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Spread ALOHA offers both the favourable transmission characteristics of spread spectrum transmission and the conceptual simplicity of the ALOHA random access protocol. Moreover, receiver complexity is reduced in comparison to code division multiple access, as it is only required to demodulate transmissions using a single spreading code. In this paper we develop a MATLAB-Simulink model in order to observe the acquisition performance of a multiple user spread ALOHA system. The receiver model used is a dynamic digital matched filter (DMF) with variable effective correlation length. Both the acquisition time and detection probabilities of the dynamic DMF receiver are measured for different interference levels (numbers of users) and varying effective correlation length. The results are compared to the conventional DMF. The results indicate a significant performance improvement for longer effective correlation lengths, equal or close to the length of the pseudo-noise code (PN-code) employed in the system. This performance improvement was significant in terms of both probability of detection and mean acquisition time.