Massive MIMO: Signal Structure, Efficient Processing, and Open Problems I
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1 Massive MIMO: Signal Structure, Efficient Processing, and Open Problems I Saeid Haghighatshoar Communications and Information Theory Group (CommIT) Technische Universität Berlin CoSIP Winter Retreat Berlin, December 2016 Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
2 Outline 1 Shannon Model of Communication 2 Overview of Linear Time Variant (LTV) Channels 3 System-level Parameters 4 MIMO Channel 5 Massive MIMO Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
3 Outline 1 Shannon Model of Communication 2 Overview of Linear Time Variant (LTV) Channels 3 System-level Parameters 4 MIMO Channel 5 Massive MIMO Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
4 Shannon Model of Communication INFORMATION SOURCE TRANSMITTER RECEIVER DESTINATION SIGNAL RECEIVED SIGNAL MESSAGE MESSAGE NOISE SOURCE Fig. 1 Schematic diagram of a general communication system. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
5 Outline 1 Shannon Model of Communication 2 Overview of Linear Time Variant (LTV) Channels 3 System-level Parameters 4 MIMO Channel 5 Massive MIMO Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
6 Communication over a Wireless Channel Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
7 Communication over a Wireless Channel A message C is to be transmitted. Message C Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
8 Communication over a Wireless Channel A message C is to be transmitted. The encoder maps the message C into channel alphabet x(t). Message C Encoder: s(t) C Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
9 Communication over a Wireless Channel A message C is to be transmitted. The encoder maps the message C into channel alphabet x(t). The distorted noisy received signal is given by y(t) = x(t) + n(t) = h(t, τ)s(t τ)dτ + n(t). y(t) = x(t) + n(t) Channel Message C Encoder: s(t) C Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
10 Communication over a Wireless Channel A message C is to be transmitted. The encoder maps the message C into channel alphabet x(t). The distorted noisy received signal is given by y(t) = x(t) + n(t) = h(t, τ)s(t τ)dτ + n(t). The received signal is decoded: y(t) Ĉ and P e = P[C Ĉ]. y(t) = x(t) + n(t) Decoder: y(t) Ĉ Channel Message C Encoder: s(t) C Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
11 Channel Impulse Response The Linear Time Variant (LTV) channel is given by h(t, τ) x(t) = h(t, τ)s(t τ)dτ. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
12 Channel Impulse Response The Linear Time Variant (LTV) channel is given by h(t, τ) x(t) = h(t, dτ)s(t τ). Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
13 Channel Impulse Response The Linear Time Variant (LTV) channel is given by h(t, τ) x(t) = h(t, τ)s(t τ)dτ. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
14 Channel Impulse Response The Linear Time Variant (LTV) channel is given by h(t, τ) x(t) = h(t, τ)s(t τ)dτ. Joint variables: time-delay (t, τ) vs. doppler-frequency (ν, f ). Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
15 Channel Impulse Response The Linear Time Variant (LTV) channel is given by h(t, τ) x(t) = h(t, τ)s(t τ)dτ. Joint variables: time-delay (t, τ) vs. doppler-frequency (ν, f ). There are 4 different ways to represent h(t, τ). Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
16 Channel Impulse Response The Linear Time Variant (LTV) channel is given by h(t, τ) x(t) = h(t, τ)s(t τ)dτ. Joint variables: time-delay (t, τ) vs. doppler-frequency (ν, f ). There are 4 different ways to represent h(t, τ). (t, f )-representation via Parseval s equality: x(t) = h(t, f )s(f )e j2πft df Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
