Chenxi Hao

Imperfect and unmatched CSIT is still useful for the frequency correlated MISO broadcast channel

Since Maddah-Ali and Tse showed that the completely stale transmitter-side channel state information (CSIT) still benefits the Degrees of Freedom (DoF) of the Multiple-Input-Multiple-Output (MISO) Broadcast Channel (BC), there has been much interest in the academic literature to investigate the impact of imperfect CSIT on DoF region of time correlated broadcast channel. Even though the research focus has been on time correlated channels so far, a similar but different problem concerns the frequency correlated channels. Indeed, the imperfect CSIT also impacts the DoF region of frequency correlated channels, as exemplified by current multi-carrier wireless systems. This contribution, for the first time in the literature, investigates a general frequency correlated setting where a two-antenna transmitter has imperfect knowledge of CSI of two single-antenna users on two adjacent subbands. A new scheme is derived as an integration of Zero-Forcing Beamforming (ZFBF) and the scheme proposed by Maddah-Ali and Tse. The achievable DoF region resulted by this scheme is expressed as a function of the qualities of CSIT.

Rate Analysis of Two-Receiver MISO Broadcast Channel With Finite Rate Feedback: A Rate-Splitting Approach

To enhance the multiplexing gain of two-receiver Multiple-Input-Single-Output Broadcast Channel with imperfect channel state information at the transmitter (CSIT), a class of Rate-Splitting (RS) approaches has been proposed recently, which divides one receivers message into a common and a private part, and superposes the common message on top of Zero-Forcing precoded private messages. In this paper, with quantized CSIT, we study the ergodic sum rate of two schemes, namely RS-S and RS-ST, where the common message(s) are transmitted via a space and space-time design, respectively. Firstly, we upper-bound the sum rate loss incurred by each scheme relative to Zero-Forcing Beamforming (ZFBF) with perfect CSIT. Secondly, we show that, to maintain a constant sum rate loss, RS-S scheme enables a feedback overhead reduction over ZFBF with quantized CSIT. Such reduction scales logarithmically with the constant rate loss at high Signal-to-Noise-Ratio (SNR). We also find that, compared to RS-S scheme, RS-ST scheme offers a further feedback overhead reduction that scales with the discrepancy between the feedback overhead employed by the two receivers when there are alternating receiver-specific feedback qualities. Finally, simulation results show that both schemes offer a significant SNR gain over conventional single-user/multiuser mode switching when the feedback overhead is fixed.

Rate splitting for MIMO wireless networks: a promising PHY-layer strategy for LTE evolution

MIMO processing plays a central part in the recent increase in spectral and energy efficiencies of wireless networks. MIMO has grown beyond the original point-to-point channel and nowadays refers to a diverse range of centralized and distributed deployments. The fundamental bottleneck toward enormous spectral and energy efficiency benefits in multiuser MIMO networks lies in a huge demand for accurate CSIT. This has become increasingly difficult to satisfy due to the increasing number of antennas and access points in next generation wireless networks relying on dense heterogeneous networks and transmitters equipped with a large number of antennas. CSIT inaccuracy results in a multi-user interference problem that is the primary bottleneck of MIMO wireless networks. Looking backward, the problem has been to strive to apply techniques designed for perfect CSIT to scenarios with imperfect CSIT. In this article, we depart from this conventional approach and introduce readers to a promising strategy based on rate-splitting. Rate-splitting relies on the transmission of common and private messages, and is shown to provide significant benefits in terms of spectral and energy efficiencies, reliability, and CSI feedback overhead reduction over conventional strategies used in LTE-A and exclusively relying on private message transmissions. Open problems, the impact on standard specifications, and operational challenges are also discussed.

MISO Broadcast Channel with imperfect and (Un)matched CSIT in the frequency domain: DoF region and transmission strategies

In this contribution, we focus on a frequency domain two-user Multiple-Input-Single-Output Broadcast Channel (MISO BC) where the transmitter has imperfect and (un)matched Channel State Information (CSI) of the two users in two subbands. We provide an upper-bound to the Degrees-of-Freedom (DoF) region, which is tight compared to the state of the art. By decomposing the subbands into subchannels according to the CSI feedback qualities, we interpret the DoF region as the weighted-sum of that in each subchannel. Moreover, we study the sum DoF loss when employing sub-optimal schemes, namely Frequency Division Multiple Access (FDMA), Zero-Forcing Beamforming (ZFBF) and the S33/2 scheme proposed by Tandon et al. The results show that by switching among the sub-optimal strategies, we can obtain at least 80% and 66.7% of the optimal sum DoF performance for the unmatched and matched CSIT scenario respectively.

Degrees-of-freedom of the K-user MISO interference channel with delayed local CSIT

This paper considers a K-user Multiple-Input-Single-Output (MISO) Interference Channel (IC), where the channel state information obtained by the transmitters (CSIT) is perfect, but completely outdated. A Retrospective Interference Alignment (RIA) using such delayed CSIT was proposed by Maddah-Ali et. al for the MISO Broadcast Channel (BC), but the extension to the MISO IC is a non-trivial step as each transmitter only has the message intended for the corresponding user. Recently, Abdoli et.al focused on a Single-Input-Single-Output (SISO) IC and solved such bottleneck by inventing a distributed higher order symbol generation. Our main work is to extend Abdolis work to the MISO case by integrating some features of Maddah-Alis scheme. The achieved sum Degrees-of-Freedom (DoF) performance is asymptotically given by 64/15 when K→∞, outperforming all the previously known results.

