Degrees Of Freedom Gain Research Articles

Faster-Than-Nyquist Asynchronous NOMA Outperforms Synchronous NOMA

Faster-than-Nyquist (FTN) signaling aided non-orthogonal multiple access (NOMA) is conceived and its achievable rate is quantified in the presence of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">random</i> link delays of the different users. We reveal that exploiting the link delays may potentially lead to a signal-to-interference-plus-noise ratio (SINR) gain, while transmitting the data symbols at FTN rates has the potential of increasing the degree-of-freedom (DoF). We then unveil the fundamental trade-off between the SINR and DoF. In particular, at a sufficiently high symbol rate, the SINR gain vanishes while the DoF gain achieves its maximum, where the achievable rate is almost <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(1+\beta)$ </tex-math></inline-formula> times higher than that of the conventional synchronous NOMA transmission in the high signal-to-noise ratio (SNR) regime, with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> being the roll-off factor of the signaling pulse. Our simulation results verify our analysis and demonstrate considerable rate improvements over the conventional power-domain NOMA scheme.

Two New Kinds of Interference Alignment Schemes for Cellular $K$-User MIMO Downlink Networks

It is known that interference alignment (IA) plays an important role in improving the degree of freedom (DoF) of multi-input and multi-output (MIMO) systems. However, most of the traditional IA schemes suffer from the high computational complexity and require the global and instantaneous channel state information (CSI), both of which make them difficult to be extended to cellular MIMO systems. To handle these issues, two new IA schemes, i.e., the retrospective interference regeneration (RIR) scheme and the beamforming based distributed retrospective interference alignment (B-DRIA) scheme, are proposed for cellular <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> -user MIMO downlink networks. For the RIR scheme, it adopts interference elimination algorithm to erase redundant symbols in inter-cell interference (ICI) signals, and then uses interference regeneration algorithm to avoid secondary interference. The RIR scheme obtains greater DoF gain than the retrospective interference alignment (RIA) scheme, but incurs performance degradation when the transceiver antennas ratio (TAR) approaches 1. Therefore, the B-DRIA scheme is further proposed. For the B-DRIA scheme, the cellular beamforming matrix is introduced to eliminate the ICI, and meanwhile distributed RIA algorithm is adopted to align inter-user interference (IUI). The simulation results show that the B-DRIA scheme obtains larger DoF than the RIR scheme locally. Specifically, when TAR approaches 1, two schemes obtain the same DoF. While TAR approaches 2, the DoF of the B-DRIA scheme is superior than the RIR scheme.

Capacity Analysis of Hybrid MIMO Using Sparse Signal Processing in mmW 5G Heterogeneous Wireless Networks

The mmW cellular systems of large bandwidths offer multiple times rise in capacity as compared to existing 4G networks with comparable cell density. These avoid the unnecessary cell splitting by enlarging the capacity of individual tiny cells significantly in a scenario of very high-density cell deployments. This work will provide an opportunity to achieve a particular capacity value by varying the mmW channel gain in the 5G and 6G wireless networks. The OMP algorithm is modified and the existing sparse signal processing concept is utilized for the capacity analysis of hybrid MIMO here. The capacity (b/s/Hz) of the conventional and hybrid MIMOs are calculated and compared against given SNR range (dB) in a 5G mmW heterogeneous network under different values of mmW channel gain. It has been found that capacity analysis curves of conventional and hybrid MIMOs both show a descending trend with the increase in SNR range as the channel gain is increased due to over-saturation of the used sparse mmW channel. These curves exhibit local variation, time dependence, frequency selectivity, reliable communication rate, and diversity on both ends and the use of MIMO has a gain in degrees of freedom. The hybrid MIMO due to hardware limitations of conventional MIMO utilized a large number of antennas with lesser radio frequency chains. At some point of channel gain, its capacity curve approached the capacity curve of conventional MIMO in a moderate SNR range, and approached very closely for all channel gains in low and high SNR ranges.

