On the Cost of CSI Acquisition in Large MIMO Systems Giuseppe - - PowerPoint PPT Presentation
On the Cost of CSI Acquisition in Large MIMO Systems Giuseppe Durisi Chalmers, Sweden June, 2013 Joint work with Wei Yang , G unther Koliander , Erwin Riegler , Franz Hlawatsch , Tobias Koch , Yury Polyanskiy Many thanks to Ericsson Research
Giuseppe Durisi Chalmers, Sweden June, 2013
Joint work with Wei Yang, G¨ unther Koliander, Erwin Riegler, Franz Hlawatsch, Tobias Koch, Yury Polyanskiy Many thanks to Ericsson Research Foundation!
TX RX . . . TX
Pilot symbols
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TX RX . . . TX
Pilot symbols
Capacity in the absence of a priori channel knowledge is the ultimate limit on the rate of reliable communication
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1
Beyond the pre-log
2
Generic block-fading models
3
From asymptotics to finite-blocklength bounds
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Constant block-memoryless Rayleigh-fading channel
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MIMO input-output relation
= × L MT MR X Y S W +
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MIMO input-output relation
= × L MT MR X Y S W +
No closed-form expression available for C(ρ)
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MIMO input-output relation
= × L MT MR X Y S W +
No closed-form expression available for C(ρ) Pre-log [Zheng & Tse, 2002] χ = lim
ρ→∞
C(ρ) log ρ = M∗
L
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= × L MT MR X Y S
χ = M
L
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= × L MT MR X Y S
χ = M
L
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= × L MT MR X Y S
χ = M
L
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= × L MT MR X Y S
χ = M
L
Grassmannian manifold
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Uniform distribution on the Grassmannian X =
U : (truncated) unitary and isotropically distributed Unitary space-time modulation (USTM)
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Case L ≥ MT + MR (“small MIMO”) [Zheng & Tse (IT 2002)]: C(ρ) = RUSTM(ρ) + o(1)
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Case L ≥ MT + MR (“small MIMO”) [Zheng & Tse (IT 2002)]: C(ρ) = RUSTM(ρ) + o(1) Conjecture for L < MT + MR (“large MIMO”) [Zheng & Tse (IT 2002)]:
USTM not o(1)-optimal
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[Yang, Durisi, Riegler (JSAC 2013)] BSTM is o(1)-optimal when L < MT + MR (large-MIMO) X = DU with U i.d. and unitary D2 diagonal; contains the eigenvalues of a complex matrix-variate beta distributed matrix
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= × L MR x Y s + W
Large MIMO ⇒ L < 1 + MR
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= × L MR x Y s + W
Large MIMO ⇒ L < 1 + MR USTM ⇒ x i.d., x2 = Lρ
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= × L MR x Y s + W
Large MIMO ⇒ L < 1 + MR USTM ⇒ x i.d., x2 = Lρ BSTM ⇒ x i.d.,
L−1 ρLMR x2 ∼ Beta(L − 1, MR + 1 − L)
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= × L MR x Y s + W
Large MIMO ⇒ L < 1 + MR USTM ⇒ x i.d., x2 = Lρ BSTM ⇒ x i.d.,
L−1 ρLMR x2 ∼ Beta(L − 1, MR + 1 − L)
I(x; Y) = h(Y) − h(Y | x)
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= × L MR x Y s + W
Large MIMO ⇒ L < 1 + MR USTM ⇒ x i.d., x2 = Lρ BSTM ⇒ x i.d.,
L−1 ρLMR x2 ∼ Beta(L − 1, MR + 1 − L)
I(x; Y) = h(Y) − h(Y | x) ≈ h(sx) + 2(L − 1 − MR) E[log x] + const
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Beyond the pre-log
2
Generic block-fading models
3
From asymptotics to finite-blocklength bounds
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Constant block-fading model for subchannel (r, t) hr,t = 1L · sr,t, sr,t ∼ CN(0, 1)
