Processing OBPSK as OQPSK I'm trying to create and process an OBPSK signal, which, as I understand it, transmits even bits on one axis and the odd bits on the opposite axis, resulting in a constellation with 4 unique points. OBPSK seems to be somewhat rare, and a lot of software doesn't have functions to handle it. I created it (if I understand it correctly) by modulating the even and odd bits as BPSK separately, and rotating one of them by 90 degrees. However, with 4 constellation points, it seems similar to QPSK, or more specifically OQPSK, which is common with software having built in functions for modulation, etc. Is there some way to process OPSK, perhaps with some sort of transformation and/or change in data rate, as OQPSK?
OBPSK in the way that you describe it is also called $\pi/2$-BPSK meaning that the signal constellation is different from bit to bit, rotating by $\pi/2$ after it is used. There are two variations of this format.


Use $\pm \cos(\omega_0 t)$ to transmit one bit and 
$\mp \sin(\omega_0 t)$ to transmit the next bit. Repeat this over and over again.  Note the $\mp$ before the $\sin$ carrier.
This method rotates the constellation by $\pi/2$ counterclockwise in going from $\pm \cos(\omega_0 t)$ to $\mp \sin(\omega_0 t)$, and clockwise when going from $\mp \sin(\omega_0 t)$ to $\pm \cos(\omega_0 t)$.
Use

$\pm \cos(\omega_0 t)$ to transmit the first bit
$\mp \sin(\omega_0 t)$ to transmit the second bit
$\mp \cos(\omega_0 t)$ to transmit the third bit
$\pm \sin(\omega_0 t)$ to transmit the fourth bit,
and repeat this over and over. Note the $\mp$ and $\pm$ signs. This
corresponds to the constellation rotating by $\pi/2$ counterclockwise after each and every bit transmission.





Neither form of OBPSK signal can be demodulated very well
using a OQPSK demodulator, though it would be possible to do
so. In OQPSK,
even-numbered bits are transmitted using $\pm\cos(\omega_0t)$ and
odd-numbered bits using $\mp\sin(\omega_0 t)$ but the important
difference is that the $2n$-th bit is transmitted during the
time interval
$[2nT, (2n+2)T)$ while the $(2n+1)$-th bit is transmitted during
the time interval $[(2n+1)T, (2n+3)T)$, i.e. in overlapping but offset time intervals.
At the demodulator, the matched filters/correlators in the I branch
and Q branch thus integrate/correlate over offset time intervals,
and the demodulated data bits come out of the OQPSK demodulator alternately on the I and Q lines, one every T seconds. 
On the other hand, in
OBPSK, the $2n$-th bit is transmitted during $[2nT, (2n+1)T)$ and
the $(2n+1)$-th bit during $[(2n+1)T, (2n+2)T)$. If demodulated with
a plain vanilla OQPSK demodulator, during $[(2n+1)T, (2n+2)T)$ the matched filter/correlator input in the I branch would be just noise 
(and similarly for the Q branch).
This will decrease the effective SNR. So, Yes, a standard OQPSK
receiver could be used to demodulate an OBPSK signal, but
there are better ways of demodulating an OBPSK signal than just
processing it through an OQPSK receiver.