Signal processing for Underwater Acoustic MIMO OFDM

Transcription

1 Signal processing for Underwaer Acousic MIMO OFDM Milica Sojanovic Norheasern Universiy ONR (N , 7 22 MURI N ) 7 738)

2 Orhogonal frequency division muliplexing (OFDM) oal bandwidh many narrow subbands easy equalizaion in he frequency domain B=K f, T=/ f in FFT... c o m b i n e r dec ou f<< /T mp, T<</B d K Radio: WLAN,DAB/DVB, 4h generaion cellular sysems Acousic: single-carrier OFDM: low-complexiy, low-mainenance MIMO: spaial muliplexing in M FFT... Signal processing: -synchronizaion -channel esimaion -daa deecion K c o m b i n e r dec ou K

3 Acousic (vs. radio) propagaion ransfer funcion of he channel f f B=K f c=5 m/s v ~ m/s a ~ -4 f a =v/c Doppler facor RF f f (+a') UWA=UWB ~MHz B << f c f ~GHz AF ~Hz ~Hz B << f c f Moion-induced Doppler disorion in a wideband d sysem: non-uniform frequency shifing/spreading across he signal bandwidh.

4 OFDM: Signal processing chec-lis pre-fft: iniial synchronizaion (acquisiion, resampling) pos-fft: phase racing, channel esimaion, daa deecion synchronizaion: iniial racing a f af << f OFDM bloc T OFDM bloc T OFDM bloc T g T=/ f guard inerval ~ mulipah spread T g T g daa deecion: non-adapive (bloc-by-bloc) adapive (bloc-o-bloc) bloc) channel esimaion: ransfer funcion domain impulse response domain full / sparse configuraions/performance: f muliple receivers: diversiy (SIMO) muliple ransmiers: spaial muliplexing (MIMO) Experimens: BB 6 AUV Fes 7 BB VHF 8 RACE 8 SPACE 8

5 MIMO configuraion H d 2 jθ 2 jθ 2 y = H e d + H e d z + H 2 d 2 y 2 =... no enough observaions o esimae he channel in he frequency domain,r: ransmier, receiver,n: subband, bloc goal: exploi frequency correlaion in an opimal manner Signal model received signal: M T jθ r r y H d e = + phase: = z θ ( n) = θ(n ) + 2πa f T'

6 Daa deecion LS ˆ ˆ' [ ˆ ˆ' ] ˆ * = y H H H Θ d Phase synchronizaion Doppler facor predicion/esimaion Idea: esimae Doppler facor; infer phase disorions in all subbands. MIMO: a differen Doppler facor may be needed for each ransmier. Assuming an exising esimae of he Doppler facor, predic phase for curren bloc: θ ( ˆ ( n) = θ (n ) + 2πâ (n )f T' Use his phase, exising channel, o obain enaive daa decisions; updae Doppler esimae, channel. ψ ) d d * â = K ψ 2 π f T' ˆθ = ˆθ (n ) + 2πâ f T'

7 Channel esimaion: SISO, SIMO ransfer funcion H K coefficiens (sysem parameer) FFT K impulse response h l L(J) coefficiens (channel parameers) non-adapive: each bloc deeced independenly, L pilos per bloc (L~BTmp) performance same as frequency domain esimaion wih all K symbols nown adapive: jθ ( y = H e d + z h (n + ) = λhˆ + ( λ)ifft[ y ˆ e jˆ θ * l l d ~ ] noe: channel may be ani-causal inser, no append, zeros before FFT channel sparsing: eep J sronges aps only. daa-aided: can use all K symbols per bloc. J/L L/K J/K MSE reducion

8 Channel esimaion: MIMO Signal model L: oal mulipah h spread (coniguous aps [/B]) J: number of significan aps L A j2j πl/k H = h e channel coefficiens i (M T xm R ) l= A l L A ( l l= A l Y n) = Φ Dθ h + KxM R KxKK KxM T M T xm R Z his model is crucial for channel esimaion Y = y (n ) M y K (n ) d ( n) Θ M D θ = M Θ ( n) diag[,..., T = θ θ ] d K ΘK Φ = diag[, e j2π/k,..., e j2π(k )/K ]

9 full size model (L) Y ( n) = h + Z h conains all coefficiens = [ Φ A D Φ L A θ D θ ] (KxM T L) sparse model (J) Y ( n) = h + Z h only significan coefficiens l θ D θ ( n) = [ Φ D... Φ J ] (KxM T J) l

