Wavecom modem command/data multiplexing?

Question

Do it yourself

I have a Wavecom q24pl003 modem trying to get it to work in data/command multiplexing mode.
When running in normal mode, everything works fine.
I found the command + WMUX in the manual. After using it, AT commands are still received well, even after receiving a CONNECT message, i.e. switching to data transfer mode. But there seems to be some problem with receiving data by the modem.
I start the ppp daemon with the following parameters:
/usr/sbin/pppd /dev/ttyS0 115200 name mts nodefaultroute ipparam 8.8.8.8/32 call gprs debug dump
pppd options in effect:
debug debug # (from command line)
nodetach # (from /etc /ppp/gprs-options)
dump # (from command line)
name mts # (from command line)
/dev/pts/3 # (from command line)
115200 # (from command line)
lock # (from /etc/ppp/gprs-options)
crtscts # (from /etc/ppp/gprs-options)
escape ff # (from /etc/ppp/peers/gprs)
asyncmap 20a0000 # (from /etc/ppp/peers/gprs)
mtu 1400 # (from /etc/ppp/gprs-options)
ipcp-accept-local # (from /etc/ppp/ gprs-options)
ipcp-accept-remote # (from /etc/ppp/gprs-options)
ipparam 8.8.8.8/32 # (from command line)
noipdefault # (from /etc/ppp/gprs-options)
ipcp-max- terminate 10 # (from /etc/ppp/gprs-options)
ipcp-max-configure 30 # (from /etc/ppp/gprs-options)
ipcp-max-failure 20 # (from /etc/ppp/gprs-options)
nodefaultroute # (from command line)
nobsdcomp # (from /etc/ppp/gprs-options)
nodeflate # (from /etc/ppp/gprs-options)
using channel 2
Using interface ppp0
Connect: ppp0 <--> /dev/pts/3
sent [LCP ConfReq id =0x1 <asyncmap 0x20a0000> <magic 0xd4e421ec> ]
rcvd [LCP ConfReq id=0x1 <mru 1500> <asyncmap 0x0> ]
sent [LCP ConfAck id=0x1 <mru 1500> <asyncmap 0x0> ]
sent [LCP ConfReq id=0x1 <asyncmap 0x20a0000> <magic 0xd4e421ec> ]
rcvd [LCP ConfReq id=0x1 <mru 1500> <asyncmap 0x0> ]
sent [LCP ConfAck id=0x1 <mru 1500> <asyncmap 0x0> ]
sent [LCP ConfReq id=0x1 <asyncmap 0x20a0000> <magic 0xd4e421ec> ]
…
LCP:timeout sending Config-Requests
Connection is not established accordingly.
I will be grateful for any help.
PS
If it helps, here is a hexdump of one of the ppp requests to the modem:
7e 7d df 7d 23 c0 21 7d 21 7d 21 7d 20 7d 34 7d
22 7d 26 7d 22 7d 2a 7d 20 7d 20 7d 25 7d 26 3b
e8 bf 46 7d 27 7d 22 7d 28 7d 22 7d 38 79 7e
And here is one of the messages from the modem:
dd 32 00 7e ff 7d 23 c0 21 7d 21 7d 21 7d 20 7d
36 7d 21 7d 24 7d 25 dc 7d 22 7d 20 7 20
7d 20 7d 20 7d 27 7d 22 7d 28 7d 22 7d 23 7d 24
c0 23 26 b4 7e 0f
The first byte is a wrapper indicating that a data packet is being transmitted.
The second is the length of the data.
The third is the type of parcel.
Then comes the data itself.
The last byte is the checksum.