Coprime Sensing via Chinese Remaindering Over Quadratic Fields—Part I: Array Designs

A coprime antenna array consists of two or more sparse subarrays featuring enhanced degrees of freedom (DOF) and reduced mutual coupling. This paper introduces a new class of planar coprime arrays, based on the theory of ideal lattices. In quadratic number fields, a splitting prime p can be decomposed into the product of two distinct prime ideals, which give rise to the two sparse subarrays. Their virtual difference coarray enjoys a quadratic gain in DOF, thanks to the generalized Chinese remainder theorem (CRT). To enlarge the contiguous aperture of the coarray, we present hole-free symmetric CRT arrays with simple closed-form expressions. The ring of Gaussian integers and the ring of Eisenstein integers are considered as examples to demonstrate the procedure of designing coprime arrays. With Eisenstein integers, our design yields a difference coarray that is a subset of the hexagonal lattice, offering a significant gain in DOF over the rectangular lattice, given the same physical areas. Maximization of CRT arrays in the aspect of essentialness and the superior performance in the context of angle estimation will be presented in the companion paper (Part II).

A Relay Can Increase Degrees of Freedom in Bursty Interference Networks

We investigate the benefits of incorporating relays in future multi-user wireless networks that seek to exploit unexplored bands of very high frequency spectrum, where transmitted signals are known to be highly susceptible to outages. To this end, we examine a two-user bursty MIMO Gaussian interference channel with an in-band relay, where Bernoulli random states conceptually capture signal outages. As our main result, we show that an in-band relay can provide a degrees of freedom (DoF) gain in this bursty channel. This beneficial role of in-band relays in the bursty channel is in direct contrast to their role in the non-bursty channel which is not as significant to provide a DoF gain. More importantly, we demonstrate that in certain antenna configurations, an in-band relay can help achieve interference-free performances with increased DoF. We find the benefits particularly substantial in high-outage circumstances, as the DoF gain can grow linearly with the number of antennas at the relay. In this paper, first we derive an outer bound from which we obtain a necessary condition for interference-free DoF performances. Then we develop a novel scheme that exploits information of the bursty channel states to achieve them.

Cyclic Interference Alignment for Full-Duplex Multi-Antenna Cellular Networks

This paper studies full-duplex (FD) cellular networks in which a base station (BS) operated in FD mode with multiple antennas supports multiple uplink and downlink users simultaneously in the same wireless channel. Two typical FD cellular scenarios are considered, one with half-duplex (HD) users and the other with FD users along with the FD BS. For both the cases, a novel constructive method is developed for finding a closed-form interference alignment (IA) solution, named cyclic IA . The core idea behind this approach is to construct a set of loop-equations enabling IA in a cyclic manner, so that beamforming vectors are sequentially determined by solving an eigenvalue problem. It is shown analytically that the proposed cyclic IA can achieve the optimal sum degrees-of-freedom (DoF) when the number of user antennas is large enough to meet the derived conditions. In particular, it is shown that the proposed scheme achieves a twofold DoF gain compared with conventional HD cellular networks even in the presence of inter-link interference, provided the number of users becomes large enough compared with the ratio of the number of BSs and user antennas. Simulation results demonstrate that not only are the analytical DoF results valid, but under a practical multi-cell scenario, the proposed cyclic IA offers significant throughput gains depending on the cell radius.

송신단 채널 정보가 없는 재구성 안테나를 사용한 다중입출력 Z-간섭 채널에서의 자유도

본 논문에서는 송신단 채널 정보가 없는 다중안테나 Z-간섭 채널에서 수신단의 재구성 안테나를 통해 얻을 수 있는 자유도(DoF: degrees of freedom) 이득을 구한다. 수신단이 가지는 재구성 안테나의 안테나 모드 스위칭 패턴 디자인을 통해 간섭 신호는 정렬하고 원하는 신호를 위해 충분한 신호부공간(signal subspace)을 남겨두는 새로운 선형 기법을 제안한다. 제안하는 기법의 핵심은 송신단에서 일정 구간동안 신호를 보내지 않음으로써 수신단에서 그 동안 받은 간섭신호를 부가 정보(side information)로 간섭 제거에 활용하는 것이다. 결론적으로, 수신단이 가지는 재구성 안테나를 활용해 재구성 안테나 모드의 개수가 RF 체인의 수 보다 클 때 더 큰 자유도 이득을 얻을 수 있음을 밝힌다. In this paper, we derive the achievable degrees of freedom (DoF) for multiple-input multiple-output (MIMO) Z-interference channels (Z-IC) with reconfigurable antennas at the receivers, assuming that channel state information is not available at the transmitters. We propose a new linear scheme to align interfering signals and to decode desired signals through the designed preset mode switching pattern of reconfigurable antennas at the receivers. The key idea of our scheme is to use interfering signals as a side information at the interfered receiver by being silent at the corresponding transmitter during some time slots. Consequently, it is shown that the reconfigurable antennas at the receivers can bring a DoF gain if the number of preset modes is greater than the number of RF chains at the receivers.

