There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Millimeter wave (mmWave) communications has been regarded as a key enabling technology for 5G networks, as it offers orders of magnitude greater spectrum than current cellular bands. In contrast to conventional multiple-input–multiple-output (MIMO) systems, precoding in mmWave MIMO cannot be performed entirely at baseband using digital precoders, as only a limited number of signal mixers and analog-to-digital converters can be supported considering their cost and power consumption. As a cost-effective alternative, a hybrid precoding transceiver architecture, combining a digital precoder and an analog precoder, has recently received considerable attention. However, the optimal design of such hybrid precoders has not been fully understood. In this paper, treating the hybrid precoder design as a matrix factorization problem, effective alternating minimization (AltMin) algorithms will be proposed for two different hybrid precoding structures, i.e., the fully-connected and partially-connected structures. In particular, for the fully-connected structure, an AltMin algorithm based on manifold optimization is proposed to approach the performance of the fully digital precoder, which, however, has a high complexity. Thus, a low-complexity AltMin algorithm is then proposed, by enforcing an orthogonal constraint on the digital precoder. Furthermore, for the partially-connected structure, an AltMin algorithm is also developed with the help of semidefinite relaxation. For practical implementation, the proposed AltMin algorithms are further extended to the broadband setting with orthogonal frequency division multiplexing modulation. Simulation results will demonstrate significant performance gains of the proposed AltMin algorithms over existing hybrid precoding algorithms. Moreover, based on the proposed algorithms, simulation comparisons between the two hybrid precoding structures will provide valuable design insights.

Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems

During the last decade, CD-quality digital audio has essentially replaced analog audio. Emerging digital audio applications for network, wireless, and multimedia computing systems face a series of constraints such as reduced channel bandwidth, limited storage capacity, and low cost. These new applications have created a demand for high-quality digital audio delivery at low bit rates. In response to this need, considerable research has been devoted to the development of algorithms for perceptually transparent coding of high-fidelity (CD-quality) digital audio. As a result, many algorithms have been proposed, and several have now become international and/or commercial product standards. This paper reviews algorithms for perceptually transparent coding of CD-quality digital audio, including both research and standardization activities. This paper is organized as follows. First, psychoacoustic principles are described, with the MPEG psychoacoustic signal analysis model 1 discussed in some detail. Next, filter bank design issues and algorithms are addressed, with a particular emphasis placed on the modified discrete cosine transform, a perfect reconstruction cosine-modulated filter bank that has become of central importance in perceptual audio coding. Then, we review methodologies that achieve perceptually transparent coding of FM- and CD-quality audio signals, including algorithms that manipulate transform components, subband signal decompositions, sinusoidal signal components, and linear prediction parameters, as well as hybrid algorithms that make use of more than one signal model. These discussions concentrate on architectures and applications of those techniques that utilize psychoacoustic models to exploit efficiently masking characteristics of the human receiver. Several algorithms that have become international and/or commercial standards receive in-depth treatment, including the ISO/IEC MPEG family (-1, -2, -4), the Lucent Technologies PAC/EPAC/MPAC, the Dolby AC-2/AC-3, and the Sony ATRAC/SDDS algorithms. Then, we describe subjective evaluation methodologies in some detail, including the ITU-R BS.1116 recommendation on subjective measurements of small impairments. This paper concludes with a discussion of future research directions.

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Perceptual coding of digital audio

Millimeter wave (mmWave) MIMO will likely use hybrid analog and digital precoding, which uses a small number of RF chains to reduce the energy consumption associated with mixed signal components like analog-to-digital components not to mention baseband processing complexity. However, most hybrid precoding techniques consider a fully connected architecture requiring a large number of phase shifters, which is also energy-intensive. In this paper, we focus on the more energy-efficient hybrid precoding with subconnected architecture, and propose a successive interference cancelation (SIC)-based hybrid precoding with near-optimal performance and low complexity. Inspired by the idea of SIC for multiuser signal detection, we first propose to decompose the total achievable rate optimization problem with nonconvex constraints into a series of simple subrate optimization problems, each of which only considers one subantenna array. Then, we prove that maximizing the achievable subrate of each subantenna array is equivalent to simply seeking a precoding vector sufficiently close (in terms of Euclidean distance) to the unconstrained optimal solution. Finally, we propose a low-complexity algorithm to realize SIC-based hybrid precoding, which can avoid the need for the singular value decomposition (SVD) and matrix inversion. Complexity evaluation shows that the complexity of SIC-based hybrid precoding is only about 10% as complex as that of the recently proposed spatially sparse precoding in typical mmWave MIMO systems. Simulation results verify that SIC-based hybrid precoding is near-optimal and enjoys higher energy efficiency than the spatially sparse precoding and the fully digital precoding.

