Most existing techniques for indoor radio propagation measurement do not resolve the angles from which signal components arrive at the receiving antenna. Knowledge of the angle-of-arrival is required for evaluation of evolving systems that employ smart antenna technology to provide features such as geolocation, interference cancellation, and space-division multiplexing. This paper presents a novel technique for the joint measurement of the angles, times and complex amplitudes of discrete path arrivals in an indoor propagation environment. A data acquisition system, based upon a vector network analyzer and multichannel antenna array is described, together with its use to collect channel measurement matrices. The inherent error sources present in these measurement matrices are investigated using a compact indoor anechoic range. Two signal processing algorithms are presented whereby the channel parameters may be estimated from raw measurements. In the first approach, an optimum beamformer is derived which compensates for systematic errors in the data acquisition system. This approach features very low computational complexity, and delivers modest resolution of path components. The second algorithm is based upon the maximum likelihood criterion, using the measured calibration matrices as space-time basis functions. This algorithm provides super-resolution of all path parameters, at the cost of increased computation. Several example measurements are given, and future directions of our research are indicated.