Optimization of Training and Feedback Overhead for Beamforming over Block Fading Channels

We examine the capacity of beamforming over a single-user, multi-antenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multi-input single-output (MISO) and multi-input multi-output (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains $L$ symbols, and is spanned by $T$ training symbols, $B$ feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing $2^B$ {\em i.i.d.} random vectors, and sends the corresponding $B$ bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (rate-maximizing) training and feedback overhead ($T$ and $B$) as $L$ and the number of transmit antennas $N_t$ both become large. The optimal $N_t$ is limited by the coherence time, and increases as $L/\log L$. For the MISO channel the optimal $T/L$ and $B/L$ (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate $1/\log N_t$. For the MIMO channel the optimal feedback overhead $B/L$ tends to zero faster (as $1/\log^2 N_t$).Comment: accepted for IEEE Trans. Info. Theory, 201

Endogenous Pensions and Retirement Behavior

This paper suggests that pension characteristics are simultaneously determined along with workers’ retirement ages. Both the age of pension eligibility and actual retirement age are determined by the productivity and marginal disutility of work, factors that are influenced by worker and job characteristics. This approach differs from previous studies of retirement that treat pensions as exogenous, implying that prior empirical work may have overestimated the responsiveness of retirement age to changes in pension structure, a possibility with obvious policy implications for efforts to raise the age of retirement. We find that, in the conventional single-equation framework, delaying the age of pension eligibility would significantly delay retirement. When treated in a recursive simultaneous system, however, age of pension eligibility retains no explanatory power.social security, early retirement, job characteristics, pension eligibility

Participation and Contributions in Tax-deferred Retirement Accounts: Evidence from Social Security Records

Social Security Administration W-2 records contain employee annual tax-deferred contributions for 1990-2003 and sufficient information to calculate tax-deferred contributions for 1984-1989. We use this information to compare tax-deferred contribution profiles of three cohorts of respondents in the Health and Retirement Study to determine whether younger cohorts saved relatively more at the same stage of the life cycle than had older cohorts. We find that participation in tax-deferred retirement plans increased substantially for all cohorts from 1984 to 2003, and that respondents in more recent cohorts were more likely to participate in such plans than respondents of the same ages in the earliest cohort. Their contributions as a percent of earnings were not significantly larger than those of the earliest cohort, however. Despite the increased availability of these employer-provided plans throughout this period, participation rates and contribution amounts remained low among respondents in the lower half of the earnings distribution.

Political Monetary Cycles and a New de facto Ranking of Central Bank Independence

This paper examines the extent to which monetary policy is manipulated for political purposes by testing for the presence of political monetary cycles between 1972 and 2001. This is the first study of its kind to include not only advanced countries but also a large sample of developing nations where these cycles are more likely to exist. We estimate panel regressions of a monetary policy indicator on an election dummy and control variables. We do not find evidence of political monetary cycles in advanced countries but find strong evidence in developing nations. Based on our results, we construct a new de facto ranking of central bank independence derived from the extent to which monetary policy varies with the election cycle. Our ranking of CBI is therefore based on the behavior of central banks during election cycles when their independence is likely to be challenged or their lack of independence is likely to be revealed. The ranking also avoids well-known problems with existing measures of central bank independence.Political monetary cycles; central bank independence

Sharing of Unlicensed Spectrum by Strategic Operators

Facing the challenge of meeting ever-increasing demand for wireless data, the industry is striving to exploit large swaths of spectrum which anyone can use for free without having to obtain a license. Major standards bodies are currently considering a proposal to retool and deploy Long Term Evolution (LTE) technologies in unlicensed bands below 6 GHz. This paper studies the fundamental questions of whether and how the unlicensed spectrum can be shared by intrinsically strategic operators without suffering from the tragedy of the commons. A class of general utility functions is considered. The spectrum sharing problem is formulated as a repeated game over a sequence of time slots. It is first shown that a simple static sharing scheme allows a given set of operators to reach a subgame perfect Nash equilibrium for mutually beneficial sharing. The question of how many operators will choose to enter the market is also addressed by studying an entry game. A sharing scheme which allows dynamic spectrum borrowing and lending between operators is then proposed to address time-varying traffic and proved to achieve perfect Bayesian equilibrium. Numerical results show that the proposed dynamic sharing scheme outperforms static sharing, which in turn achieves much higher revenue than uncoordinated full-spectrum sharing. Implications of the results to the standardization and deployment of LTE in unlicensed bands (LTE-U) are also discussed.Comment: To appear in the IEEE Journal on Selected Areas in Communications, Special Issue on Game Theory for Network