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Constant block-fading model for subchannel (r, t) hr,t = 1L · sr,t, sr,t ∼ CN(0, 1) A more accurate model for MIMO CP-OFDM systems hr,t = zr,t · sr,t, sr,t ∼ CN(0, 1) zr,t ∈ CL ⇒ Fourier transf. of power-delay profile
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Constant block-fading model for subchannel (r, t) hr,t = 1L · sr,t, sr,t ∼ CN(0, 1) A more accurate model for MIMO CP-OFDM systems hr,t = zr,t · sr,t, sr,t ∼ CN(0, 1) zr,t ∈ CL ⇒ Fourier transf. of power-delay profile We assume that {zr,t} are generic
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[Riegler, Koliander, Durisi, Hlawatsch (ISIT 2013)] {zr,t} generic and MR > MT (L−1)
L−T
with MT < L/2
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[Riegler, Koliander, Durisi, Hlawatsch (ISIT 2013)] {zr,t} generic and MR > MT (L−1)
L−T
with MT < L/2 Then χgen = MT
L
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[Riegler, Koliander, Durisi, Hlawatsch (ISIT 2013)] {zr,t} generic and MR > MT (L−1)
L−T
with MT < L/2 Then χgen = MT
L
χconst = MT
L
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Constant block-fading: χconst = MT
L
= × L MT MR X Y S
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Constant block-fading: χconst = MT
L
= × L MT MR X Y S
Generic block-fading: χgen = MT
L
2 = + yr diag{zr,1} diag{zr,2} x1 x2 s1,r s2,r
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1
Beyond the pre-log
2
Generic block-fading models
3
From asymptotics to finite-blocklength bounds
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capacity characterizations up to o(1) yield tight bounds pre-log sensitive to small changes in the channel model
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[Yang, Durisi, Koch, Polyanskiy (ITW 2012)]
2 4 6 8 10 12 14 16 18 20 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
SNR [dB] Capacity bounds / Capacity with channel knowledge Lower bound Upper bound L = 20 χ = 1 − 1 20 = 0.95
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[Yang, Durisi, Koch, Polyanskiy (ITW 2012)]
10 10
1
10
2
10
3
10
4
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
P{error} ≤ 10−3 blocklength = 4 × 104 SNR = 10 dB Coherence time L Rate [bits/channel use] Perfect channel knowledge Lower bound Upper bound
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[Yang, Durisi, Koch, Polyanskiy (ISIT 2013)]
Outage capacity (Cǫ) LTE-Advanced codes Converse Achievability Normal Approximation Blocklength, n Rate, bits/ch. use 1000 100 200 300 400 500 600 700 800 900 0.2 0.4 0.6 0.8 1
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AWGN channel [Polyanskiy, Poor, Verd´ u (IT 2010)] R∗
awgn(n, ǫ) = Cawgn −
n Q−1(ǫ) − O log n n
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AWGN channel [Polyanskiy, Poor, Verd´ u (IT 2010)] R∗
awgn(n, ǫ) = Cawgn −
n Q−1(ǫ) − O log n n
{R∗
csirt(n, ǫ), R∗ no(n, ǫ)} = Cǫ −
❅ ❅
n − O log n n
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Capacity without a-priori CSI
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Capacity without a-priori CSI
TX RX . . . TX
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Too conservative estimates? USTM ⇒ BSTM M (1 − M/L) ⇒ M (1 − 1/L)
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Capacity without a-priori CSI
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Too conservative estimates? USTM ⇒ BSTM M (1 − M/L) ⇒ M (1 − 1/L) From asymptotia to finite blocklength
10 10 1 10 2 10 3 10 4 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 P{error} ≤ 10−3 blocklength = 4 × 104 SNR = 10 dB Coherence time L Rate [bits/channel use] Perfect channel knowledge Lower bound Upper bound19 / 19
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10 20 30 40 50 60 70 80 90 100 0.02 0.04 0.06 0.08 0.1 0.12 0.14 RBSTM − RUSTM RUSTM MR L = 100 L = 50 L = 20 L = 10 ρ = 30 dB MT = min{MR, L/2}
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