Wideband code-division multiple-access (WCDMA) enhanced uplink (EUL) channel transmissions are typically scheduled to time intervals where the interference and load conditions of a cell are favorable-hence, load estimation is central for EUL performance. This paper first proves that the uplink load, which is expressed as the rise over thermal (RoT), is unobservable with any linear estimation technique using measurements in a single radio base station (RBS) of (1) received total wideband power (RTWP) and (2) cell channel powers. A soft nonlinear Bayesian load estimator is proposed to circumvent these problems. The three-stage algorithm first estimates the RTWP, as well as residual power consisting of the sum of the thermal noise floor power and the neighbor cell interference. A time-variable Kalman estimator is used for this first step. The thermal noise power is then approximated by the Bayesian conditional probability density function (pdf) of the minimum of the estimated residual power. The 1-D conditional pdf of the RoT then follows from the quotient of two pdf's-the estimated pdf of the RTWP and the estimated conditional pdf of the thermal noise power. After discretization, the optimal RoT is calculated as a conditional mean.