[Sony Ericsson XPERIA X10 Mini] plouic:
OK, thank you for the explanation ! lsmod returns two lines when wifi is turned on, so this looks good.

Here is the logcat when I enable wifi :

D/WifiService( 1671): setWifiEnabled: true pid=1743, uid=10021
D/LocalBluetoothProfileManager( 3537): LocalBluetoothProfileManager construction complete
I/ActivityManager( 1671): Process com.google.android.talk (pid 3684) has died.
D/CommandListener( 1389): Setting iface cfg
D/CommandListener( 1389): Trying to bring down tiwlan0
[B]E/CommandListener( 1389): Failed to open /proc/sys/net/ipv6/conf/tiwlan0/use_tempaddr: No such file or directory
E/WifiStateMachine( 1671): Unable to change interface settings: java.lang.IllegalStateException: command '55 interface ipv6privacyextensions tiwlan0 enable' failed with '400 55 Failed to set ipv6 privacy extensions (No such file or directory)'[/B]
W/InputMethodManagerService( 1671): Window already focused, ignoring focus gain of: com.android.internal.view.IInputMethodClient$Stub$Proxy@40ef88a0 attribute=android.view.inputmethod.EditorInfo@40e77280
D/PhoneStatusBar( 1743): disable: < expand icons alerts ticker* system_info back home recent clock >
I/ChargAlg( 1401): USB maximum current: 0
I/wpa_supplicant( 3852): CTRL-EVENT-STATE-CHANGE id=-1 state=3 BSSID=00:00:00:00:00:00 SSID=
[B]E/WifiStateMachine( 1671): Failed to set device name E10i
E/WifiStateMachine( 1671): Failed to set manufacturer Sony Ericsson
E/WifiStateMachine( 1671): Failed to set model name E10i
E/WifiStateMachine( 1671): Failed to set model number E10i
E/WifiStateMachine( 1671): Failed to set serial number
E/WifiStateMachine( 1671): Failed to set WPS config methods
E/WifiStateMachine( 1671): Failed to set primary device type 10-0050F204-5
E/wpa_supplicant( 3852): ERROR - wpa_driver_tista_private_send - error sending Wext private IOCTL to STA driver (ioctl_cmd = 8000306, res = -1, errno = 95)
E/wpa_supplicant( 3852): ERROR - Failed to handle rx data filter command!
E/WifiStateMachine( 1671): Failed to set country code fr
E/WifiStateMachine( 1671): Failed to set frequency band 0[/B]
I/StorageNotification( 1743): UMS connection changed to true (media state mounted)
I/ChargAlg( 1401): USB maximum current: 500
I/wpa_supplicant( 3852): Trying to associate with 00:XX:XX:XX:XX:00 (SSID='XXXXXXXXX' freq=2462 MHz)
I/wpa_supplicant( 3852): CTRL-EVENT-STATE-CHANGE id=-1 state=5 BSSID=00:XX:XX:XX:XX:00 SSID=
I/wpa_supplicant( 3852): CTRL-EVENT-STATE-CHANGE id=0 state=6 BSSID=00:XX:XX:XX:XX:00 SSID=XXXXXXXXX
I/wpa_supplicant( 3852): Associated with 00:XX:XX:XX:XX:00
I/wpa_supplicant( 3852): CTRL-EVENT-STATE-CHANGE id=0 state=7 BSSID=00:00:00:00:00:00 SSID=XXXXXXXXX
I/wpa_supplicant( 3852): CTRL-EVENT-STATE-CHANGE id=0 state=7 BSSID=00:00:00:00:00:00 SSID=XXXXXXXXX
I/wpa_supplicant( 3852): CTRL-EVENT-STATE-CHANGE id=0 state=8 BSSID=00:00:00:00:00:00 SSID=XXXXXXXXX
I/wpa_supplicant( 3852): CTRL-EVENT-STATE-CHANGE id=0 state=8 BSSID=00:00:00:00:00:00 SSID=XXXXXXXXX
I/wpa_supplicant( 3852): WPA: Key negotiation completed with 00:XX:XX:XX:XX:00 [PTK=CCMP GTK=CCMP]
I/wpa_supplicant( 3852): CTRL-EVENT-STATE-CHANGE id=0 state=9 BSSID=00:00:00:00:00:00 SSID=XXXXXXXXX
I/wpa_supplicant( 3852): CTRL-EVENT-CONNECTED - Connection to 00:XX:XX:XX:XX:00 completed (auth) [id=0 id_str=]
D/DhcpInfoInternal( 1671): makeLinkProperties with empty dns2!
