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Convex Analysisの二,三の進展について

Massive multiple-input multiple-output (MIMO) wireless communications refers to the idea equipping cellular base stations (BSs) with a very large number of antennas, and has been shown to potentially allow for orders of magnitude improvement in spectral and energy efficiency using relatively simple (linear) processing. In this paper, we present a comprehensive overview of state-of-the-art research on the topic, which has recently attracted considerable attention. We begin with an information theoretic analysis to illustrate the conjectured advantages of massive MIMO, and then we address implementation issues related to channel estimation, detection and precoding schemes. We particularly focus on the potential impact of pilot contamination caused by the use of non-orthogonal pilot sequences by users in adjacent cells. We also analyze the energy efficiency achieved by massive MIMO systems, and demonstrate how the degrees of freedom provided by massive MIMO systems enable efficient single-carrier transmission. Finally, the challenges and opportunities associated with implementing massive MIMO in future wireless communications systems are discussed.

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An Overview of Massive MIMO: Benefits and Challenges

Millimeter wave (mmWave) communications have recently attracted large research interest, since the huge available bandwidth can potentially lead to the rates of multiple gigabit per second per user Though mmWave can be readily used in stationary scenarios, such as indoor hotspots or backhaul, it is challenging to use mmWave in mobile networks, where the transmitting/receiving nodes may be moving, channels may have a complicated structure, and the coordination among multiple nodes is difficult To fully exploit the high potential rates of mmWave in mobile networks, lots of technical problems must be addressed This paper presents a comprehensive survey of mmWave communications for future mobile networks (5G and beyond) We first summarize the recent channel measurement campaigns and modeling results Then, we discuss in detail recent progresses in multiple input multiple output transceiver design for mmWave communications After that, we provide an overview of the solution for multiple access and backhauling, followed by the analysis of coverage and connectivity Finally, the progresses in the standardization and deployment of mmWave for mobile networks are discussed

Millimeter Wave Communications for Future Mobile Networks

To study the operational behaviour of λ-terms, we will use the denotational (mathematical) approach. A denotational semantics for a language is based on the choice of a space of semantics values, or denotations, where terms are to be interpreted. Choosing a space with nice mathematical properties can help in proving the semantic properties of terms, since to this aim standard mathematical techniques can be used.

λ Δ -Models

The emerging massive/large-scale multiple-input multiple-output (LS-MIMO) systems that rely on very large antenna arrays have become a hot topic of wireless communications. Compared to multi-antenna aided systems being built at the time of this writing, such as the long-term evolution (LTE) based fourth generation (4G) mobile communication system which allows for up to eight antenna elements at the base station (BS), the LS-MIMO system entails an unprecedented number of antennas, say 100 or more, at the BS. The huge leap in the number of BS antennas opens the door to a new research field in communication theory, propagation and electronics, where random matrix theory begins to play a dominant role. Interestingly, LS-MIMOs also constitute a perfect example of one of the key philosophical principles of the Hegelian Dialectics, namely, that “quantitative change leads to qualitative change.” In this treatise, we provide a recital on the historic heritages and novel challenges facing LS-MIMOs from a detection perspective. First, we highlight the fundamentals of MIMO detection, including the nature of co-channel interference (CCI), the generality of the MIMO detection problem, the received signal models of both linear memoryless MIMO channels and dispersive MIMO channels exhibiting memory, as well as the complex-valued versus real-valued MIMO system models. Then, an extensive review of the representative MIMO detection methods conceived during the past 50 years (1965–2015) is presented, and relevant insights as well as lessons are inferred for the sake of designing complexity-scalable MIMO detection algorithms that are potentially applicable to LS-MIMO systems. Furthermore, we divide the LS-MIMO systems into two types, and elaborate on the distinct detection strategies suitable for each of them. The type-I LS-MIMO corresponds to the case where the number of active users is much smaller than the number of BS antennas, which is currently the mainstream definition of LS-MIMO. The type-II LS-MIMO corresponds to the case where the number of active users is comparable to the number of BS antennas. Finally, we discuss the applicability of existing MIMO detection algorithms in LS-MIMO systems, and review some of the recent advances in LS-MIMO detection.