Energy-Efficient Hybrid Analog and Digital Precoding for MmWave MIMO Systems With Large Antenna Arrays

Millimeter wave (mmWave) MIMO will likely use hybrid analog and digital precoding, which uses a small number of RF chains to avoid energy consumption associated with mixed signal components like analog-to-digital components not to mention baseband processing complexity. However, most hybrid precoding techniques consider a fully-connected architecture requiring a large number of phase shifters, which is also energyintensive. In this paper, we focus on the more energy-efficient hybrid precoding with sub-connected architecture, and propose a successive interference cancelation (SIC)-based hybrid precoding with near-optimal performance and low complexity. Inspired by the idea of SIC for multi-user signal detection, we first propose to decompose the total achievable rate optimization problem with non-convex constraints into a series of simple sub-rate optimization problems, each of which only considers one sub-antenna array. Then, we prove that maximizing the achievable sub-rate of each sub-antenna array is equivalent to simply seeking a precoding vector sufficiently close (in terms of Euclidean distance) to the unconstrained optimal solution. Finally, we propose a low-complexity algorithm to realize SICbased hybrid precoding, which can avoid the need for the singular value decomposition (SVD) and matrix inversion. Complexity evaluation shows that the complexity of SIC-based hybrid precoding is only about 10% as complex as that of the recently proposed spatially sparse precoding in typical mmWave MIMO systems. Simulation results verify the near-optimal performance of SIC-based hybrid precoding.

Energy-Efficient Hybrid Analog and Digital Precoding for mmWave MIMO Systems with Large Antenna Arrays

A millimeter wave (mm-wave) communication system provides multi-Gb/s data rates in short-distance transmission. Because millimeter waves have short wavelength, transceivers can be composed of large antenna arrays to alleviate severe signal attenuation. Furthermore, the link performance can be improved by adopting precoding technology in multiple data stream transmission. However, the complexity of radio frequency (RF) chains increases when large antenna arrays are used in mm-wave systems. To reduce the hardware cost, the precoding circuit can be jointly designed in both analog and digital domains to reduce the required number of RF chains. This paper proposes a new method of building the joint RF and baseband precoder that reduces the computation complexity of the original precoder reconstruction algorithm and enables highly parallel hardware architecture. Moreover, the proposed precoder reconstruction algorithm was designed and implemented using TSMC 90-nm UTM CMOS technology. The proposed precoder reconstruction processor supports the transmissions of one to four data streams for 8 × 8 mm-wave multiple-input multiple-output systems. The operating frequency of this chip was 167 MHz, and the power consumption was 243.2 mW when the supply voltage was 1 V. The core area of the postlayout result was about 3.94 mm 2
. The proposed processor achieved 4, 4.9, 6.7, and 6.7 M channel matrices per second in four-, three-, two-, and one-stream modes, respectively.

A Hybrid RF/Baseband Precoding Processor Based on Parallel-Index-Selection Matrix-Inversion-Bypass Simultaneous Orthogonal Matching Pursuit for Millimeter Wave MIMO Systems

Physiologically, the thoracic (THO) and abdominal (ABD) movement signals, captured using wearable piezo-electric bands, provide information about various types of apnea, including central sleep apnea (CSA) and obstructive sleep apnea (OSA). However, the use of piezo-electric wearables in detecting sleep apnea events has been seldom explored in the literature. This study explored the possibility of identifying sleep apnea events, including OSA and CSA, by solely analyzing one or both the THO and ABD signals. An adaptive non-harmonic model was introduced to model the THO and ABD signals, which allows us to design features for sleep apnea events. To confirm the suitability of the extracted features, a support vector machine was applied to classify three categories - normal and hypopnea, OSA, and CSA. According to a database of 34 subjects, the overall classification accuracies were on average 75.9%±11.7% and 73.8%±4.4%, respectively, based on the cross validation. When the features determined from the THO and ABD signals were combined, the overall classification accuracy became 81.8%±9.4%. These features were applied for designing a state machine for online apnea event detection. Two event-byevent accuracy indices, S and I, were proposed for evaluating the performance of the state machine. For the same database, the S index was 84.01%±9.06%, and the I index was 77.21%±19.01%. The results indicate the considerable potential of applying the proposed algorithm to clinical examinations for both screening and homecare purposes.

