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In this article, the effect a moving target has on the signal-to-interference-plus-noise-ratio (SINR) for high time-bandwidth noise radars is investigated. To compensate for cell migration we apply a computationally efficient stretch processing algorithm that is tailored for batched processing and suitable for implementation onto a real-time radar processor. The performance of the algorithm is studied using experimental data. In the experiment, pseudorandom noise, with a bandwidth of 100 MHz, is generated and transmitted in real-time. An unmanned aerial vehicle (UAV), flown at a speed of 11 m/s, is acting as a target. For an integration time of 1 s, the algorithm is shown to yield an increase in SINR of roughly 13 dB, compared to no compensation. It is also shown that coherent integration times of 2.5 s can be achieved., Comment: Presented at 2023 20th European Radar Conference (EuRAD)