An ultra wide bandwidth, high speed, spread spectrum communications system uses short wavelets of electromagnetic energy to transmit information through objects such as walls or earth. The communication system uses baseband codes formed from time shifted and inverted wavelets to encode data on a RF signal. The combination of short duration wavelets and encoding techniques are used to spread the signal energy over an ultra wide frequency band such that the energy is not concentrated in any particular narrow band and is not detected by conventional narrow band receivers so it does not interfere with those communication systems. The use of pulse codes composed of time shifted and inverted wavelets gives the system according to the present invention a spatial resolution on the order of 1 foot which is sufficient to minimize the negative effects of multipath interference and permit time domain rake processing.