Well, the different methods to use a second mixing matrix to enhance front/back separation by reducing the left/right channel separation aren't really a good solution.
To achieve an acceptable channel separation the decoder needs to apply algorithms like "Shadow Vector", "VarioMatrix" or "Tate DES". In today's implementations successors of those variable gain matrices are part of Dolby Pro Logic which works quite good.
I was up all night - absolutely no sleep, with stomach flu, so if this post makes no sense, I apologize.
Sadly, the reduced Left/Right separation in both non-decoded stereo AND decoded (non-logic) Sansui QS playback is why the action of the Vario-Matrix is so audible to many listeners (and why Dolby dropped it from the experimental prototype theatrical Dolby Stereo units) unless expensive split-band techniques or vastly reduced levels of inter-channel separation are acceptable. Humans are 20 times more sensitive to left/right amplitude (level) variations than to front/back variations or to phase changes: SQ reduced separation, and thus placed all logic action,
only along the front/back axis. For the left/right axis, in both the front
and back channels, and even with a non-logic decoder (and
no 10/40 or 10/20 blend), full separation is achieved at all times - and with 10% blend, it's reduced from 'infinity' (effectively the LP stylus or digital/tape source inherent levels) to 'only' 20db of separation, which is plenty for full stereo/quad localization, even when located directly next to the adjacent 'crosstalk bearing' speaker/channel. Thus, for
any 'amount' of Logic action, SQ - by its virtue of its logic action being kept along the front/back axis - will always be less audible than any 'regular' matrix, due to its encoding/decoding specifications.
Shure Bros came across this in the initial design of their Stereosurround encoding process and the, to-this-day-unequaled, Acra-Vector Logic decoding for Dolby Stereo/Surround films and music; the side-to-side logic action required to create a highly separated Center Front (from L/R Front) is always much more audible than even very heavy amounts of Logic required to keep L/R front fully separated from the mono surround since it's on the front to back axis. It's another reason some gain-riding of the surround channel (separate from Constant Power operation) is permissible, in addition to the selective cancellation via matrix multiplier circuits; a more 'discrete' effect can be achieved for hard-panned, surround only signals, by allowing a modest amount of gain riding power transfer. That can't really be allowed for side-to-side logic because it would be so very audible. It's also the major reason that Sansui never created a gain-riding logic decoder for QS (like CBS and everyone else did for SQ) before jumping directly to a decoder that adaptively changes its output decoding structure as a condition of the input signal. Vario-Matrix is probably the best named technology ever created! It's just too bad that Sansui never took it to the next step and added front-to-back Vario-Matrix enhancement for the corner signals of the SQ matrix - they only ever kept it to Front-Back Vario-Matrix for SQ - since the basic SQ matrix provided full side-to-side separation, the Vario-Matrix for SQ, as Sansui did it, was even simpler - and with less accurate decoding - than their Type-B VM circuit for QS. Of course, no one bothered to create Shadow Vector, Scheiber 360, Tate DES, or Paramatrix, with any advanced decoding mode for QS.
As a side-note, does anyone know if anyone other than Sansui ever implemented QS Vario-Matrix decoding using Sansui's VM IC's? In one AES paper from Sansui, they claim Marantz had engineered their own fully Type-A multi-band Vario-Matrix circuit into a receiver using the Sansui's Hitachi-manufactured QS Vario-Matrix IC's - and that its (the Marantz VM) attack/decay times are substantially different from Sansui's own designs (which was easily done since it was all done off-chip). Except for the SQ "adapters" for the "Quadradial" receivers, I don't know of any other advanced decoding in Marantz gear. Anyone know anything about it?