The double angle theorems of Davis and Kahan bound the change in an invariant subspace when a Hermitian matrix A is subject to an additive perturbation A → Ã = A+1A. This paper supplies analogous results when A is subject to a congruential, or multiplicative, perturbation A → Ã = D∗AD. The relative gaps that appear in the bounds involve the spectrum of only one matrix, either A or Ã, in contras...

Higher the data rates and spectrum efficiency of wireless mobile communications have been significantly improved over the last decade, such as 3GPP Long-Term Evolution (LTE) and terrestrial digital TV broadcasting which are sophisticatedly developed using OFDM. Orthogonal frequency division multiplexing (OFDM) is a modulation technique that achieves high data rates, increased bandwidth efficien...