We consider the problem of time domain (TD) channel estimation for wideband millimeter wave systems with a hybrid architecture. TD channel estimators can exploit both angular and delay domain sparsity, and can perform better than frequency domain (FD) estimators exploiting only angular domain sparsity; however, the former usually require a heavier computational load than the latter. To overcome this difficulty, we propose an efficient, two-step TD channel estimator: in the first step, an effective channel incorporated with beamforming, array responses, and pulse shaping is estimated by the least squares (LS) method; in the second, the desired channel is estimated via an orthogonal matching pursuit (OMP) algorithm. It is analytically shown that the proposed two-step method can yield the same outputs as the original single-step TD estimator when an identity pulse shaping matrix and a unitary pilot matrix are employed. The proposed algorithm is simpler to implement than the other estimators based on OMP, because its sensing matrix is block-diagonal. The simulation results demonstrate that complexity reduction of the proposed method is achieved without (or with minor) performance degradation.

In millimeter wave (mmWave) communication systems with hybrid multiple-input multiple-output (MIMO) processors, it is often necessary to employ analog beam sweeping during pilot signal transmission/reception to increase the signal to noise ratio (SNR). In this paper, we develop a process, called the space-time (ST) alignment, for receiving pilot sequences for mmWave channel estimation from the signal received during beam sweeping. The spatial alignment removes the effect of beam sweeping on pilot arrival time (PATs). The process for locating the temporal windows on the received signal to obtain pilot-containing sequences for channel estimation is called the temporal alignment. Simulation results demonstrate that mmWave channels can be estimated successfully using the sequences obtained via the ST alignment.

This paper investigates spectral shaping of multi-carrier-modulation waveforms based on combination of Nyquist windowing and subband filtering. The combined windowing/filtering allows simultaneous control on both subcarrier and subband spectra. When compared with the existing Nyquist windowing or subband filtering techniques under a fixed excess frame length constraint, the proposed scheme offers reduced sensitivity to carrier frequency and symbol timing offsets. Establishing an analytical tool based on the error spectrum stack consisting of the error signals evaluated at different signal delay positions, we explore the window-filter trade-off and provide the minimum interference power solution for given ranges of carrier frequency and symbol timing offsets. Our design targets low-latency applications having no provisions for high-precision synchronization and having potential need for spectrum aggregation.

We consider extensions of orthogonal matching pursuit (OMP) and oblique matching pursuit (ObMP) detectors for generalized space shift keying (GSSK). In particular, the maximum a posteriori (MAP) principle is incorporated with the OMP/ObMP so that the posteriori ratio can be maximized iteratively. Due to the fact that the posteriori ratio cannot be evaluated at the receiver unless the activated transmit antennas are known, two types of approximated posteriori ratios are derived. One is a simple approximation that ignores the terms in the posteriori ratio which need the information on transmit antenna activity, and the other is a more complex approximation developed by exploiting the transmit antenna activation probabilities. As a result, two types of MAP-OMPs and MAP-ObMPs are proposed based on these approximations. The performances and computational loads of the proposed schemes are examined and compared with existing OMP- based GSSK detectors. The results demonstrate that incorporating the MAP policies can significantly enhance performances of OMP/ObMP detectors and can yield efficient detectors that can outperform existing methods with little increase in complexity.

We propose the use of uniform circular array of subarrays (UCA-SAs) for millimeter wave (MMW) communication systems over line of sight (LoS) channels and design beamforming coefficients for each subarray. Specifically, for a UCA-SA consisting of Nssubarrays, which are M × M square arrays, the beamforming coefficients are designed so that the Ns× Nseffective channel becomes circulant. To this end, we first show that the UCA-SA can be decomposed into M2concentric UCAs having Nsantenna elements. Then, based on this result, we show that the set of beamforming coefficients making the effective channel circulant consist of identical values. The proposed UCA-SA system employs this type of beamformers, called the constant beamformers. The effective channel of the proposed UCA-SA system can be diagonalized by the discrete Fourier transform (DFT) precoder and the inverse DFT (IDFT) combiner, without the knowledge of channel state information (CSI) at the transmitter. This indicates that constant beamformers are optimal beamformers maximizing the Ns× Nseffective channel's mutual information. Simulation results show that the proposed UCASA can outperform the conventional UCA with NsM2antenna elements which are equally spaced on a ring.

