This paper deals with the design and simulation of narrowband indoor propagation channels under line-of-sight (LOS) and non-LOS (NLOS) propagation conditions. We propose a reference channel model assuming that the scatterers are uniformly distributed in the two-dimensional (2D) horizontal space of a room. We derive analytical expressions for the probability density function (PDF) of the angle-of-arrival (AOA), the Doppler power spectral density (PSD), and the temporal autocorrelation function (ACF). We derive a sum-of-cisoids (SOC) channel simulator from the reference model. It is shown by numerical results that the statistical properties of the SOC channel simulator match very closely with the ones of the reference model. It turns out that our indoor reference model can be approximated by an SOC channel simulator with reduced realization expenditure. The resulting SOC channel simulator allows us to evaluate the performance of mobile communication systems in indoor environments by simulations. It is demonstrated that the generalized method of equal areas (GMEA) and the basic Riemann sum method (BRSM) are efficient parameter computation methods for the design of SOC indoor channel simulators.