Optimal Training Sequences for Joint Timing Synchronization and Channel Estimation in Distributed Communication Networks

In this paper, we study the Cramer-Rao bound (CRB) for continuous phase modulation (CPM) signals. Based on the CRB computations, we propose the optimum training sequence for joint estimation of carrier phase, frequency offset and symbol timing. Our proposed training sequence is optimum in the sense that it minimizes the CRBs for all three estimation parameters simultaneously. The results are useful in the design of training sequences attached to data packets in burst-mode transmissions where data-aided (DA) synchronization is employed.

We consider the problem of data-aided frequency-offset and channel estimation in the case of frequency-selective channels. More precisely, we address the problem of training sequence selection with the goal of providing accurate frequency offset and channel estimates. Toward this end, we consider the Crame/spl acute/r-Rao bound (CRB), for which we derive a closed-form expression. Since the CRB is a complicated function of the training sequence and the channel parameters, a much simpler asymptotic CRB is derived. Two criteria for training sequence design based on the asymptotic CRB are proposed, and a minmax approach is presented to optimize them. Our main contribution is to show that a white sequence is minmax optimal for both criteria considered, and that the quest for a generally optimal sequence is hardly motivated.

In this paper, while considering the impact of antenna correlation and the interference from neighboring users, we study the problem of channel estimation and training sequence design in multi-input multi-output (MIMO) two-way relaying (TWR) systems. To this end, we propose to decompose the bidirectional transmission links into two phases, i.e., the multiple access (MAC) and the broadcast (BC) phases. By deriving the optimal linear minimum mean-square-error estimators, the corresponding training design problems for the MAC and BC phases are formulated and solved. Subsequently, algorithms and, in some special cases, closed-form solutions for obtaining the optimal training sequences for channel estimation in TWR systems are derived. Moreover, to further reduce channel estimation overhead, the minimum required length of the training sequences are determined. Simulation results verify the effectiveness of the proposed training designs in improving channel estimation performance in TWR systems.

An iterative training sequence design scheme called Iterative SuperImposed training sequence design with Multiple Interferers, or ISIMI, is proposed for estimating MIMO channels with colored noise. The proposed approach decomposes the MIMO channel and design the training sequence on a per channel basis, thus making the use of sequential minimum mean-squared error (MMSE) estimator ideal for channel estimation. The time-multiplexed-superimposed training (TM-SIT) transmission format is also proposed to accommodate the different training sequences obtained via the proposed ISIMI method. The proposed approach does not use nonlinear optimization as utilized in previous literature, nor make any assumption about the lack of interdependence between the transmitter and receiver. The approach can be proven to converge to at least a local optimal solution and is shown consistently by Monte Carlo simulation to outperform previously proposed MMSE based approaches by 4 dB for 4×4 MIMO systems, respectively, in terms of MSE when the sequential MMSE estimator is used.

Channel estimation is crucial in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, especially with a few training sequences. To solve the problem of uplink channel estimation in mmWave massive MIMO systems, a PARAFAC-based algorithm is proposed for joint estimation of multiuser channels. The orthogonal frequency divisional multiplexing (OFDM) technique is exploited to combat the frequency selective fading channels. In this paper, the received signal at the base station (BS) is formulated as a third-order parallel factor (PARAFAC) tensor, and then a low-complexity algorithm is designed for fast estimation of the factor matrices related to channel parameters, thus leading to joint estimation of multiuser channel parameters via one-dimensional search. Moreover, the Cramér–Rao Bound (CRB) results for multiuser channel parameters are derived for evaluation. Theorical analysis and numerical results reveal that the algorithm performs well with a few training sequences. Compared with existing algorithms, the proposed algorithm has clear advantages both in estimation accuracy and computational complexity.

In this paper, we study the joint estimation of inphase and quadrature-phase (I/Q) imbalance, carrier frequency offset (CFO), and channel response for multiple-input multipleoutput (MIMO) orthogonal frequency division multiplexing (OFDM) systems using training sequences. A new concept called channel residual energy (CRE) is introduced. We show that by minimizing the CRE, we can jointly estimate the I/Q imbalance and CFO without knowing the channel response. The proposed method needs only one OFDM block for training and the training symbols can be arbitrary. Moreover when the training block consists of two repeated sequences, a low complexity two-step approach is proposed to solve the joint estimation problem. Simulation results show that the mean-squared error (MSE) of the proposed method is close to the Cramer-Rao bound (CRB).

