Acquisition times of carrier tracking sampled data phase-locked loops

Phase acquisition times of type II and III loops typical of the Advanced Receiver are studied by computer simulations when the loops are disturbed by gaussian noise. Reliable estimates are obtained by running 5000 trials for each combination of loop signal-to-noise ratio (SNR) and frequency offset. The probabilities of acquisition are shown versus time from start of acquisition for various loop SNRs and frequency offsets. For frequency offsets smaller than one-fourth of the loop bandwidth and for loop SNRs of 10 dB and higher, the loops acquire with probability 0.99 within 2.5 B sub L for type II loops and within 7/B sub L for type III loops

An automatic frequency control loop using overlapping DFTs (Discrete Fourier Transforms)

An automatic frequency control (AFC) loop is introduced and analyzed in detail. The new scheme is a generalization of the well known Cross Product AFC loop that uses running overlapping discrete Fourier transforms (DFTs) to create a discriminator curve. Linear analysis is included and supported with computer simulations. The algorithm is tested in a low carrier to noise ratio (CNR) dynamic environment, and the probability of loss of lock is estimated via computer simulations. The algorithm discussed is a suboptimum tracking scheme with a larger frequency error variance compared to an optimum strategy, but offers simplicity of implementation and a very low operating threshold CNR. This technique can be applied during the carrier acquisition and re-acquisition process in the Advanced Receiver

A Boomtown at Risk: Austin's Mounting Public Pension Debt

The increase in Austin's pension debt over the last decade is due in part to the fact that as the population grew, demand for public services increased and the city added more than 1,000 public employees between 2010 and 2015. As the cost of providing benefits rose, the city failed to keep up with contributions to the system—skipping nearly $170 million in payments to the Employees' Retirement Plan, which is the city's largest retirement plan, over eight years. At the same time, it suffered a series of investment shortfalls system wide, which compounded the effect of the missed contributions and led to a widening gap between assets and liabilities.Despite the fact that the city is paying more and more into the plans each year, unfunded liabilities are continuing to rise. In fact, Austin spends more than half of its pension payments on debt—rather than benefits for public workers. Yet even these payments might not be sufficient to pay off the unfunded liabilities, and if the city earns less than expected on its investments, debt will rapidly rise.The brief explains that the city must take immediate steps to pay down the unfunded liabilities in order to improve the stability of its pension plans. Local leaders in Austin should take note of the pension crisis that is unfolding in Dallas. Two years ago, Dallas' pension system was in a similar position to the one that Austin is currently in. However, Dallas' pension debt doubled to$4 billion and its funded ratio plummeted to 56 percent after the plan administrators made a series of reckless decisions that have pushed the city's largest plan, the police and fire fund, to the brink of bankruptcy.The situation in Dallas should provide a cautionary example of how quickly debt can spiral out of control. In the brief, McGee and Diaz Aguirre call on Austin's leaders to make the changes necessary to ensure that the city is able to uphold its retirement promises to public workers. The authors present a number of recommendations that would help stabilize the system and address the plan's underlying structural flaws, including:Making adequate funding non-negotiable and committing to pay down current unfunded liabilities in 30 years or less.Establishing prudent and realistic funding and investment policies.Establishing local control of the pension fund in order to improve oversight and accountability.Consider enrolling new workers in plans that are simpler and easier to manage, like Defined Contribution or Cash Balance plans