10 MIMO channel esimaion: some observaions Y ( n) = h + Z If all he daa symbols are nown, can be consruced (using phase esimaes). LS esimae (one sho) ˆ h = [ ' ] ' Y K MT L for a given number of carriers K, a mos K/M T channel coefficiens can be esimaed for a given channel span L, a leas M T L observaions are needed (per receiver) If only pilo symbols are nown, corresponding rows are exraced from Y,, ) o form a reduced se of observaions (P= M T L). Decision-direced operaion: more observaions, beer channel esimaes. Also, less overhead. win-win in eiher case, an M T L inverse is required

11 Channel esimaion: iniial (LS) ˆ h () = [ '() ()] '() Y () Mae full size iniial esimae. Idenify significan coefficiens, if any (magniude). Noe: he inverse can be pre-compued (phase esimaes are zero a n=).. Channel esimaion: adapive hˆ ˆ = λh ˆ + ( λ)[ ' ] ' Y ˆ ˆ(n 2 h = h ) + μ '[ Y ˆ(n h )] Swich o decision-direced mode, and coninue o updae (reduced-size) esimae. Noe: furher sparsing can be performed before daa deecion. Alg. 2 can be inerpreed as: -LMS for he in/ou relaionship Y= h+z -Alg. under sochasic approximaion KI ) K and wih μ=(-λ)/k. Noe: his approximaion is beer jusified if all K carriers, no only pilos, are used.

12 Receiver algorihm. Iniial channel esimaion (full size, LS) 2. Mae enaive symbol decisions i using old channel esimae, prediced d phases 3. Esimae Doppler facors, updae phases for curren bloc 4. Calculae new channel esimaes: updae impulse response esimaes; runcae (sparse) compue corresponding frequency-domain coefficiens 5. Esimae daa symbol (LS); mae final decisions (sof-decision decoder in he loop)

13 Experimen: SPACE Hz 4&8 PSK, BCH(64,) Souh of Marha s Vineyard, Ocober 28 B= Hz Tg=6 ms K=28-24 carriers f= Hz T=3-5 5 ms 5m N=28-6 blocs β = sps/hz/x M T =4 M R =2 2.5m 2m m R b B = M T m r + β..2 channel magniude from probe maching gains pah g.6.4 onse, model channel respo delay [ms] delay [ms] delay [ms] pah gains, model channel response, model channel response, measured

14 ime [s] SPACE 8: example (297, 2:53) 24 carriers, x # ou of 3, QPSK/8PSK phase esimaes [rad] channel esimaes (magniude) bloc index 5 delay [/B] MSE ime [db] bloc index MSE frequency [db] subcarrier index 4 PSK M =3 ransmi elemens (showing # ) T M R =2 receive elemens K=24 carriers, N=6 blocs L=28 coefficiens per channel (~3 ms) A=2 coefficiens before reference J=28 significan coefficiens no sparsing P= pilo channels μ=.5 overlap add: 3 ms, 7 ms MSE= 5.9 db, BER= w/bch (64,)

15 SPACE 8: example summary (297, 2:53) MSE [db] M T K ms 2 L=K/M T <BTmp M T =3 M T =2 more observaions Im Im oupu scaer plo Re oupu scaer plo Re 2 M T = less imecoherence Im oupu scaer plo number of subcarriers, K Re

16 Pushing performance limis: MIMO OFDM bandwidh efficiency R/B = M T / (+T mp B/K) symbols/sec/hz Wan: M T, K as large as possible. (M T K/L) R / B K 2 LK+ L 2 ~ K L frequency coherence: f<</t mp L<<K Increasing M T increases cross-al beween channels, size of he esimaor; MIMO channel esimaion becomes more difficul. Increasing K increases bloc duraion (T=K/B), racing becomes more difficul; ICI arises. Q: Wha is he performance limi? Time variabiliy? Does i depend on he weaher?

17 SPACE 8: environmenal condiions & performance wave heigh [m] MSE [db] 8 2 wave period [s] Day of he year (Ocober 4 28, 28) number of subcarriers, K 2 2 wind speed [m/s] db] MSE [d 8 4 wind direcion [deg] Day of he year (Ocober 4 28, 28) number of subcarriers, K

18 Summary OFDM = low complexiy MIMO = spaial muliplexing impulse response esimaion = opimal exploiaion of frequency correlaion phase, channel predicion = decision direced operaion => => low (no) overhead; all symbols available for channel esimaion. adapive algorihms: # requires marix inversion useful only in reduced-size (J). # 2 does no require marix inversion can be run in full size oo (L). Design principles: choose K as large as ime-coherence will permi (win-win) choose h M T as large as BER will permi, max. K/L (win-loose) Fuure wor: ICI compensaion (coheren/differenially coheren, SIMO/MIMO) long-erm channel observaion / modeling of ime-variaion