In this paper, we present a study of optimal training sequences for robust joint channel estimation and signal detection. Particularly, we study the case of virtual MIMO links, where there are more co-channel signals M than receive antennas N, i.e., N <M. A training sequence based on the one-dimensional chaotic Chebyshev map is presented herein. This sequence delivers robust performance in terms of Bit Error rate (BER), Normalized Mean-Squared-Error (NMSE) of the estimation and computation complexity. The proposed sequence exhibits an optimal performance by spanning only a minimal number of training symbols, i.e., L=M. The proposed chaotic-based training sequence performs adequatly on both i.i.d. and correlated Rayleigh Fading Channels without the need for a priori statistics of the channel.

In this paper, the training sequence design for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems under the minimum mean square error (MMSE) criterion is addressed. The optimal training sequence for channel estimation in spatially correlated MIMO-OFDM systems was not known for an arbitrary signal-to-noise ratio (SNR). Only one class of training sequences was proposed in the literature in which the power allocation is given only for the extreme conditions of low and high SNRs. The current paper presents a necessary and sufficient condition for the optimal training sequence, and reformulates the training design problem as a convex optimization problem whose optimal solution is efficiently solved. In addition, tight upper bounds for MMSE and resulting low complexity iterative algorithms with the closed-form expression in iterations to find the optimum training sequence are derived. Simulation results confirm the superiority of the proposed design over the existing one in terms of both MSE estimation and BER performance. The proposed methods are also shown to be robust with respect to the spatial correlation mismatch at the transmitter.

Acoustic noise induced by multilayer ceramic capacitors (MLCCs) in power distribution network (PDN) is a critical issue regarding product user experience. In this work, design guidelines for decoupling capacitor selection, layout geometries are proposed targeting the acoustic noise, through analysis of the acoustic noise generation mechanism in printed circuit board (PCB). A test board is designed to validate the proposed design guidelines. With sound pressure level measurement of the test vehicle, the effectiveness of the proposed design guidelines is confirmed. In general, the decoupling capacitor layout design guidelines for acoustic noise consideration are consistent with the requirements for PDN to achieve high electrical performance.

In this chapter, we investigate the design of training sequences for time-multiplexed channel training in C-RANs. Orthogonal training sequences were shown to be optimal or nearly optimal in conventional MIMO systems, where the transmit antennas are co-located, and so are the receive antennas. However, orthogonal training design is very inefficient when applied to C-RAN, for that a C-RAN system usually covers a large number of users and RRHs. Allocating orthogonal training sequences to users leads to an unaffordable overhead to the system. As proved in the previous chapter, the signals from far-away users can be largely ignored without causing significant performance loss. Hence, rather than global orthogonality, we introduce the notion of local orthogonality, in which the training sequences of the users in the neighborhood of an RRH (i.e., the area centered around the RRH with distance below a certain threshold d0) are required to be orthogonal to each other. The training design problem is then formulated as to find the minimum training length that preserves local orthogonality. This problem can be recast as a vertex-coloring problem, and the existing vertex-coloring algorithms can be applied to solve the problem. Further, we analyze the minimum training length as a function of the network size. Based on the theory of random geometric graph, we show that the training length is \(O(\ln K)\) almost surely, where K is the number of users. This guarantees a scalable training-based C-RAN design, i.e., the proposed training design can be applied to a large-size C-RAN system satisfying local orthogonality at the cost of a moderate training length. Note that , on one hand, with local orthogonality, the larger the neighborhood of an RRH, the more interference from the neighboring users can be eliminated in channel estimation. Then, local orthogonality achieves a channel-estimation accuracy close to that of global orthogonality. On the other hand, a larger neighborhood area implies more channel coefficients to be estimated, thereby incurring a greater overhead to the system. As such, there is a balance to strike between the accuracy and the overhead in channel estimation. In this chapter, we study this tradeoff from the perspective of throughput maximization. We show that, with local orthogonality, the optimal d0 for throughput maximization can be numerically determined.

