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The paper arises from authors' will to overcome some of the limits that currently available instruments exhibit in performance testing of digital wireless communication systems and apparatus. Repeatability problems, usually accompanied by low accuracy, are, in fact, often experienced in power measurements, especially in those involving spread spectrum signals and requiring an integration process over a specified frequency range. Due to this concern, a new method for power measurements in digital wireless communication systems is presented. The method applies original and straightforward digital signal-processing algorithms to the input signal power spectrum, preliminarily provided by optimized versions of well-known estimators, such as those based on weighted overlapped segment averaging (WOSA) and multitaper approaches. The results of many experiments, conducted on spread spectrum signals typical of third generation telecommunication systems, confirm the efficacy of the proposed method in assuring reliable and accurate results in various types of power measurement.