Borzoo Rassouli

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.

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.

On the capacity of vector Gaussian channels with bounded inputs

The capacity of a multiple-input multiple-output (MIMO) identity channel under the peak and average power constraints is investigated. The approach of Shamai et al. is generalized to the higher dimension settings to derive the necessary and sufficient conditions for the optimal input probability density function. This approach prevents the usage of the identity theorem of the holomorphic functions of several complex variables which seems to fail in the multi-dimensional scenarios. It is proved that in the spherical coordinates, the magnitude and phases of the capacity-achieving distribution are mutually independent and its support is a finite set of hyper-spheres where the points are uniformly distributed on them. Subsequently, it is shown that when the average power constraint is relaxed, if the number of antennas is large enough (e.g. massive MIMO), the capacity has a closed form solution and constant amplitude signaling at the peak power achieves it. Finally, it will be observed that in a discrete-time memoryless Gaussian channel, the average power constrained capacity, which results from a Gaussian input distribution, can be closely obtained by an input where the support of its magnitude is a discrete finite set.

Periodic spectrum sensing parameters optimization in cognitive radio networks

Spectrum sensing is one of the main features of cognitive radio that enables secondary users (SUs) to detect spectrum holes. In this study, the authors propose a more realistic measure of interference which is based on the collision between secondary and primary signals. Considering the single SU scenario, the authors find optimal sensing time, transmission time and energy detector threshold to maximise its efficiency while keeping its interference on primary users below a certain threshold. Then, cooperative sensing schemes in a centralised network are investigated in which, the authors derive the optimal cooperation method in the Neyman–Pearson framework and subsequently propose simpler suboptimal cooperative schemes. Furthermore, the authors formulate the limited feedback scheme that uses a two bit quantiser for energy detectors, and compare its performance with other cooperation schemes and it will be shown to have the closest performance to the optimal scheme among all other mentioned methods.

Zero-delay joint source-channel coding with a 1-bit ADC front end and receiver side information

Zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel with a 1-bit analog-to-digital converter (ADC) front end is investigated in the presence of correlated side information at the receiver. The design of the optimal encoder is considered for the mean squared error (MSE) distortion criterion under an average power constraint on the channel input. A necessary condition for the optimality of the encoder is derived. A numerically optimized encoder (NOE) is then obtained that aims that enforcing the necessary condition. It is observed that, due to the availability of receiver side information, the optimal encoder mapping is periodic, with its period depending on the correlation coefficient between the source and the side information. We then propose two parameterized encoder mappings, referred to as periodic linear transmission (PLT) and periodic BPSK transmission (PBT), which trade-off optimality for reduced complexity as compared to the NOE solution. We observe via numerical results that PBT performs close to the NOE in the high signal-to-noise ratio (SNR) regime, while PLT approaches the NOE performance in the low SNR regime.

Gaussian Multiple Access Channels with One-Bit Quantizer at the Receiver

The capacity region of a two-transmitter Gaussian multiple access channel (MAC) under average input power constraints is studied, when the receiver employs a zero-threshold one-bit analogue-to-digital converter (ADC). It is proven that the input distributions of the two transmitters that achieve the boundary points of the capacity region are discrete. Based on the position of a boundary point, upper bounds on the number of the mass points of the corresponding distributions are derived. Furthermore, a lower bound on the sum capacity is proposed that can be achieved by time division with power control. Finally, inspired by the numerical results, the proposed lower bound is conjectured to be tight.

On the Capacity of Vector Gaussian Channels With Bounded Inputs

The capacity of a multiple-input multiple-output (MIMO) identity channel under the peak and average power constraints is investigated. The approach of Shamai et al. is generalized to the higher dimension settings to derive the necessary and sufficient conditions for the optimal input probability density function. This approach prevents the usage of the identity theorem of the holomorphic functions of several complex variables which seems to fail in the multi-dimensional scenarios. It is proved that in the spherical coordinates, the magnitude and phases of the capacity-achieving distribution are mutually independent and its support is a finite set of hyper-spheres where the points are uniformly distributed on them. Subsequently, it is shown that when the average power constraint is relaxed, if the number of antennas is large enough (e.g. massive MIMO), the capacity has a closed form solution and constant amplitude signaling at the peak power achieves it. Finally, it will be observed that in a discrete-time memoryless Gaussian channel, the average power constrained capacity, which results from a Gaussian input distribution, can be closely obtained by an input where the support of its magnitude is a discrete finite set.

Zero-Delay Source-Channel Coding With a Low-Resolution ADC Front End

Motivated by the practical constraints arising in emerging sensor network and Internet-of-Things (IoT) applications, the zero-delay transmission of a Gaussian measurement over a real single-input multiple-output (SIMO) additive white Gaussian noise (AWGN) channel is studied with a low-resolution analog-to-digital converter (ADC) front end. Joint optimization of the encoder and the decoder mapping is tackled under both the mean squared error (MSE) distortion and the distortion outage probability (DOP) criteria, with an average power constraint on the channel input. Optimal encoder and decoder mappings are identified for a one-bit ADC front end under both criteria. For the MSE distortion, the optimal encoder mapping is shown to be non-linear in general, while it tends to a linear encoder in the low signal-to-noise ratio (SNR) regime, and to an antipodal digital encoder in the high SNR regime. This is in contrast to the optimality of linear encoding at all SNR values in the presence of a full-precision front end. For the DOP criterion, it is shown that the optimal encoder mapping is piecewise constant and can take only two opposite values when it is non-zero. For both the MSE distortion and the DOP criteria, necessary optimality conditions are then derived for