Sources of uncertainties and artefacts in back-projection results

Back-projecting high-frequency (HF) waves is a common procedure for imaging rupture processes of large earthquakes (i.e. M_w > 7.0). However, obtained back-projection (BP) results could suffer from large uncertainties since high-frequency seismic waveforms are strongly affected by factors like source depth, focal mechanisms, and the Earth's 3-D velocity structures. So far, these uncertainties have not been thoroughly investigated. Here, we use synthetic tests to investigate the influencing factors for which scenarios with various source and/or velocity set-ups are designed, using either Tohoku-Oki (Japan), Kaikoura (New Zealand), Java/Wharton Basin (Indonesia) as test areas. For the scenarios, we generate either 1-D or 3-D teleseismic synthetic data, which are then back-projected using a representative BP method, MUltiple SIgnal Classification (MUSIC). We also analyse corresponding real cases to verify the synthetic test results. The Tohoku-Oki scenario shows that depth phases of a point source can be back-projected as artefacts at their bounce points on the earth's surface, with these artefacts located far away from the epicentre if earthquakes occur at large depths, which could significantly contaminate BP images of large intermediate-depth earthquakes. The Kaikoura scenario shows that for complicated earthquakes, composed of multiple subevents with varying focal mechanisms, BP tends to image subevents emanating large amplitude coherent waveforms, while missing subevents whose P nodal directions point to the arrays, leading to discrepancies either between BP images from different arrays, or between BP images and other source models. Using the Java event, we investigate the impact of 3-D source-side velocity structures. The 3-D bathymetry together with a water layer can generate strong and long-lasting coda waves, which are mirrored as artefacts far from the true source location. Finally, we use a Wharton Basin outer-rise event to show that the wavefields generated by 3-D near trench structures contain frequency-dependent coda waves, leading to frequency-dependent BP results. In summary, our analyses indicate that depth phases, focal mechanism variations and 3-D source-side structures can affect various aspects of BP results. Thus, we suggest that target-oriented synthetic tests, for example, synthetic tests for subduction earthquakes using more realistic 3-D source-side velocity structures, should be conducted to understand the uncertainties and artefacts before we interpret detailed BP images to infer earthquake rupture kinematics and dynamics

Performance Analysis of Channel Extrapolation in FDD Massive MIMO Systems

Channel estimation for the downlink of frequency division duplex (FDD) massive MIMO systems is well known to generate a large overhead as the amount of training generally scales with the number of transmit antennas in a MIMO system. In this paper, we consider the solution of extrapolating the channel frequency response from uplink pilot estimates to the downlink frequency band, which completely removes the training overhead. We first show that conventional estimators fail to achieve reasonable accuracy. We propose instead to use high-resolution channel estimation. We derive theoretical lower bounds (LB) for the mean squared error (MSE) of the extrapolated channel. Assuming that the paths are well separated, the LB is simplified in an expression that gives considerable physical insight. It is then shown that the MSE is inversely proportional to the number of receive antennas while the extrapolation performance penalty scales with the square of the ratio of the frequency offset and the training bandwidth. The channel extrapolation performance is validated through numeric simulations and experimental measurements taken in an anechoic chamber. Our main conclusion is that channel extrapolation is a viable solution for FDD massive MIMO systems if accurate system calibration is performed and favorable propagation conditions are present.Comment: arXiv admin note: substantial text overlap with arXiv:1902.0684

Indoor off-body wireless communication: static beamforming versus space-time coding

The performance of beamforming versus space-time coding using a body-worn textile antenna array is experimentally evaluated for an indoor environment, where a walking rescue worker transmits data in the 2.45 GHz ISM band, relying on a vertical textile four-antenna array integrated into his garment. The two transmission scenarios considered are static beamforming at low-elevation angles and space-time code based transmit diversity. Signals are received by a base station equipped with a horizontal array of four dipole antennas providing spatial receive diversity through maximum-ratio combining. Signal-to-noise ratios, bit error rate characteristics, and signal correlation properties are assessed for both off-body transmission scenarios. Without receiver diversity, the performance of space-time coding is generally better. In case of fourth-order receiver diversity, beamforming is superior in line-of-sight conditions. For non-line-of-sight propagation, the space-time codes perform better as soon as bit error rates are low enough for a reliable data link

Optimal Multiuser Transmit Beamforming: A Difficult Problem with a Simple Solution Structure

Transmit beamforming is a versatile technique for signal transmission from an array of $N$ antennas to one or multiple users [1]. In wireless communications, the goal is to increase the signal power at the intended user and reduce interference to non-intended users. A high signal power is achieved by transmitting the same data signal from all antennas, but with different amplitudes and phases, such that the signal components add coherently at the user. Low interference is accomplished by making the signal components add destructively at non-intended users. This corresponds mathematically to designing beamforming vectors (that describe the amplitudes and phases) to have large inner products with the vectors describing the intended channels and small inner products with non-intended user channels. While it is fairly easy to design a beamforming vector that maximizes the signal power at the intended user, it is difficult to strike a perfect balance between maximizing the signal power and minimizing the interference leakage. In fact, the optimization of multiuser transmit beamforming is generally a nondeterministic polynomial-time (NP) hard problem [2]. Nevertheless, this lecture shows that the optimal transmit beamforming has a simple structure with very intuitive properties and interpretations. This structure provides a theoretical foundation for practical low-complexity beamforming schemes. (See this lecture note for the complete abstract/introduction)Comment: Accepted for publication as lecture note in IEEE Signal Processing Magazine, 11 pages, 3 figures. The results can be reproduced using the following Matlab code: https://github.com/emilbjornson/optimal-beamformin