The paper discusses the operation of wireless sensor networks consisting of nodes based on the IEEE 802.15.4 ZigBee transceiver operating in the presence of Rayleigh or Nakagami-m fading, additive white Gaussian noise (AWGN) and interference. Analytical expressions for bit error rate (BER) for the IEEE 802.15.4 network were obtained when Rayleigh and Nakagami-m fading were processed with a selection-combining (SC) and maximum-ratio-combining (MRC) combiner and when AWGN and interference were present. Analytical results are presented graphically in the form of BER change, depending on the signal-to-noise ratio (SNR) for different values of network parameters: fading parameter (m), number of branches of MRC combiner (L), modulation parameter (M), and spreading sequence lengths (Lc). Graphical results are presented for the system when there are no combiners and when the SC and MRC combiners are included. Numerical results were confirmed by Monte Carlo simulation. Analysis of the SC and MRC combiner application impact on the performance improvement of the IEEE 802.15.4 network and the received signal was performed.