The Dallas Public Pension Crisis: A Warning for Cities Across Texas

In the brief, LJAF Vice President Josh McGee and LJAF Sustainable Public Finance Analyst Paulina S. Diaz Aguirre explain that unless local leaders take immediate steps to pay down the pension debt and address the plans' underlying systemic flaws, the challenges will continue to escalate."Dallas is at a tipping point," McGee said. "Without immediate reforms, the city's pension problems will become too big to fix. Workers deserve a fair and secure retirement. Local leaders must work with public servants and taxpayers to develop a sustainable solution. This is true not only in Dallas, where the problems are particularly acute, but in cities across the state. Officials must take action now to ensure that their communities remain vibrant and financially stable."The most immediate pension problem facing the city of Dallas involves its Police and Fire Pension System. The fund's Deferred Retirement Option Program (DROP), a savings account provided to members when they reach retirement eligibility, is nearly bankrupt. In the past six months alone, retirees have withdrawn at least $300 million in savings. If this "run on the bank" continues, the police and fire fund may run out of cash to pay retirees' benefits.The issues with the Dallas pension system stem from a decade of insufficient funding for both the police and fire fund as well as the plan for other municipal employees. With the police and fire fund, the problems have been compounded by two key factors. First, a broken governance structure allowed members to increase their own benefits without establishing a plan to pay for those increases. Second, a series of reckless investment decisions made by the plan's prior leadership went unnoticed. Former plan administrators invested more than half of the fund's assets in private equity and real estate, including high-risk properties such as luxury homes in Hawaii and a resort and vineyard in Napa, California. The city made less than expected on these investments, which led to a nearly$1 billion investment shortfall, hundreds of millions of dollars in asset devaluations, and a reported Federal Bureau of Investigation (FBI) review.In addition, the police and fire fund is controlled by the state legislature, which means that local leaders do not have the authority they need to make the changes that are urgently required.In the brief, McGee and Diaz Aguirre explain that plan administrators, city officials, and state legislators must immediately come together to enact comprehensive reforms. The co-authors present a number of recommendations that would help protect workers' retirement security and improve the stability of the pension system.These include:Obtaining local control of the police and fire fundStabilizing DROPDeveloping a fair and sustainable plan to pay down the pension deb

A Pivotal Moment: Assessing Houston's Plan for Pension Reform

The Laura and John Arnold Foundation (LJAF) released "A Pivotal Moment: Assessing Houston's Plan for Pension Reform," a report that provides an in-depth analysis of the City of Houston's pension reform proposal currently pending in the Texas Legislature. The report finds that the proposal includes important changes that would help protect workers and taxpayers. The reform plan was developed following discussions between Mayor Sylvester Turner and the Houston Police Officers' Pension System, the Houston Municipal Employees Pension System, and the Houston Firefighters' Relief and Retirement Fund.LJAF Vice President Josh McGee and LJAF Sustainable Public Finance Analyst Paulina S. Diaz Aguirre co-authored the report after analyzing the city's proposal and conducting independent pension modeling. They say that it is incumbent on local leaders and state legislators to work together. "There are just a few weeks left in the 2017 session—and without the ability to make changes to the pension systems on its own—the city is running out of time," the report states. "Without changes, the debt could spiral into a full-scale financial crisis. The city cannot allow that to happen. Its financial future hangs in the balance and will be decided in large part in the next month."Houston currently owes $8.2 billion in pension debt—more than any other city in Texas. It does not have enough money to pay for nearly half of the retirement benefits workers have already earned. This unfunded liability threatens workers' retirement security and has a direct impact on city finances. During the past 10 years, the city has cut public safety positions even as spending on public safety has grown by hundreds of millions of dollars due to a 55 percent increase in pension costs.The proposal seeks to address critical flaws in the city's funding practices. Under the proposal, the city would lower its assumed rate of return on investments for all plans from 8 percent or more to 7 percent; reduce benefits for public workers; and implement a financial corridor provision that would cap the city's contributions to the pension plans.The financial corridor provision is a key element of the proposal. The provision would set a minimum and maximum city contribution rate for each plan. If the city were to hit or surpass the maximum, workers would be required to make additional benefit concessions to bring costs back under the cap. LJAF's analysis shows that this mechanism would provide substantial new protections for taxpayers but would also significantly increase workers' exposure to risk.The report states that the proposal's long-term impact on workers would depend on demographic trends and the plans' investment performance, two factors that would influence how often the city would hit the cap. For example, LJAF's modeling shows that there is a two in five (40 percent) chance that the city's contribution rate would hit the maximum for the police fund at least once by 2027. If the police plan were to earn less than 7 percent on its investments in the short or long term, contribution rates would hit the cap even sooner.If investment returns match the city's assumptions, there is roughly a one in three (33 percent) chance that contribution rates for members of the police plan would increase by five percentage points or more in the next decade. Given that members of the police plan—as well as members of the other plans—have already agreed to billions of dollars in concessions, McGee and Diaz Aguirre explain that the city has an obligation to uphold its end of the bargain. They state that the city should make payments on time and in full and should take steps—such as limiting investments in risky assets including real estate, private equity, and hedge funds—to protect workers.In addition, if the proposal is implemented, the report states that the city should also make good on its promise to provide a lump-sum payment to the two plans with the largest deficits—the police and municipal employees plans. The city has proposed issuing$1 billion in pension obligation bonds to cover the payments. To benefit financially, Houston would need to earn more in the market than it costs to borrow the money. Given the current market conditions, the spread between expected bond interest rates and expected returns is relatively small. Despite the fact that the bonds pose some risk, the report argues that they are a good-faith measure that reflects the city's commitment to upholding funding promises.The report concludes that, "In the short term, the proposal would place the pension plans—and the city—on firmer financial footing. The long-term impact would depend on how the changes are implemented." It also states that Houston should make further changes to establish a comprehensive, permanent solution to its pension problems. This would include creating retirement systems for new workers that are simpler and easier to manage such as a Defined Contribution plan or a Cash Balance plan

