I was, "OK, this is feasible"... But then I traced how it worked and it simply blocked current through Drain and Source when a P and N pair are reverse biased; then when the other P and N pair are forward biased current flows through Forward Diodes; then alternatingly... Then it's the same, one is just using diodes to Bridge Rectify. Worse still, MOSFETs generally don't have a low diode voltage drop... Or maybe I'm missing something here....
The rectifier has no voltage drop at no current.The availability of low RDs on mosfets means that the volt drop could be very low .It can be lower than a shottky diode .The effective resistance is the sum of the N chan and the P chan .I did this in a previous life but for production I used a dual schottky instead of the 2 P chan fets.P channel was a big penalty 25 years ago so I figured that 2 n chans and 1 dual schottky was better value for money.Everything was fine for 12V 10 Amp battery charger .Nowdays the p chan could be economic depending on your application .Remember that if you do the p chan into a big electrolytic cap you will have to do something about high reverse currents .Maybe a Fiode connection or some reverse current sense that shuts the gates down .
There have been a couple of comments and answers here about the failure of the MOSFET bridge rectifier: That it conducts in both directions, so if you have a capacitor-filtered power supply the capacitors will simply drain on the AC downslope, back to the source.
There are a couple of commercial solutions to this problem: at least two that I know of, the LT4320 and LM74670-Q1.
I tested this rectifier in LTSpice. Using only a resistive load it worked perfectly, generating a full-wave rectified current over the load resistor, with a very small voltage drop in the transistors (depending on on-resistance, not on the body diode forward voltage).
Then I added a capacitor to make it a continous DC current. In that case the rectifier faled totally. When there was a voltage over the capacitor, the MOSFET's was conducting in the wrong direction, making the current flow back to the AC source again.
If you replace the two P-MOS transistors with two diodes, it works, because the diodes will block any reverse current. That's why Autistic's solution worked (described in the last post).