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In this paper, we consider the rate-distortion optimized resource allocation for video transmission over multi-rate wireless direct-sequence code-division-multiple-access (DS-CDMA) channels. We consider the performance of transmitting scalable video over a multipath Rayleigh fading channel via a combination of multi-code multirate CDMA and variable sequence length multirate CDMA channel system. At the receiver, despreading is done using adaptive space-time auxiliary-vector (AV) filters. We propose a new interference cancelling design that uses just a single AV filter for single-user mutirate despreading. Our experimental results show that the proposed interference cancelling design has excellent performance in scalable video transmission over DS-CDMA systems that use a combination of multicode multirate and variable processing gain multirate CDMA. The proposed design takes advantage of the fact that single user's video data is transmitted using two spreading codes, one for the base layer and one for the enhancement layers, and of the fact that these spreading codes can have different processing gains. The proposed interference cancelling design is compared with two conventional single-user multirate CDMA receiver configurations, however now we use an AV filter rather than a simple matched filter. We also propose a resource allocation algorithm for the optimal determination of source coding rate, channel coding rate and processing gain for each scalable layer, in order to minimize the expected distortion at the receiver.