Sleep Apnea Detection Based on Thoracic and Abdominal Movement Signals of Wearable Piezo-Electric Bands

In this letter, an improved ordered-block minimum-mean-squared-error (OB-MMSE) detector for generalized spatial modulation systems is presented. We first propose to use the concentrated distance metric derived from the conditional maximum likelihood estimator as the ordering metric for the OB-MMSE and then design a computationally-efficient algorithm for computing this metric. The improved ordering performance of the proposed algorithm allows the early-termination of the OB-MMSE detector without noticeable performance loss which can be exploited to further reduce its complexity. Simulation results show that the proposed algorithm can achieve better performance-complexity tradeoff compared to the existing OB-MMSE detector.

An Improved Ordered-Block MMSE Detector for Generalized Spatial Modulation

This paper presents a modified interpolation-based QR decomposition algorithm for the grouped-ordering multiple input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. Based on the original research that integrates the calculations of the frequency-domain channel estimation and the QR decomposition for the MIMO-OFDM system, this study proposes a modified algorithm that possesses a scalable property to save the power consumption for interpolation-based QR decomposition in the variable-rank MIMO scheme. Furthermore, we also develop the general equations and a timing scheduling method for the hardware design of the proposed QR decomposition processor for the higher-dimension MIMO system. Based on the pro posed algorithm, a configurable interpolation-based QR decomposition and channel estimation processor was designed and implemented using a 90-nm one-poly nine-metal CMOS technology. The processor supports 2 × 2, 2 × 4 and 4 × 4 QR-based MIMO detection for the 3GPP-LTE MIMO-OFDM system and achieves the throughput of 35.16 MQRD/s at its maximum clock rate 140.65 MHz.

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Interpolation-Based QR Decomposition and Channel Estimation Processor for MIMO-OFDM System

The soft error problem in digital circuits is becoming increasingly important as the IC fabrication technology progresses from the deep submicrometer scale to the nanometer scale. This paper proposes a subword-detection processing (SDP) technique and a fine-grain soft-error-tolerance (FGSET) architecture to improve the performance of the digital signal processing circuit. In the SDP technique, the logic masking property of the soft error in the combinational circuit is utilized to mask the single-event upset (SEU) caused by disturbing particles in the inactive area. To further improve the performance, the masked portion of the datapath can be used as the estimation redundancy in the algorithmic softerror-tolerance (ASET) technique. This technique is called subword-detection and redundant processing (SDRP). In the FGSET architecture, the soft error in each processing element (fine grain) can be recovered by the arithmetic datapath-level ASET technique. Analysis of the fast Fourier transform processor example shows that the proposed FGSET architecture can improve the performance of the coarse-grain SET (CGSET) by 8.5 dB. The low-cost SDP technique (1.03x) yields a noise reduction of 5.3 dB over the CGSET approach (1.40x), while the efficient SDRP I (1.57x) and SDRP II (1.88x) techniques outperform the CGSET approach by 24.5 and 30.5 dB, respectively.

Yuan-Hao Huang

Papers

A Hybrid RF/Baseband Precoding Processor Based on Parallel-Index-Selection Matrix-Inversion-Bypass Simultaneous Orthogonal Matching Pursuit for Millimeter Wave MIMO Systems

Sleep Apnea Detection Based on Thoracic and Abdominal Movement Signals of Wearable Piezo-Electric Bands

An Improved Ordered-Block MMSE Detector for Generalized Spatial Modulation

Interpolation-Based QR Decomposition and Channel Estimation Processor for MIMO-OFDM System

High-Efficiency Soft-Error-Tolerant Digital Signal Processing Using Fine-Grain Subword-Detection Processing