The paper presents an orthogonal least squares (OLS) learning algorithm for radial basis function (RBF) networks, which offers a viable alternative to the two-layer neural network in signal processing applications. The traditional method of randomly selecting RBF centers is shown to have several drawbacks, including numerical ill-conditioning and poor performance. The OLS algorithm, based on subset model selection, systematically selects RBF centers to maximize the increment to the explained variance of the desired output. This approach avoids the issues of random center selection and ensures numerical stability. The algorithm is efficient and easy to implement, as demonstrated through examples in time series modeling and communications channel equalization. The OLS method is compared with random center selection, showing superior performance in both applications. The paper also discusses the trade-offs between accuracy and complexity in network design and provides a detailed explanation of the OLS learning procedure, including its geometric interpretation and implementation details.The paper presents an orthogonal least squares (OLS) learning algorithm for radial basis function (RBF) networks, which offers a viable alternative to the two-layer neural network in signal processing applications. The traditional method of randomly selecting RBF centers is shown to have several drawbacks, including numerical ill-conditioning and poor performance. The OLS algorithm, based on subset model selection, systematically selects RBF centers to maximize the increment to the explained variance of the desired output. This approach avoids the issues of random center selection and ensures numerical stability. The algorithm is efficient and easy to implement, as demonstrated through examples in time series modeling and communications channel equalization. The OLS method is compared with random center selection, showing superior performance in both applications. The paper also discusses the trade-offs between accuracy and complexity in network design and provides a detailed explanation of the OLS learning procedure, including its geometric interpretation and implementation details.