This paper proposes a chaotic waveform-based multi-antenna receiver design for simultaneous wireless information and power transfer (SWIPT). Particularly, we present a differential chaos shift keying (DCSK)-based SWIPT multiantenna receiver architecture, where each antenna switches between information transfer (IT) and energy harvesting (EH) modes depending on the receiver's requirements. We take into account a generalized frequency-selective Nakagami-m fading model as well as the nonlinearities of the EH process to derive closed-form analytical expressions for the associated bit error rate (BER) and the harvested direct current (DC), respectively. We show that, both depend on the parameters of the transmitted waveform and the number of receiver antennas being utilized in the IT and EH mode. We investigate a trade-off in terms of the BER and energy transfer by introducing a novel achievable `success rate - harvested energy' region. Moreover, we demonstrate that energy and information transfer are two conflicting tasks and hence, a single waveform cannot be simultaneously optimal for both IT and EH. Accordingly, we propose appropriate transmit waveform designs based on the application specific requirements of acceptable BER or harvested DC or both. Numerical results demonstrate the importance of chaotic waveform-based signal design and its impact on the proposed receiver architecture.