DoF analysis of the K-user MISO broadcast channel with hybrid CSIT

We consider a K-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user i(i = 1, 2, ..., K) may be either instantaneously perfect (P), delayed (D) or not known (N) at the transmitter with probabilities λ_Pⁱ, λ_Dⁱ and λ_Nⁱ, respectively. In this setting, according to the three possible CSIT for each user, knowledge of the joint CSIT of the K users could have at most 3^K states. Although the results by Tandon et al. show that for the symmetric two user MISO BC (i.e., λ_Qⁱ = λ_Q, ∀_i ∈ {1, 2}, Q ∈ {P, D, N}), the Degrees of Freedom (DoF) region depends only on the marginal probabilities, we show that this interesting result does not hold in general when K ≥ 3. In other words, the DoF region is a function of all the joint probabilities. In this paper, given the marginal probabilities of CSIT, we derive an outer bound for the DoF region of the K-user MISO BC. Subsequently, we investigate the achievability of the outer bound in some scenarios. Finally, we show the dependence of the DoF region on the joint probabilities.

DoF Analysis of the MIMO Broadcast Channel With Alternating/Hybrid CSIT

We consider a K-user multiple-input singleoutput (MISO) broadcast channel (BC) where the channel state information (CSI) of user i(i = 1,2, .. ., K) may be instantaneously perfect (P), delayed (D), or not known (N) at the transmitter with probabilities λ_Pⁱ, λ_Dⁱ, and λ_Nⁱ, respectively. In this setting, according to the three possible CSI at the transmitter (CSIT) for each user, knowledge of the joint CSIT of the K users could have at most 3K states. In this paper, given the marginal probabilities of CSIT (i.e., λ_Pⁱ, λ_Dⁱ, and λ_Nⁱ), we derive an outer bound for the degrees of freedom (DoF) region of the K-user MISO BC. Subsequently, we tighten this outer bound by considering a set of inequalities that capture some of the 3K states of the joint CSIT. One of the consequences of this set of inequalities is that for K ≥ 3, it is shown that the DoF region is not completely characterized by the marginal probabilities in contrast to the two-user case. Afterwards, the tightness of these bounds is investigated through the discussion on the achievability. Finally, a two user multiple-input multipleoutput BC having CSIT among P and N is considered in which an outer bound for the DoF region is provided, and it is shown that in some scenarios, it is tight.

Achievable DoF Regions of MIMO Networks With Imperfect CSIT

We focus on a two-receiver multiple-input-multiple-output (MIMO), broadcast channel (BC), and interference channel (IC) with an arbitrary number of antennas at each node. We assume an imperfect knowledge of local channel state information at the transmitters, whose error decays with the signal-to-noise-ratio. With such configuration, we characterize the achievable degrees-of-freedom (DoF) regions in both BC and IC, by proposing a rate-splitting (RS) approach, which divides each receiver’s message into a common part and a private part. Compared with the RS scheme designed for the symmetric MIMO case, the novelties of the proposed block lie in: 1) delivering additional non-ZF-precoded private symbols to the receiver with the greater number of antennas and 2) a space-time implementation. These features provide more flexibilities in balancing the common-message-decodabilities at the two receivers, and fully exploit asymmetric antenna arrays. Besides, in IC, we modify the power allocation designed for the asymmetric BC based on the signal space, where the two transmitted signals interfere with each other. We also derive an outer-bound for the DoF regions and show that the proposed achievable DoF regions are optimal under some antenna configurations and channel state information at the transmitter side qualities.

Achievable Sum DoF of the

This paper considers a K-user multiple-input multiple-output (MIMO) interference channel (IC) where 1) the channel state information obtained by the transmitters (CSIT) is completely outdated and 2) the number of transmit antennas at each transmitter, i.e., M is greater than the number of receive antennas at each user, i.e., N. The usefulness of the delayed CSIT was first identified in a K-phase retrospective interference alignment (RIA) scheme proposed by Maddah-Ali and Tse for the multiple-input single-output broadcast channel, but the extension to the MIMO IC is a non-trivial step as each transmitter only has the message intended for the corresponding user. Recently, Abdoli et al. focused on a single-input single-output IC and solved such bottleneck by inventing a K-phase RIA with distributed overheard interference retransmission. In this paper, we propose two K-phase RIA schemes suitable for the MIMO IC by generalizing and integrating some key features of both Abdolis and Maddah-Alis works. The two schemes jointly yield the best known sum degrees-of-freedom (DoF) performance so far. For the case (M/N)≥K, the achieved sum DoF is asymptotically given by (64/15)N when K→∞.

{K}

In this paper, a new proof for the degrees of freedom (DoF) region of the K-user multiple-input multiple-output (MIMO) broadcast channel (BC) with no channel state information at the transmitter (CSIT) and perfect channel state information at the receivers (CSIR) is provided. Based on this proof, the capacity region of a certain class of MIMO BC with channel distribution information at the transmitter (CDIT) and perfect CSIR is derived. Finally, an outer bound for the DoF region of the K-user MIMO interference channel (IC) with no CSIT is provided.