Level crossing rates for MIMO channel Eigenvalues: implications for adaptive systems

Abstract

Abstract-MIMO systems using adaptive transmission down the eigenchannels require the level crossing rate of the eigenvalues to compute adaptation rates and possibly feedback rates. Examples of such systems include MIMO systems using singular value decomposition (SVD) transmission. Similarly, the average fade durations of the eigenvalues give the average length of time that a particular constellation is used in adaptive modulation. Other systems which require the minimum eigenvalue to be above a certain threshold (for example, channel inversion) can also use these level crossing rates in system analysis. Hence, in this paper we derive approximate level crossing rates for the eigenvalues in the baseline case of an uncorrelated Rayleigh fading channel. Our results are remarkably accurate and compact and further improvements are also discussed.

On the Probability of Adaptation Error in MIMO Systems

“…Thus, following [14], we can substitute for λ i (t) and λ i (t + τ ) in (2) and evaluate E[C(t)C(t + τ )] for small values of τ . Finding the coefficient of τ 2 in the resulting expression gives, after a little algebra,R…”

Level Crossing Rates of MIMO-MRC Ricean Channels and Their Implications on Adaptive Systems

“…General discussion about the scalar and vector crossing problems in MIMO systems is given in [7]. Approximate expressions for the level crossing rate of a MIMO channel eigenvalues, accurate for lower-order systems, are given in [8].…”

Signal power variation with applications to cognitive radio

“…The subscript, m, denotes mobility. For small time lags, τ ≈ 0, we further assume that ρ m (τ ) = 1 − aτ 2 + o(τ 2 ) as in [13] and [15]. By standard usage, f (τ ) = o(τ 2 ) is used to indicate that…”

“…the level crossing rate (LCR) of signal strength across a given threshold is particularly useful in CR analysis. LCR analysis for Rayleigh fading [10], [11] is very well known and more recently, exact [12] and approximate [13] results have appeared for the LCRs of multiple-input multiple-output (MIMO) eigenvalues. For shadow fading, an excellent LCR analysis is given in [14].…”