We propose an efficient open-loop channel estimator for a millimeter-wave (mm-wave) hybrid multiple-input multiple-output (MIMO) system consisting of radio-frequency (RF) beamformers with large antenna arrays followed by a baseband MIMO processor. A sparse signal recovery problem exploiting the sparse nature of mm-wave channels is formulated for channel estimation based on the parametric channel model with quantized angles of departures/arrivals (AoDs/AoAs), called the angle grids. The problem is solved by the orthogonal matching pursuit (OMP) algorithm employing a redundant dictionary consisting of array response vectors with finely quantized angle grids. We suggest the use of non-uniformly quantized angle grids and show that such grids reduce the coherence of the redundant dictionary. The lower and upper bounds of the sum-of-squared errors of the proposed OMP-based estimator are derived analytically: the lower bound is derived by considering the oracle estimator that assumes the knowledge of AoDs/AoAs, and the upper bound is derived based on the results of the OMP performance guarantees. The design of training vectors (or sensing matrix) is particularly important in hybrid MIMO systems, because the RF beamformer prevents the use of independent and identically distributed random training vectors, which are popular in compressed sensing. We design training vectors so that the total coherence of the equivalent sensing matrix is minimized for a given RF beamforming matrix, which is assumed to be unitary. It is observed that the estimation accuracy can be improved significantly by randomly permuting the columns of the RF beamforming matrix. The simulation results demonstrate the advantage of the proposed OMP with a redundant dictionary over the existing methods such as the least squares method and the OMP based on the virtual channel model.

Hybrid multiple input multiple output (MIMO) systems consist of an analog beamformer with large antenna arrays followed by a digital MIMO processor. Channel estimation for hybrid MIMO systems in millimeter wave (mm-wave) communications is challenging because of the large antenna array and the low signal-to-noise ratio (SNR) before beamforming. In this paper, we propose an open-loop channel estimator for mm-wave hybrid MIMO systems exploiting the sparse nature of mm-wave channels. A sparse signal recovery problem is formulated for channel estimation and solved by the orthogonal matching pursuit (OMP) based methods. A modification of the OMP algorithm, called the multi-grid (MG) OMP, is proposed. It is shown that the MG-OMP can significantly reduce the computational load of the OMP method. A process for designing the training beams is also developed. Specifically, given the analog training beams the baseband processor for beam training is designed. Simulation results demonstrate the advantage of the OMP based methods over the conventional least squares (LS) method and the efficiency of the MG-OMP over the original OMP.

Due to the high cost and power consumption of radio frequency (RF) chains, millimeter wave (mm-wave) communication systems equipped with large antenna arrays typically employ less RF chains than the antenna elements. This leads to the use of a hybrid MIMO processor consisting of a RF beamformer and a baseband MIMO processor in mm-wave communications. In this paper, we consider amplify-and-forward (AF) relay-assisted mm-wave systems with the hybrid MIMO processors over frequency-selective channels. We develop an iterative algorithm for jointly designing the receive/transmit (Rx/Tx) RF/baseband processors of the relay based on the orthogonal matching pursuit (OMP) algorithm for sparse approximation, while assuming orthogonal frequency division multiplexing (OFDM) signaling. Simulation results show that the proposed method outperforms the conventional method that designs the baseband processor after steering the RF beams.

We study the benefits of opportunistic routing in wireless networks by examining how the power and delay scale as the number of source-destination (S-D) pairs increases, where S-D pairs are randomly located over the network. The scaling behavior of conventional multi-hop transmission that does not employ opportunistic routing is also examined. The results indicate that the opportunistic routing can exhibit better power- delay trade-off than the conventional routing while providing up to a logarithmic boost in the scaling law. The gain comes from the fact that the system with opportunistic routing can tolerate more interference due to increased received signal power from utilizing the multi-user diversity gain. Furthermore, we derive an upper bound on the total throughput using the cut-set theorem. It is shown that the achievable rates of the conventional and opportunistic routing schemes become close to the upper bound when the number of S-D pairs is large enough.

We analyze the outage performance and diversity-multiplexing tradeoff (DMT), originally introduced by Zheng and Tse, for multiple antenna Rician channels or channels with partial channel state information at the transmitter (CSIT). The asymptotic behaviors of the outage are analyzed in the limit of high signal-to-noise ratio (SNR). We also analyze the SNR where the maximum diversity order (MDO) is obtained for Rician channels, which serves as a desired operation point. In addition, by applying the outage analysis for Rician channels we present the differential DMT (DDMT) to develop a better understanding of the asymptotic relationship between the outage probability, transmission rate, SNR, and Rician factor

L-smoothers and M-smoothers are introduced as generalizations of the median filter for nonlinear smoothing of noisy data, and their properties are derived. In addition, a double-window smoothing algorithm which is shown to be a data-dependent modification of L- and M-smoothers is proposed for filtering noisy signals with sharp edges. Simulation results are given to demonstrate the performance characteristics of these smoothing algorithms.