D/DhcpInfoInternal( 1671): makeLinkProperties with empty dns2!
D/ConnectivityService( 1671): ConnectivityChange for WIFI: CONNECTED/CONNECTED
D/ConnectivityService( 1671): Policy requires mobile teardown
D/ConnectivityService( 1671): ConnectivityChange for WIFI: CONNECTED/CONNECTED
D/ConnectivityService( 1671): handleConnectivityChange: address are the same reset per doReset linkProperty[1]: resetMask=0
D/ConnectivityService( 1671): ConnectivityChange for mobile: DISCONNECTED/DISCONNECTED
D/ConnectivityService( 1671): Attempting to switch to WIFI
D/NetUtils( 1671): android_net_utils_resetConnections in env=0x28c380 clazz=0xca600001 iface=rmnet0 mask=0x3
D/ConnectivityService( 1671): resetConnections(rmnet0, 3)
W/Smack/Packet( 1880): notify conn break (IOEx), close connection
I/qtaguid ( 1880): Failed write_ctrl(u 73) res=-1 errno=22
I/qtaguid ( 1880): Untagging socket 73 failed errno=-22
W/NetworkManagementSocketTagger( 1880): untagSocket(73) failed with errno -22
D/ConnectivityService( 1671): handleInetConditionChange: net=0 != default=1 - ignore
D/Tethering( 1671): MasterInitialState.processMessage what=3
D/Tethering( 1671): MasterInitialState.processMessage what=3
I/GTalkService/c( 1880): [AndroidEndpoint@1089272800] connect: acct=1000000, state=CONNECTING
I/GTalkService/c( 1880): [GTalkConnection@1089745560] connect: acct=1, state=CONNECTING
D/PicasaUploaderSyncManager( 3652): active network: NetworkInfo: type: WIFI[], state: CONNECTED/CONNECTED, reason: (unspecified), extra: (none), roaming: false, failover: false, isAvailable: true
D/PicasaUploaderSyncManager( 3652): background data: true
D/MiniCMUpdates( 2519): CONNECTIVITY_ACTION: noConnectivity = false
D/MiniCMUpdates( 2519): CONNECTIVITY_ACTION: starting service
D/MiniCMUpdates( 2519): CONNECTIVITY_ACTION: noConnectivity = false
D/MiniCMUpdates( 2519): CONNECTIVITY_ACTION: starting service
D/PicasaUploaderSyncManager( 3652): active network: NetworkInfo: type: WIFI[], state: CONNECTED/CONNECTED, reason: (unspecified), extra: (none), roaming: false, failover: false, isAvailable: true
D/PicasaUploaderSyncManager( 3652): background data: true
I/DownloadManager( 1804): Initiating request for download 21
D/Tethering( 1671): MasterInitialState.processMessage what=3
D/Tethering( 1671): MasterInitialState.processMessage what=3
D/PicasaUploaderSyncManager( 3652): active network: NetworkInfo: type: WIFI[], state: CONNECTED/CONNECTED, reason: (unspecified), extra: (none), roaming: false, failover: false, isAvailable: true
D/PicasaUploaderSyncManager( 3652): background data: true
D/MiniCMUpdates( 2519): CONNECTIVITY_ACTION: noConnectivity = false
D/MiniCMUpdates( 2519): CONNECTIVITY_ACTION: starting service
D/ConnectivityService( 1671): handleInetConditionHoldEnd: net=1, condition=100, published condition=0
D/MiniCMUpdates( 2519): CONNECTIVITY_ACTION: noConnectivity = false
D/MiniCMUpdates( 2519): CONNECTIVITY_ACTION: starting service
D/dalvikvm( 1839): GC_EXPLICIT freed 839K, 41% free 5046K/8519K, paused 104ms+11ms, total 704ms
D/PicasaUploaderSyncManager( 3652): active network: NetworkInfo: type: WIFI[], state: CONNECTED/CONNECTED, reason: (unspecified), extra: (none), roaming: false, failover: false, isAvailable: true
D/PicasaUploaderSyncManager( 3652): background data: true

It looks like a lot a things are failing, I don't understand if they have consequences (all I can say is my wifi is turned on, I'm connected and it seems to work for a while before rebooting, usually because I'm downloading an app or using the browser).

