Convergence analysis of chip- and fractionally spaced LMS adaptive multiuser CDMA detectors

This paper analyzes the convergence behavior of the least mean square (LMS) filter when used in an adaptive code division multiple access (CDMA) detector consisting of a tapped delay line with adjustable tap weights. The sampling rate may be equal to or higher than the chip rate, and these correspond to chip-spaced (CS) and fractionally spaced (FS) detection, respectively. It is shown that CS and FS detectors with the same time-span exhibit identical convergence behavior if the baseband received signal is strictly bandlimited to half the chip rate. Even in the practical case when this condition is not met, deviations from this observation are imperceptible unless the initial tap-weight vector gives an extremely large mean squared error (MSE). This phenomenon is carefully explained with reference to the eigenvalues of the correlation matrix when the input signal is not perfectly bandlimited. The inadequacy of the eigenvalue spread of the tap-input correlation matrix as an indicator of the transient behavior and the influence of the initial tap weight vector on convergence speed are highlighted. Specifically, a initialization within the signal subspace or to the origin leads to very much faster convergence compared with initialization in the a noise subspace.

Depreciation, income distribution and the UK REIT

Purpose – The purpose of this paper is to consider prospects for UK REITs, which were introduced on 1 January 2007. It specifically focuses on the potential influence of depreciation and expenditure on income and distributions. Design/methodology/approach – First, the ways in which depreciation can affect vehicle earnings and value are discussed. This is then set in the context of the specific rules and features of REITs. An analysis using property income and expenditure data from the Investment Property Databank (IPD) then assesses what gross and net income for a UK REIT might have been like for the period 1984-2003. Findings – A UK REIT must distribute at least 90 per cent of net income from its property rental business. Expenditure therefore plays a significant part in determining what funds remain for distribution. Over 1984-2003, expenditure has absorbed 20 per cent of gross income and been a source of earnings volatility, which would have been exacerbated by gearing. Practical implications – Expenditure must take place to help UK REITs maintain and renew their real estate portfolios. In view of this, investors should moderate expectations of a high and stable income return, although it may well still be so relative to alternative investments. Originality/value – Previous literature on depreciation has not quantified amounts spent on portfolios to keep depreciation at those rates. Nor, to our knowledge, has its ideas been placed in the indirect investor context.