A method for improving performance of an uplink non-orthogonal multiple access system under imperfect received user power control. The method is based on a plurality of user-specific transmitter filters assigned to a plurality of users. At a transmitter of each user, a signal to be transmitted according to the uplink non-orthogonal multiple access (NOMA) method is filtered by a unique filter assigned to a corresponding user, and then a baseband-to-RF processing is performed onto a symbol sequence to generate a transmitted signal. Each user transmits their respective signal using a same time-frequency resource, and receiver receives a superimposed signal which is transmitted through a plurality of respective uplink channels under imperfect received power control. An RF-to-baseband conversion is applied onto a received superimposed signal. Then, a receiver signal detection module; including an interference-cancellation multi-user detector detects each user data using knowledge of a plurality of transmitter filters of each user.