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- Lester Mackey, Michael I. Jordan, Richard Y Chen, Brendan Farrell, Joel A Tropp
- 2013

This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein's method of exchange-able pairs. When applied to a sum of independent random matrices, this approach… (More)

High peak values of transmission signals in wireless communication systems lead to wasteful energy consumption and out-of-band radiation. However, reducing peak values generally comes at the cost some other resource. We provide a theoretical contribution towards understanding the relationship between peak value reduction and the resulting cost in… (More)

We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order √ log n, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order log log n. This is a noteworthy difference to… (More)

We address the peak-to-average power ratio (PAPR) of transmission signals in OFDM and consider the performance of tone reservation for reduction of the PAPR. Tone reservation is unique among methods for reducing PAPR, because it does not affect information bearing coefficients and involves no additional coordination of transmitter and receiver. It is shown… (More)

- Michael B. McCoy, Richard Chen, Simon Chien, Brendan Farrell, Tomek Tyranowski, Andrea Reinhardt +1 other
- 2013

We consider linear time-varying channels with additive white Gaussian noise. For a large class of such channels we derive rigorous estimates of the eigenvalues of the correlation matrix of the effective channel in terms of the sampled time-varying transfer function and, thus, provide a theoretical justification for a relationship that has been frequently… (More)

—We consider the performance of tone reservation for reduction of the Peak-to-Average Power Ratio (PAPR) in OFDM signals. Tone reservation is unique among methods for reducing PAPR because it does not affect information bearing coefficients and involves no additional coordination of transmitter and receiver. It is shown that if the OFDM system always… (More)

—We present several results that show, according to several criteria, that the large peaks that occur in OFDM are common to all orthonormal systems that are uniformly bounded. In particular, worst case peak-to-average values are always at least the square-root of the number of signals, and the expected peak value of a signal always increases logarithmically… (More)

Previous results on certain sampling series have left open if divergence only occurs for certain subsequences or, in fact, in the limit. Here we prove that divergence occurs in the limit. We consider three canonical reconstruction methods for functions in the Paley-Wiener space PW 1 π. For each of these we prove an instance when the reconstruction diverges… (More)