Power calculation for gravitational radiation: oversimplification and the importance of time scale

A simplified formula for gravitational-radiation power is examined. It is shown to give completely erroneous answers in three situations, making it useless even for rough estimates. It is emphasized that short timescales, as well as fast speeds, make classical approximations to relativistic calculations untenable.Comment: Three pages, no figures, accepted for publication in Astronomische Nachrichte

The kinematical center and mass profile of the Local Group

Abandoning the assumption that light traces mass, I seek the location of the center of the Local Group of galaxies based solely on kinematic data and the plausible assumption of infall. The available set of positions and radial velocities is shown to be a misleading indicator of Local Group motions, giving a direction to the center offset from the true one; statistical techniques of moderate sophistication do not catch the offset. Corrected calculations show the center to lie in the direction to M31 within the uncertainty of the method, a few degrees. The distance to the center is not well determined, lying about 0.5 Mpc from the Milky Way. The pattern of observed (galactocentric) radial velocities excludes both dynamically important `orphan haloes' and any extended dark matter halo for the Group as a whole, and shows the Group to have formed from a much more extended volume than it presently occupies. Kinematics alone indicates that the mass of the Group is concentrated effectively in M31 and the Milky Way.Comment: Accepted by Ap

A New Galaxy in the Local Group: the Antlia Dwarf Galaxy

We report the discovery of new member of the Local Group in the constellation of Antlia. Optically the system appears to be a typical dwarf spheroidal galaxy of type dE3.5 with no apparent young blue stars or unusual features. A color-magnitude diagram in I, V-I shows the tip of the red giant branch, giving a distance modulus of 25.3 +/- 0.2 (1.15 Mpc +/- 0.1) and a metallicity of -1.6 +/- 0.3. Although Antlia is in a relatively isolated part of the Local Group it is only 1.2 degrees away on the sky from the Local Group dwarf NGC3109, and may be an associated system.Comment: AJ in press, 15 pages, 7 figures, figure 2 in b/w for space saving, full postscript version available at http://www.ast.cam.ac.uk/~gkth/antlia-pp.htm

Design and Analysis of Transmit Beamforming for Millimetre Wave Base Station Discovery

In this paper, we develop an analytical framework for the initial access (a.k.a. Base Station (BS) discovery) in a millimeter-wave (mm-wave) communication system and propose an effective strategy for transmitting the Reference Signals (RSs) used for BS discovery. Specifically, by formulating the problem of BS discovery at User Equipments (UEs) as hypothesis tests, we derive a detector based on the Generalised Likelihood Ratio Test (GLRT) and characterise the statistical behaviour of the detector. The theoretical results obtained allow analysis of the impact of key system parameters on the performance of BS discovery, and show that RS transmission with narrow beams may not be helpful in improving the overall BS discovery performance due to the cost of spatial scanning. Using the method of large deviations, we identify the desirable beam pattern that minimises the average miss-discovery probability of UEs within a targeted detectable region. We then propose to transmit the RS with sequential scanning, using a pre-designed codebook with narrow and/or wide beams to approximate the desirable patterns. The proposed design allows flexible choices of the codebook sizes and the associated beam widths to better approximate the desirable patterns. Numerical results demonstrate the effectiveness of the proposed method.Comment: 30 pages, 13 figures, submitte

Millimeter Wave Beam Alignment: Large Deviations Analysis and Design Insights

In millimeter wave cellular communication, fast and reliable beam alignment via beam training is crucial to harvest sufficient beamforming gain for the subsequent data transmission. In this paper, we establish fundamental limits in beam-alignment performance under both the exhaustive search and the hierarchical search that adopts multi-resolution beamforming codebooks, accounting for time-domain training overhead. Specifically, we derive lower and upper bounds on the probability of misalignment for an arbitrary level in the hierarchical search, based on a single-path channel model. Using the method of large deviations, we characterize the decay rate functions of both bounds and show that the bounds coincide as the training sequence length goes large. We go on to characterize the asymptotic misalignment probability of both the hierarchical and exhaustive search, and show that the latter asymptotically outperforms the former, subject to the same training overhead and codebook resolution. We show via numerical results that this relative performance behavior holds in the non-asymptotic regime. Moreover, the exhaustive search is shown to achieve significantly higher worst-case spectrum efficiency than the hierarchical search, when the pre-beamforming signal-to-noise ratio (SNR) is relatively low. This study hence implies that the exhaustive search is more effective for users situated further from base stations, as they tend to have low SNR.Comment: Author final manuscript, to appear in IEEE Journal on Selected Areas in Communications (JSAC), Special Issue on Millimeter Wave Communications for Future Mobile Networks, 2017 (corresponding author: Min Li