We present an efficient CDMA detection core suited for multiuser indoor acoustic positioning. An ultrasonic multi-code despreader is proposed, allowing simultaneous broadband acoustic ranging signals to be processed in real time by embedded sensors. The ranging performance is characterised using a dataset gathered from a real deployment of ultrasonic devices and is shown to be favourable. The proposed core can be used as a basis for more sophisticated receivers, such as those capable of detecting heavily Doppler-shifted signals.