Achievable degrees of freedom of MIMO two-way X relay channel with delayed CSIT

The previous work on interference alignment for multiple-input-multiple-output (MIMO) two-way X relay channel assumes perfect channel state information at the transmitter (CSIT), which is reasonable in slow fading channel. However, in fast fading scenario, this assumption is impractical. In this paper, assuming that each node has delayed CSIT, we study the achievable degrees of freedom (DOF) for MIMO two-way X relay channel in frequency division duplex (FDD) systems. Specifically, in the broadcast (BC) phase, we propose a new multiple-stage transmission (MST) scheme, which utilizes retrospective interference alignment for physical layer network coding (PLNC). We show that MST can achieve significant DOF gain and tremendous power gain over other schemes. When the number of antennas for each user, N, is smaller than the number of the relays, M, the time division multiple access (TDMA) scheme can only achieve an ergodic sum-rate increase by N bps/Hz for every increasing of 3 dB of signal-to-noise power ratio (SNR), while the proposed MST scheme can achieve an ergodic sum-rate increase by M bps/Hz.

On the Degrees of Freedom of Interference Broadcast Channels With Topological Interference Management

Topological interference management is the study of achievable rates within communication networks with no channel state information at the transmitter (CSIT) beyond knowledge of the network structure itself. In this work, we study the degrees of freedom (DoF) of a two-cell two-user-per-cell interference broadcast channel (IBC) with alternating connectivity and global topological interference management. The topological information allows transmitters to track the changing network topology and exploit the varying connectivity states to achieve a DoF gain. We derive novel DoF outer bounds for the two-cell two-user-per-cell IBC with alternating connectivity. This analysis is carried out for different system configurations, namely, single-input single-output (SISO), multiple-input single-output (MISO), and multiple-input multiple-output (MIMO) systems. While global channel knowledge is always restricted to topological information only, we introduce a mixed CSIT setting where varying degrees of local CSIT availability are considered depending on the system configuration. Additionally, we investigate the achievability of the derived bounds and propose new transmission schemes based on joint coding across states. Results show that DoF higher than those conventionally obtained without global topological information are achievable, indicating that even such a minimal level of global CSIT is still highly useful.

Rover-to-Orbiter Communication in Mars: Taking Advantage of the Varying Topology

In this paper, we study the communication problem from rovers on Mars’ surface to Mars-orbiting satellites. We first justify that, to a good extent, the rover-to-orbiter communication problem can be modeled as communication over a $2 \times 2$ X-channel with the network topology varying over time. For such a fading X-channel where transmitters are only aware of the time-varying topology but not the time-varying channel state (i.e., no CSIT), we propose coding strategies that code across topologies , and develop upper bounds on the sum degrees-of-freedom (DoF) that is shown to be tight under certain pattern of the topology variation. Furthermore, we demonstrate that the proposed scheme approximately achieves the ergodic sum-capacity of the network. Using the proposed coding scheme, we numerically evaluate the ergodic rate gain over a time-division-multiple-access (TDMA) scheme for Rayleigh and Rice fading channels. We also numerically demonstrate that with practical orbital parameters, a 9.6% DoF gain, as well as more than 11.6% throughput gain can be achieved for a rover-to-orbiter communication network.

Degrees of Freedom in Cached MIMO Relay Networks

It is well known that conventional cooperative relay schemes cannot provide Degrees of Freedom (DoF) gains due to the cut-set bound. In this paper, we propose a physical layer (PHY) caching scheme for relay networks to achieve DoF gains over conventional relay schemes. By properly caching some popular content at the relay station (RS), the proposed PHY caching can opportunistically transform the unfavorable relay channel topology into a more favorable MIMO broadcast channel topology (cache-induced MIMO cooperation opportunity) and enjoy a large DoF gain. Specifically, we first propose a maximum distance separable (MDS) coded PHY caching scheme to significantly improve the MIMO cooperation opportunity induced by PHY caching. Then we propose a global optimal cache content placement solution to maximize the DoF gain. We also propose a low complexity cache content placement algorithm to find a near-optimal solution without explicit knowledge of the popularity of the content files. Finally, we quantify the DoF gain w.r.t. some important system parameters. Simulations show that the proposed scheme can achieve significant throughput gains over various baselines.

Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. The family nests as particular cases several important asymmetric distributions like the Generalized Hyperbolic distribution. The Generalized Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multivariate setting, an extension of the standard location and scale mixture concept is proposed into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm and extended to cover the case of mixtures of such multiple scaled distributions for application to clustering. Assessments on simulated and real data confirm the gain in degrees of freedom and flexibility in modelling data of varying tail behaviour and directional shape.

Performance Analysis of IA Techniques in the MIMO IBC With Imperfect CSI

In this work we consider the multiple-input multiple-output (MIMO) interference broadcast channel (IBC) and analyse the performance of interference alignment (IA) under imperfect channel state information (CSI), where the variance of the CSI error depends on the signal-to-noise ratio (SNR). First, we derive an upper bound on asymptotic mean loss in sum rate compared to the perfect CSI case and then we quantify the achievable degrees of freedom (DoF) with imperfect CSI. Both sum rate loss and achievable DoF are found to be dependent on the number of cells in the system and the amount of users per cell, in addition to the CSI error parameters themselves. Results show that when error variance is inversely proportional to SNR, full DoF are achievable and the asymptotic sum rate loss is bounded by a derived value. Additionally if the CSI imperfection does not disappear for asymptotically high SNR, then the full DoF gain promised by IA cannot be achieved; we quantify this loss in relation to the CSI mismatch itself. The analytically derived bounds are validated via system simulation, with the cellular counterparts of the maximum signal-to-interference-plus-noise ratio (Max-SINR) and the minimum weighted leakage interference (Min-WLI) algorithms being the IA techniques of choice. Secondly, inspired by the CSI mismatch model used to derive the bounds, we present a novel Max-SINR algorithm with stochastic CSI error knowledge (Max-SINR-SCEK) for the MIMO IBC. Simulations show that the proposed algorithm improves performance over the standard one under imperfect CSI conditions, without any additional computational costs.

Multi-User Multi-Hop Relay Networks: Transmission Schemes and Degrees of Freedom

We study the achievable sum degrees of freedom (DoF) in wireless single-antenna multi-user multi-hop relay networks. In most existing works targeting this problem, it is assumed that relays operate in perfect full-duplex fashion and can also shield their receptions from the transmissions of other relays in the same and rear layers. In practice, such ideal assumptions are normally hard to realize. And a naive adoption of half-duplex operation in relays may result in significantly inefficient use of available radio resources. We propose spectrally-efficient transmission schemes to address this issue. A lower-bound to the networks' available DoF (i.e., optimally achievable sum DoF) hence can be attained. Our results indicate that besides providing information delivery paths, relays can also bring DoF gain over single-hop networks, even when relay interference issues are taken into consideration. This lower-bound would approach the upper-bound of the available DoF, if each relay layer deploys more nodes. When the number of relays in every layer is infinitely large, the exact available DoF is identified, which shows that handling interference issues through distributed signal processing and half-duplex operation across multiple layers of terminals may not negatively affect DoF performance, compared with ideal full-duplex and multi-antenna networks.

Two Branch Beamforming for the Three User Constant MIMO Interference Channel

We consider the interference alignment (IA) in the three user constant multiple input multiple output (MIMO) interference channel. A two branch transmit and receive beam-forming scheme is proposed, where the IA scheme of Cadambe and Jafar is applied to the top branches while the bottom branches help additional stream transmission without causing interference to the other users. This scheme is applicable without any restriction on the numbers of transmit and receive antennas and affords additional degree of freedom gain compared to the Cadambe and Jafar scheme. With the proposed scheme, the known degree of freedom upper bound $$\frac{3(M+N)}{4}$$3(M+N)4 of the beam-forming based IA is achieved in more general condition than the previous result for the three user constant MIMO interference channel, where $$M$$M is the number of antennas at the transmitter and $$N$$N is the number of antennas at the receivers.