This paper is focused on training sequence design for efficient channel estimation in multiple-input multiple-output filterbank multicarrier (MIMO-FBMC) communications using offset quadrature amplitude modulation (OQAM). MIMO-FBMC is a promising technique to achieve high spectrum efficiency as well as strong robustness against dispersive channels due to its feature of time-frequency localization. A salient drawback of FBMC/OQAM signals is that only real-field orthogonality can be kept, leading to the intrinsic imaginary interference being a barrier for high-performance channel estimations. Also, conventional channel estimations in the MIMO-FBMC systems mostly suffer from high training overhead especially for large number of transmit antennas. Motivated by these problems, in this paper, we propose a new class of training sequences, which are formed by concatenation of two identical zero-correlation zone sequences whose auto-correlation and cross correlation are zero within a time-shift window around the in-phase position. Since only real-valued symbols can be transmitted in MIMO-FBMC systems, we propose “complex training sequence decomposition (CTSD)” to facilitate the reconstruction of the complex-field orthogonality of MIMO-FBMC signals. Our simulations validate that the proposed CTSD is an efficient channel estimation approach for practical preamble-based MIMO-FBMC systems.

We study how to design a worst-case robust training sequence for multiple-input multiple-output (MIMO) channel estimation. We consider mean-squared error of channel estimates as the figure of merit which is a function of second-order statistics of the MIMO channel, i.e., channel covariance matrix, in order to optimize training sequences under a total power constraint. In practical applications, the channel covariance matrix is not known perfectly. Thus the main aspect of our design is to improve robustness of the training sequences against possible uncertainties in the available channel covariance matrix. Using a deterministic uncertainty model, we formulate a robust training sequence design as a minimax optimization problem where we take such imperfections into account. We investigate the robust design problem assuming the general case of an arbitrarily correlated MIMO channel and a non-empty compact convex uncertainty set. We prove that such a problem admits a globally optimal solution by exploiting the convex-concave structure of the objective function, and propose numerical algorithms to address the robust training design problem. We proceed the analysis by considering multiple-input single-output (MISO) channels and Kronecker structured MIMO channels along with unitarily-invariant uncertainty sets. For these scenarios, we show that the problem is diagonalized by the eigenvectors of the nominal covariance matrices so that the robust design is significantly simplified from a complex matrix-variable problem to a real vector-variable power allocation problem. For the MISO channel, we provide closed-form solutions for the robust training sequences with the uncertainty sets defined by the spectral norm and nuclear norm.

Massive multiple-input multiple-output (massive-MIMO) is considered as the key technology to meet the huge demands of data rates in the future wireless communications networks. However, for massive-MIMO systems to realize their maximum potential gain, sufficiently accurate downlink (DL) channel state information (CSI) with low overhead to meet the short coherence time (CT) is required. Therefore, this article aims to overcome the technical challenge of DL CSI estimation in a frequency-division-duplex (FDD) massive-MIMO with short CT considering five different physical correlation models. To this end, the statistical structure of the massive-MIMO channel, which is captured by the physical correlation is exploited to find sufficiently accurate DL CSI estimation. Specifically, to reduce the DL CSI estimation overhead, the training sequence is designed based on the eigenvectors of the transmit correlation matrix. To this end, the achievable sum rate (ASR) maximization and the mean square error (MSE) of CSI estimation with short CT are investigated using the proposed training sequence design. Furthermore, this article examines the effect of channel hardening in an FDD massive-MIMO system. The results demonstrate that in high correlation scenarios, a large loss in channel hardening is obtained. The results reveal that increasing the correlation level reduces the MSE but does not increase the ASR. However, exploiting the spatial correction structure is still very essential for the FDD massive-MIMO systems under limited CT. This finding holds for all the physical correlation models considered.

Semantics-aware content-based recommender systems: Design and architecture guidelines

48V voltage regulator modules (VRMs) are critical for telecom power supplies and are becoming popular for future data centers. By using a novel sigma converter topology, an outstanding performance in terms of efficiency (95%) and power density (700 W/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) have been demonstrated. However, the control of the Sigma converter is challenging due to the quasi-parallel structure and has not been solved properly yet. In this paper, a control method combining V <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> control and active droop control is adopted for the Sigma converter. A design guideline is proposed to achieve adaptive voltage positioning (AVP). Following the proposed design guideline, simulation and experimental results demonstrate good transient responses.