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 Foundation !

CSI acquisition limits large-MIMO gains Pilot symbols TX . . . ? RX TX 2 / 19 G. Durisi

CSI acquisition limits large-MIMO gains Pilot symbols TX . . . ? RX TX Capacity in the absence of a priori channel knowledge is the ultimate limit on the rate of reliable communication 2 / 19 G. Durisi

Outline Beyond the pre-log 1 2 Generic block-fading models 3 From asymptotics to finite-blocklength bounds 3 / 19 G. Durisi

A simple channel model | h n | n L Constant block-memoryless Rayleigh-fading channel 4 / 19 G. Durisi

Coherence time is the bottleneck MIMO input-output relation Y S X W M T × + = M R L 5 / 19 G. Durisi

Coherence time is the bottleneck MIMO input-output relation Y S X W M T × + = M R L No closed-form expression available for C ( ρ ) 5 / 19 G. Durisi

Coherence time is the bottleneck MIMO input-output relation Y S X W M T × + = M R L No closed-form expression available for C ( ρ ) Pre-log [ Zheng & Tse, 2002 ] C ( ρ ) � 1 − M ∗ � log ρ = M ∗ χ = lim L ρ →∞ where M ∗ = min { M T , M R , L/ 2 } 5 / 19 G. Durisi

The underlying geometry: M T = M R = M X Y S = × M R M T L � � 1 − M χ = M L 6 / 19 G. Durisi

The underlying geometry: M T = M R = M Y X S × M R = M T L � � 1 − M χ = M L 6 / 19 G. Durisi

The underlying geometry: M T = M R = M Y X S × M R = M T L � � 1 − M χ = M L 6 / 19 G. Durisi

The underlying geometry: M T = M R = M Y X S × M R = M T L � � 1 − M χ = M L Communications on the Grassmannian manifold 6 / 19 G. Durisi

Geometry suggests a signaling scheme Uniform distribution on the Grassmannian � X = Lρ U U : (truncated) unitary and isotropically distributed Unitary space-time modulation ( USTM ) 7 / 19 G. Durisi

A conjecture Case L ≥ M T + M R (“small MIMO”) [ Zheng & Tse (IT 2002) ]: C ( ρ ) = R USTM ( ρ ) + o (1) 8 / 19 G. Durisi

A conjecture Case L ≥ M T + M R (“small MIMO”) [ Zheng & Tse (IT 2002) ]: C ( ρ ) = R USTM ( ρ ) + o (1) Conjecture for L < M T + M R (“large MIMO”) [ Zheng & Tse (IT 2002) ]: USTM not o (1) -optimal 8 / 19 G. Durisi

BSTM is the optimal distribution [ Yang, Durisi, Riegler (JSAC 2013) ] BSTM is o (1) -optimal when L < M T + M R (large-MIMO) X = DU with U i.d. and unitary D 2 diagonal; contains the eigenvalues of a complex matrix-variate beta distributed matrix 9 / 19 G. Durisi

Why is BSTM optimal? The SIMO case s x Y W × + = M R L Large MIMO ⇒ L < 1 + M R 10 / 19 G. Durisi

Why is BSTM optimal? The SIMO case s x Y W × + = M R L Large MIMO ⇒ L < 1 + M R USTM ⇒ x i.d., � x � 2 = Lρ 10 / 19 G. Durisi

Why is BSTM optimal? The SIMO case s x Y W × + = M R L Large MIMO ⇒ L < 1 + M R USTM ⇒ x i.d., � x � 2 = Lρ ρLM R � x � 2 ∼ Beta ( L − 1 , M R + 1 − L ) L − 1 BSTM ⇒ x i.d., 10 / 19 G. Durisi

Why is BSTM optimal? The SIMO case s x Y W × + = M R L Large MIMO ⇒ L < 1 + M R USTM ⇒ x i.d., � x � 2 = Lρ ρLM R � x � 2 ∼ Beta ( L − 1 , M R + 1 − L ) L − 1 BSTM ⇒ x i.d., I ( x ; Y ) = h ( Y ) − h ( Y | x ) 10 / 19 G. Durisi

Why is BSTM optimal? The SIMO case s x Y W × + = M R L Large MIMO ⇒ L < 1 + M R USTM ⇒ x i.d., � x � 2 = Lρ ρLM R � x � 2 ∼ Beta ( L − 1 , M R + 1 − L ) L − 1 BSTM ⇒ x i.d., I ( x ; Y ) = h ( Y ) − h ( Y | x ) ≈ h ( s � x � ) + 2( L − 1 − M R ) E [log � x � ] + const 10 / 19 G. Durisi

Outline Beyond the pre-log 1 2 Generic block-fading models 3 From asymptotics to finite-blocklength bounds 11 / 19 G. Durisi

The “generic” block-fading model Constant block-fading model for subchannel ( r, t ) h r,t = 1 L · s r,t , s r,t ∼ CN (0 , 1) 12 / 19 G. Durisi

The “generic” block-fading model Constant block-fading model for subchannel ( r, t ) h r,t = 1 L · s r,t , s r,t ∼ CN (0 , 1) A more accurate model for MIMO CP-OFDM systems h r,t = z r,t · s r,t , s r,t ∼ CN (0 , 1) z r,t ∈ C L ⇒ Fourier transf. of power-delay profile 12 / 19 G. Durisi

The “generic” block-fading model Constant block-fading model for subchannel ( r, t ) h r,t = 1 L · s r,t , s r,t ∼ CN (0 , 1) A more accurate model for MIMO CP-OFDM systems h r,t = z r,t · s r,t , s r,t ∼ CN (0 , 1) z r,t ∈ C L ⇒ Fourier transf. of power-delay profile We assume that { z r,t } are generic 12 / 19 G. Durisi