Space-Time Interference Alignment and Degree-of-Freedom Regions for the MISO Broadcast Channel With Periodic CSI Feedback

This paper characterizes the degree-of-freedom (DoF) regions for the multiuser vector broadcast channel with periodic channel state information (CSI) feedback. As a part of the characterization, a new transmission method called space-time interference alignment is proposed, which exploits both the current and past CSI jointly. Using the proposed alignment technique, an inner bound of the sum-DoF region is characterized as a function of a normalized CSI feedback frequency, which measures CSI feedback speed compared to the speed of user's channel variations. One consequence of the result is that the achievable sum-DoF gain is improved significantly when a user sends back both current and outdated CSI compared to the case where the user sends back current CSI only. Then, a tradeoff between CSI feedback delay and the sum-DoF gain is characterized for the multiuser vector broadcast channel in terms of a normalized CSI feedback delay that measures CSI obsoleteness compared to channel coherence time. A crucial insight is that it is possible to achieve the optimal DoF gain if the feedback delay is less than a derived fraction of the channel coherence time. This precisely characterizes the intuition that a small delay should be negligible.

Opportunistic Scheduling With BIA Under Block Fading Broadcast Channels

We propose an opportunistic scheduling method to achieve DoF (degrees of freedom) gain by BIA (blind interference alignment) in block fading K-user 2 × 1 MISO broadcast channel. The optimal scheduling method is obtained by solving a general model of linear integer program. All the users are divided into user pairs to form a 2-user 2 × 1 BIA. Each pair has the same opportunity to be scheduled. When K ≥ 10, the expectation of the achieved DoF can be very close to 4/3.

Multiuser Diversity in Interfering Broadcast Channels: Achievable Degrees of Freedom and User Scaling Law

This paper investigates how multiuser dimensions can effectively be exploited for target degrees of freedom (DoF) in interfering broadcast channels (IBC) consisting of K-transmitters and their user groups. First, each transmitter is assumed to have a single antenna and serve a singe user in its user group where each user has receive antennas less than K. In this case, a K-transmitter single-input multiple-output (SIMO) interference channel (IC) is constituted after user selection. Without help of multiuser diversity, K-1 interfering signals cannot be perfectly removed at each user since the number of receive antennas is smaller than or equal to the number of interferers. Only with proper user selection, non-zero DoF per transmitter is achievable as the number of users increases. Through geometric interpretation of interfering channels, we show that the multiuser dimensions have to be used first for reducing the DoF loss caused by the interfering signals, and then have to be used for increasing the DoF gain from its own signal. The sufficient number of users for the target DoF is derived. We also discuss how the optimal strategy of exploiting multiuser diversity can be realized by practical user selection schemes. Finally, the single transmit antenna case is extended to the multiple-input multiple-output (MIMO) IBC where each transmitter with multiple antennas serves multiple users.

Aligned Interference Neutralization and the Degrees of Freedom of the Two-User Wireless Networks with an Instantaneous Relay

A conventional relay causes a processing delay of at least one symbol duration relative to the direct paths between a source and a destination. This delay caused by using the conventional relay limits the degrees of freedom (DoF) gain in a wireless interference network. In this paper, it is shown that the exploitation of an instantaneous relay (relay-without-delay) improves DoF gain significantly for a two-user wireless network. Specifically, for two different message settings: the interference channel and the X channel, it is shown that a total of 3/2 and 5/3 DoF are achievable almost surely, respectively. The achievable schemes are inspired by the notion of aligned interference neutralization recently proposed for the layered two-user two-hop interference channel.

Maximum-Rate Transmission With Improved Diversity Gain for Interference Networks

Interference alignment (IA) was shown to be effective for interference management in improving transmission rate in terms of the degree of freedom (DoF) gain. On the other hand, orthogonal space-time block codes were widely used in point-to-point multiantenna channels to enhance transmission reliability in terms of the diversity gain. In this paper, we connect these two ideas, i.e., IA and space-time block coding, to improve the designs of alignment precoders for multiuser networks. Specifically, we consider the use of Alamouti codes for IA because of their rate-one transmission and achievability of full diversity in point-to-point systems. The Alamouti codes protect the desired link by introducing orthogonality between the two symbols in one Alamouti codeword, and create alignment at the interfering receiver. We show that the proposed alignment methods can maintain the maximum DoF gain and improve the ergodic mutual information in the long-term regime, while increasing the diversity gain to 2 in the short-term regime. The presented examples of interference networks have two antennas at each node and include the two-user X channel, the interfering multiaccess channel, and the interfering broadcast channel.