design problem is formulated as a convex optimization problem, on which a delay-sensitive jointly optimal power, rate and subcarrier allocation scheme is proposed so as to maintain heterogeneous users' delay requirement as well as achieving a target packet outage probability through combining queueing theory and information theory. Furthermore, we obtain closed-form asymptotic performance of the proposed delay-sensitive scheduler. Unlike the well-known SNR gain of Theta(log - sigma2 DeltaH) in conventional cross-layer scheduler with perfect CSIT, we demonstrate a cross-layer SNR gain of Theta((1 - sigma2 DeltaH)log K)can still be achieved under heterogeneous delay constraints and outdated CSIT with error variance sigma2 DeltaH. Finally, simulation results show that our proposed delay-sensitive CSIT error considerate schemes provide robust system performance enhancement over conventional CSIT error inconsiderate opportunistic scheduler and naive queue length based MAX-Weight scheduler while satisfying heterogeneous delay requirements even at moderate to high CSIT errors.

Closed-loop cross-layer SDMA designs with outdated CSIT

In this paper, we propose a novel closed-loop approach for robust downlink multi-antenna cross-layer design with outdated channel state information at the transmitter (CSIT). Based on the ACK/NAK feedbacks from the mobiles, the proposed cross-layer design does not require the knowledge of CSIT error statistics. We formulate the cross-layer design as a mixed combinatorial search and Markov decision process (MDP). While it is well-known that general solutions for MDP are very complex, one important contribution of this paper is that we obtain simple closed-form power, rate and user allocation policies which are asymptotically optimal for small target frame error rate (FER). Simulation results illustrate that the performance of the proposed closed-loop cross-layer design is very robust with respect to the outdated CSIT, CSIT error model mismatch as well as channel variations due to Doppler.