Signal bandwidth of an 802.15.4 signal at 2.4 GHz
I found this link that details the spectrum for 802.15.4: https://www.semanticscholar.org/paper/IEEE-802.15.4-PHY-analysis%3A-Power-spectrum-and-Gupta-Wilson/2892da39a7ecec1945595d46950438a5bb8777af

And pasted the plot below.



This is consistent with what I would expect for a half-sine pulse-shaped pulse for a symbol rate of 1 MHz (and that would apply to BPSK, QPSK, OQPSK etc where the power spectrum for a random data sequence is the Fourier Tranform squared of the base pulse that is transmitted.).  In Offset-QPSK the I and Q channels can be viewed as two independent (in data content) BPSK transmissions, in quadrature, offset in time by half a symbol. Thus each produces an independent but identical power spectrum that adds in power. 

Below I compare the Fourier Transforms for a rectangular pulse of 1 us duration vs the half-sine windowed pulse of the same duration. I normalized the power of the two to be the same. Although the pulse shape increases the width of the main lobe, there is a clear spectral improvement by doing the half-sine pulse shape as demonstrated in this plot (Notably, the power spectrum of the rectangular pulse rolls of at a rate of $1/f^2$, or -20dB/decade, while the power spectrum of the half-sine pulse rolls of at a rate of $1/f^4$ in spectrum). 

Fourier Transform of rectangular pulse (Red) vs half-sine pulse (Blue):


This clearly is not as good as that which can be achieved with more spectral efficient pulse shaping such as raised-cosine shapes but offers the significant advantage to low power systems of being a constant envelope modulation when used in an O-QPSK modulation. In this case we are able to drive the power amplifier (PA, which typically dominates power dissipation in the transceiver) into saturation without introducing AM/PM distortion. In saturation the PA can operate at a much higher efficiency (Tx power radiated at a given DC power in).