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Fifty Years of MIMO Detection: The Road to Large-Scale MIMOs

In this letter, we are concerned with low-complexity detection in large multiple-input multiple-output (MIMO) systems with tens of transmit/receive antennas. Our new contributions in this letter are two-fold. First, we propose a low-complexity algorithm for large-MIMO detection based on a layered low-complexity local neighborhood search. Second, we obtain a lower bound on the maximum-likelihood (ML) bit error performance using the local neighborhood search. The advantages of the proposed ML lower bound are i) it is easily obtained for MIMO systems with large number of antennas because of the inherent low complexity of the search algorithm, ii) it is tight at moderate-to-high SNRs, and iii) it can be tightened at low SNRs by increasing the number of symbols in the neighborhood definition. The proposed detection algorithm based on the layered local neighborhood search achieves bit error performances which are quite close to this lower bound for large number of antennas and higher-order QAM.

Layered Tabu Search Algorithm for Large-MIMO Detection and a Lower Bound on ML Performance

We present a low-complexity algorithm based on reactive tabu search (RTS) for near maximum likelihood (ML) detection in large-MIMO systems. The conventional RTS algorithm achieves near-ML performance for 4-QAM in large-MIMO systems. But its performance for higher-order QAM is far from ML performance. Here, we propose a random-restart RTS (R3TS) algorithm which achieves significantly better bit error rate (BER) performance compared to that of the conventional RTS algorithm in higher-order QAM. The key idea is to run multiple tabu searches, each search starting with a random initial vector and choosing the best among the resulting solution vectors. A criterion to limit the number of searches is also proposed. Computer simulations show that the R3TS algorithm achieves almost the ML performance in 16 × 16 V-BLAST MIMO system with 16-QAM and 64-QAM at significantly less complexities than the sphere decoder. Also, in a 32 × 32 V-BLAST MIMO system, the R3TS performs close to ML lower bound within 1.6 dB for 16-QAM (128 bps/Hz), and within 2.4 dB for 64-QAM (192 bps/Hz) at 10-3 BER.

Random-Restart Reactive Tabu Search Algorithm for Detection in Large-MIMO Systems

In this paper, we deal with low-complexity near-optimal detection/equalization in large-dimension multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that near-optimal performance in MIMO-ISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov random field (MRF)-based graphical model with pairwise interaction, in conjunction with message damping, and 2) use of factor graph (FG)-based graphical model with Gaussian approximation of interference (GAI). The per-symbol complexities are O(K2nt2) and O(Knt) for the MRF and the FG with GAI approaches, respectively, where K and nt denote the number of channel uses per frame, and number of transmit antennas, respectively. These low-complexities are quite attractive for large dimensions, i.e., for large Knt. From a performance perspective, these algorithms are even more interesting in large-dimensions since they achieve increasingly closer to optimum detection performance for increasing Knt. Also, we show that these message passing algorithms can be used in an iterative manner with local neighborhood search algorithms to improve the reliability/performance of M-QAM symbol detection.

Low-Complexity Detection in Large-Dimension MIMO-ISI Channels Using Graphical Models

Non-orthogonal space-time block codes (STBC) with {\em large dimensions} are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) {\em as well as} full transmit diversity. Decoding of non-orthogonal STBCs with large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having large dimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of $12\times 12$ STBC from CDA and 4-QAM with 288 real dimensions achieves $i)$ $10^{-3}$ uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and $ii)$ a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS. We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlated MIMO channel model, and by using a training based iterative RTS decoding/channel estimation scheme.

Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs using Reactive Tabu Search

Non-orthogonal space-time block codes (STBC) with large dimensions are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having large dimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of 12 × 12 STBC from CDA and 4-QAM with 288 real dimensions achieves i) 10−3 uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and ii) a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS.We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlatedMIMO channelmodel, and by using a training based iterative RTS decoding/channel estimation scheme.

N. Srinidhi

Papers

Layered Tabu Search Algorithm for Large-MIMO Detection and a Lower Bound on ML Performance

Random-Restart Reactive Tabu Search Algorithm for Detection in Large-MIMO Systems

Low-Complexity Detection in Large-Dimension MIMO-ISI Channels Using Graphical Models

Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs using Reactive Tabu Search

Low-complexity near-ML decoding of large non-orthogonal STBCs using reactive tabu search