When I open the browser:

/SurfaceFlinger( 1392): Screen about to return, flinger = 0xfb88
I/ActivityManager( 1671): START {act=android.intent.action.MAIN cat=[android.intent.category.LAUNCHER] flg=0x10200000 cmp=com.android.browser/.BrowserActivity bnds=[192,273][240,320] u=0} from pid 1856
I/ActivityManager( 1671): Start proc com.android.browser for activity com.android.browser/.BrowserActivity: pid=3993 uid=10059 gids={3003, 1015, 1028}
I/ActivityManager( 1671): Process com.bel.android.dspmanager (pid 2022) has died.
W/ActivityManager( 1671): Scheduling restart of crashed service com.bel.android.dspmanager/.service.HeadsetService in 5000ms
I/ActivityThread( 3993): Pub com.android.browser;browser: com.android.browser.provider.BrowserProvider2
I/ActivityThread( 3993): Pub com.android.browser.home: com.android.browser.homepages.HomeProvider
I/ActivityThread( 3993): Pub com.android.browser.snapshots: com.android.browser.provider.SnapshotProvider
I/ActivityManager( 1671): Process com.android.deskclock (pid 3768) has died.
D/webcoreglue( 3993): netstack: Memory Cache feature is OFF
D/WebViewTimersControl( 3993): onBrowserActivityResume
D/WebViewTimersControl( 3993): Resuming webview timers, view=com.android.browser.BrowserWebView@4102afa0
V/NFC ( 3993): this device does not have NFC support
I/ActivityManager( 1671): Process com.android.vending (pid 2325) has died.
W/ActivityManager( 1671): Scheduling restart of crashed service com.android.vending/com.google.android.finsky.billing.iab.PendingNotificationsService in 12624ms
D/libEGL ( 3993): loaded /system/lib/egl/libEGL_adreno200.so
D/libEGL ( 3993): loaded /system/lib/egl/libGLESv1_CM_adreno200.so
D/libEGL ( 3993): loaded /system/lib/egl/libGLESv2_adreno200.so
W/webhistory( 3993): String length is suspiciously large (>10000); tag="Document state" end=0x41029ee7 data=0x40fe7b7b stringLength=263524
W/webhistory( 3993):	decodeFailed=0 (flag is ignored) content="({"f":"2","c":{"5e213ef80d1fec34":{"funcs":[{"i":"gstyle","css":"body{color:#000;margin:3px 0}body,#leftnav,#tbdi,#hidden_modes,#hmp{background:#fff}a.gb1,a.gb2,a.gb3,.link{color:#12c!important}.ts{border-collapse:collapse}.ts td{padding:0}.ti,.bl,#res h3{display:inline}.ti{display:inline-table}#tads a.mblink,#tads a.mblink b,#tadsb a.mblink,#tadsb a.mblink b,#tadsto a.mblink,#tadsto a.mblink b,#rhs a.mblink,#rhs a.mblink b{color:#1122cc!important}#tads .ch,#tadsb .ch,#tadsto .ch,#rhs .ch{margin-top:4px;}a:link,.w,#prs a:visited,#prs a:active,.q:active,.q:visited,.kl:active{color:#12c}.mblink:visited,a:visited{color:#609}.vst:link{color:#609}.cur,.b{font-weight:bold}.j{width:42em;font-size:82%}.s{max-width:42em}.sl{font-size:82%}.hd{position:absolute;width:1px;height:1px;top:-1000em;overflow:hidden}.f,.f a:link,.m,.c h2,#mbEnd h2,#tads h2,#tadsb h2,#tadsto h2,.descbox{color:#666}.a,cite,cite a:link,cite a:visited,.cite,.cite:link,#mbEnd cite b,#tads cite b,#tadsb ci
D/OpenGLRenderer( 3993): Enabling debug mode 0
V/chromium( 3993): external/chromium/net/host_resolver_helper/host_resolver_helper.cc:66: [0927/120034:INFO:host_resolver_helper.cc(66)] DNSPreResolver::Init got hostprovider:0x00000000
V/chromium( 3993): external/chromium/net/base/host_resolver_impl.cc:1510: [0927/120034:INFO:host_resolver_impl.cc(1510)] HostResolverImpl::SetPreresolver preresolver:0x002916e0
D/ ( 3993): dl error message Cannot load library: load_library[1118]: Library 'libtcpfinaggr.so' not found
D/Socket_Pool( 3993): Failed to create TCP Fin Aggregation interface.
