In this paper, we present the baseband receiver design for the two mandatory physical-layer modes, i.e. the O-QPSK and BPSK modes, for ZigBee or IEEE802.15.4 operating in 2.4GHz and 868/915 MHz respectively. We propose new key receiver algorithms, including coarse frequency offset estimation, timing synchronization, fine frequency offset estimation and phase tracking. We also propose double-correlation based coarse frequency offset estimation without fine frequency offset in applications where hardware complexity or cost is of g reat concerns. Extensive simulations have been conducted to demonstrate the superior performance as opposed to those in literature.