On the Superradiance of Spin-1 Waves in an Equatorial Wedge around a Kerr Hole

Recently Van Putten has suggested that superradiance of magnetosonic waves in a toroidal magnetosphere around a Kerr black hole may play a role in the central engine of gamma-ray bursts. In this context, he computed (in the WKB approximation) the superradiant amplification of scalar waves confined to a thin equatorial wedge around a Kerr hole and found that the superradiance is higher than for radiation incident over all angles. This paper presents calculations of both spin-0 (scalar) superradiance (integrating the radial equation rather than using the WKB method) and and spin-1 (electromagnetic/magnetosonic) superradiance, in Van Putten's wedge geometry. In contrast to the scalar case, spin-1 superradiance decreases in the wedge geometry, decreasing the likelihood of its astrophysical importance.Comment: Submitted to The Astrophysical Journal Letter

On the asymptotic acoustic-mode phase in red-giant stars and its dependence on evolutionary state

Asteroseismic investigations based on the wealth of data now available,in particular from the CoRoT and Kepler missions, require a good understanding of the relation between the observed quantities and the properties of the underlying stellar structure. Kallinger et al. 2012 found a relation between their determination of the asymptotic phase of radial oscillations in evolved stars and the evolutionary state, separating ascending-branch red giants from helium-burning stars in the `red clump'. Here we provide a detailed analysis of this relation, which is found to derive from differences between these two classes of stars in the thermodynamic state of the convective envelope. There is potential for distinguishing red giants and clump stars based on the phase determined from observations that are too short to allow distinction based on determination of the period spacing for mixed modes. The analysis of the phase may also point to a better understanding of the potential for using the helium-ionization-induced acoustic glitch to determine the helium abundance in the envelopes of these stars.Comment: MNRAS, in the pres

Tests of the asymptotic large frequency separation of acoustic oscillations in solar-type and red giant stars

Asteroseismology, i.e. the study of the internal structures of stars via their global oscillations, is a valuable tool to obtain stellar parameters such as mass, radius, surface gravity and mean density. These parameters can be obtained using certain scaling relations which are based on an asymptotic approximation. Usually the observed oscillation parameters are assumed to follow these scaling relations. Recently, it has been questioned whether this is a valid approach, i.e., whether the order of the observed oscillation modes are high enough to be approximated with an asymptotic theory. In this work we use stellar models to investigate whether the differences between observable oscillation parameters and their asymptotic estimates are indeed significant. We compute the asymptotic values directly from the stellar models and derive the observable values from adiabatic pulsation calculations of the same models. We find that the extent to which the atmosphere is included in the models is a key parameter. Considering a larger extension of the atmosphere beyond the photosphere reduces the difference between the asymptotic and observable values of the large frequency separation. Therefore, we conclude that the currently suggested discrepancies in the scaling relations might have been overestimated. Hence, based on the results presented here we believe that the suggestions of Mosser et al. (2013) should not be followed without careful consideration.Comment: 6 pages, 4 figures, 1 table, accepted for publication by MNRAS as a Letter to the Edito