D/Socket_Pool( 3993): netstack: CloseUnusedSockets is ON
D/Socket_Pool( 3993): netstack: system net.statistics value: 0
D/Socket_Pool( 3993): Failed to create TCP Fin Aggregation interface.
D/Socket_Pool( 3993): netstack: CloseUnusedSockets is ON
D/Socket_Pool( 3993): netstack: system net.statistics value: 0
D/ ( 3993): external/chromium/net/http/http_getzip_factory.cc: Failed to construct GETzip manager, didn't find the library!
D/netstack( 3993): netstack: Request Priority is ON
I/Choreographer( 3993): Skipped 78 frames! The application may be doing too much work on its main thread.
V/chromium( 3993): external/chromium/net/disk_cache/hostres_plugin_bridge.cc:52: [0927/120034:INFO:hostres_plugin_bridge.cc(52)] StatHubCreateHostResPlugin initializing...
V/chromium( 3993): external/chromium/net/disk_cache/hostres_plugin_bridge.cc:68: [0927/120034:INFO:hostres_plugin_bridge.cc(68)] netstack: Failed to open plugin:libdnshostprio.so
V/chromium( 3993): external/chromium/net/disk_cache/hostres_plugin_bridge.cc:73: [0927/120034:INFO:hostres_plugin_bridge.cc(73)] netstack: Failed to find symbols in plugin: libdnshostprio.so
V/chromium( 3993): external/chromium/net/disk_cache/stat_hub.h:159: [0927/120034:INFO:stat_hub.h(159)] Failed to open plugin:pp_proc_plugin.so
V/chromium( 3993): external/chromium/net/disk_cache/stat_hub.cc:118: [0927/120034:INFO:stat_hub.cc(118)] netstack: failed to load StatHub plugin: pp_proc_plugin.so
V/chromium( 3993): external/chromium/net/disk_cache/stat_hub.h:159: [0927/120034:INFO:stat_hub.h(159)] Failed to open plugin:pageload_proc_plugin.so
V/chromium( 3993): external/chromium/net/disk_cache/stat_hub.cc:118: [0927/120034:INFO:stat_hub.cc(118)] netstack: failed to load StatHub plugin: pageload_proc_plugin.so
V/chromium( 3993): external/chromium/net/disk_cache/stat_hub.cc:330: [0927/120034:INFO:stat_hub.cc(330)] netstack: StatHub was initialized
V/chromium( 3993): external/chromium/net/http/http_cache.cc:1171: [0927/120034:INFO:http_cache.cc(1171)] HttpCache::eek:nBackendCreated : StatHub is ready.
D/ ( 3993): Failed to load DoObserveConnections symbol in tcp-connections.so
I/ActivityManager( 1671): Displayed com.android.browser/.BrowserActivity: +6s586ms
I/ActivityManager( 1671): Start proc com.bel.android.dspmanager for service com.bel.android.dspmanager/.service.HeadsetService: pid=4027 uid=10052 gids={3002, 1028}
I/ActivityManager( 1671): Process com.android.providers.calendar (pid 3800) has died.
I/Choreographer( 3993): Skipped 37 frames! The application may be doing too much work on its main thread.
I/HeadsetService( 4027): Starting service.
I/HeadsetService( 4027): Headset=false; Bluetooth=false
I/ActivityManager( 1671): Process com.google.android.gsf.login (pid 3380) has died.
D/TilesManager( 3993): new EGLContext from framework: 277e98
D/GLWebViewState( 3993): Reinit shader
D/GLWebViewState( 3993): Reinit transferQueue
D/dalvikvm( 3993): GC_FOR_ALLOC freed 2471K, 51% free 3683K/7427K, paused 220ms, total 282ms
I/ActivityManager( 1671): Process com.google.android.gm (pid 3731) has died.
I/Choreographer( 3339): Skipped 123 frames! The application may be doing too much work on its main thread.
I/Choreographer( 3339): Skipped 32 frames! The application may be doing too much work on its main thread.

then the phone reboots, but reading the log I don't really understand why. Any advice ? :)