Generic { z r,t } yield larger pre-log [ Riegler, Koliander, Durisi, Hlawatsch (ISIT 2013) ] { z r,t } generic and M R > M T ( L − 1) with M T < L/ 2 L − T 13 / 19 G. Durisi

Generic { z r,t } yield larger pre-log [ Riegler, Koliander, Durisi, Hlawatsch (ISIT 2013) ] { z r,t } generic and M R > M T ( L − 1) with M T < L/ 2 L − T Then � � 1 − 1 χ gen = M T L 13 / 19 G. Durisi

Generic { z r,t } yield larger pre-log [ Riegler, Koliander, Durisi, Hlawatsch (ISIT 2013) ] { z r,t } generic and M R > M T ( L − 1) with M T < L/ 2 L − T Then � � 1 − 1 χ gen = M T L Compare with constant block-fading model � 1 − M T � χ const = M T L 13 / 19 G. Durisi

Intuition behind pre-log increase: M R = 3 , M T = 2 , L = 4 � � 1 − M T Constant block-fading: χ const = M T = 1 L Y S X = × M T M R L 14 / 19 G. Durisi

Intuition behind pre-log increase: M R = 3 , M T = 2 , L = 4 � � 1 − M T Constant block-fading: χ const = M T = 1 L Y S X = × M T M R L 1 − 1 = 3 � � Generic block-fading: χ gen = M T L 2 diag { z r, 1 } diag { z r, 2 } y r s 1 ,r s 2 ,r x 1 x 2 = + 14 / 19 G. Durisi

Outline Beyond the pre-log 1 2 Generic block-fading models 3 From asymptotics to finite-blocklength bounds 15 / 19 G. Durisi

Lost in “asymptotia”? 16 / 19 G. Durisi

Lost in “asymptotia”? capacity characterizations up to o (1) yield tight bounds � pre-log sensitive to small changes in the channel model � 16 / 19 G. Durisi

From asymptotia to tight bounds [ Yang, Durisi, Koch, Polyanskiy (ITW 2012) ] Capacity bounds / Capacity with channel knowledge 1 0.95 Upper bound 0.9 0.85 Lower bound 0.8 L = 20 0.75 χ = 1 − 1 0.7 20 = 0 . 95 0.65 0.6 0.55 0.5 0 2 4 6 8 10 12 14 16 18 20 SNR [dB] 17 / 19 G. Durisi

From asymptotia to tight bounds [ Yang, Durisi, Koch, Polyanskiy (ITW 2012) ] 3 2.8 Perfect channel knowledge Upper bound 2.6 Rate [bits/channel use] 2.4 Lower bound 2.2 2 1.8 blocklength = 4 × 10 4 1.6 P { error } ≤ 10 − 3 1.4 SNR = 10 dB 1.2 1 0 1 2 3 4 10 10 10 10 10 Coherence time L 17 / 19 G. Durisi

From asymptotia to tight bounds [ Yang, Durisi, Koch, Polyanskiy (ISIT 2013) ] Outage capacity ( C ǫ ) 1 0.8 Converse Rate, bits/ch. use Normal Approximation 0.6 LTE-Advanced codes Achievability 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Blocklength, n 17 / 19 G. Durisi

Zero dispersion AWGN channel [ Polyanskiy, Poor, Verd´ u (IT 2010) ] � V � log n � n Q − 1 ( ǫ ) − O R ∗ awgn ( n, ǫ ) = C awgn − n 18 / 19 G. Durisi

Zero dispersion AWGN channel [ Polyanskiy, Poor, Verd´ u (IT 2010) ] � V � log n � n Q − 1 ( ǫ ) − O R ∗ awgn ( n, ǫ ) = C awgn − n SISO quasi static [ Yang, Durisi, Koch, Polyanskiy (ISIT 2013) ] ❅ � � 1 � log n � � ❅ { R ∗ csirt ( n, ǫ ) , R ∗ no ( n, ǫ ) } = C ǫ − 0 n − O � ❅ n 18 / 19 G. Durisi

Summary Capacity without a-priori CSI Pilot symbols TX . . . ? RX TX 19 / 19 G. Durisi

Summary Capacity without a-priori CSI Too conservative estimates? USTM ⇒ BSTM Pilot symbols M (1 − M/L ) ⇒ M (1 − 1 /L ) TX . . . ? RX TX 19 / 19 G. Durisi

Summary Capacity without a-priori CSI Too conservative estimates? USTM ⇒ BSTM Pilot symbols M (1 − M/L ) ⇒ M (1 − 1 /L ) TX . . . ? RX TX From asymptotia to finite blocklength 3 2.8 Perfect channel knowledge 2.6 Upper bound Rate [bits/channel use] 2.4 Lower bound 2.2 2 1.8 blocklength = 4 × 10 4 1.6 P { error } ≤ 10 − 3 1.4 SNR = 10 dB 1.2 1 0 1 2 3 4 10 10 10 10 10 Coherence time L 19 / 19 G. Durisi

Backup Slides 20 / 19 G. Durisi

Gain of BSTM over USTM for large-MIMO systems 0.14 ρ = 30 dB M T = min { M R , L/ 2 } 0.12 L = 10 0.1 L = 20 0.08 R BSTM − R USTM R USTM 0.06 L = 50 0.04 L = 100 0.02 0 10 20 30 40 50 60 70 80 90 100 M R 21 / 19 G. Durisi

Achievability for finite blocklength 22 / 19 G. Durisi