17 Channel Impulse Response The Linear Time Variant (LTV) channel is given by h(t, τ) x(t) = h(t, τ)s(t τ)dτ. Joint variables: time-delay (t, τ) vs. doppler-frequency (ν, f ). There are 4 different ways to represent h(t, τ). (t, f )-representation via Parseval s equality: x(t) = h(t, f )s(f )e j2πft df x(f ) = h(t, f )s(f ). Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
18 Channel Impulse Response The Linear Time Variant (LTV) channel is given by h(t, τ) x(t) = h(t, τ)s(t τ)dτ. Joint variables: time-delay (t, τ) vs. doppler-frequency (ν, f ). There are 4 different ways to represent h(t, τ). (t, f )-representation via Parseval s equality: x(t) = h(t, f )s(f )e j2πft df x(f ) = h(t, f )s(f ). (ν, f )-representation via Fourier trans. w.r.t. t x(t) = (h(ν, f ) s(ν)) e j2πft dt ν=f Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
19 Channel Impulse Response The Linear Time Variant (LTV) channel is given by h(t, τ) x(t) = h(t, τ)s(t τ)dτ. Joint variables: time-delay (t, τ) vs. doppler-frequency (ν, f ). There are 4 different ways to represent h(t, τ). (t, f )-representation via Parseval s equality: x(t) = h(t, f )s(f )e j2πft df x(f ) = h(t, f )s(f ). (ν, f )-representation via Fourier trans. w.r.t. t x(t) = (h(ν, f ) s(ν)) e j2πft dt x(f ) = (h(ν, f ) s(ν)). ν=f ν=f Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
20 Representation of Channel Response (t, f )-representation: Time-variant Filter in Frequency x(f ) = h(t, f )s(f ) s(f ) f h(t, f ) x(f ) f Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
21 Representation of Channel Response (ν, f )-representation: Doppler Spread Kernel s(f ) = (h(ν, f ) x(ν)) = ν=f h(ν, f )x(f ν)dν s(f ) f ν f f + ν x(f ) h(ν, f )dν h( ν, f )dν f Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
22 A Simple Example h(t, τ) = a 0 δ(τ τ 0 v0 c t), c (speed of light). v 0 Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
23 A Simple Example h(t, τ) = a 0 δ(τ τ 0 v0 c t), c (speed of light). h(t, f ) = a 0 e j2πf (τ0 v 0 c t) Time-variant phase distortion. v 0 Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
24 A Simple Example h(t, τ) = a 0 δ(τ τ 0 v0 c t), c (speed of light). h(t, f ) = a 0 e j2πf (τ0 v 0 c t) Time-variant phase distortion. h(ν, f ) = a 0 e j2πf τ0 δ(ν fv0 fv0 c ) A discrete doppler tap at c. v 0 Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
25 Summary of Channel Representation Different (t, τ) (ν, f ) Representations h(t, τ) h(t, f ) h(ν, τ) h(ν, f ) Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
26 Summary of Channel Representation Different (t, τ) (ν, f ) Representations h(t, τ) h(t, f ) h(ν, τ) h(ν, f ) Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
27 Summary of Channel Representation Different (t, τ) (ν, f ) Representations h(t, τ) h(t, f ) h(ν, τ) h(ν, f ) Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
28 Outline 1 Shannon Model of Communication 2 Overview of Linear Time Variant (LTV) Channels 3 System-level Parameters 4 MIMO Channel 5 Massive MIMO Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
29 Parameters of h(t, f ) In WL Communication h(t, f ) is typically a Gaussian process. s(f ) f h(t, f ) x(f ) f Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
30 Parameters of h(t, f ) In WL Communication h(t, f ) is typically a Gaussian process. Time-variations of h(t, f ) s(f ) f h(t, f ) x(f ) f Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
31 Parameters of h(t, f ) In WL Communication h(t, f ) is typically a Gaussian process. Time-variations of h(t, f ) h(ν, f ) Coherence Time t c Doppler Spread ν c s(f ) f h(t, f ) x(f ) f Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
32 Parameters of h(t, f ) In WL Communication h(t, f ) is typically a Gaussian process. Time-variations of h(t, f ) h(ν, f ) Coherence Time t c Doppler Spread ν c Frequency-variations of h(t, f ) s(f ) f h(t, f ) x(f ) f Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
33 Parameters of h(t, f ) In WL Communication h(t, f ) is typically a Gaussian process. Time-variations of h(t, f ) h(ν, f ) Coherence Time t c Doppler Spread ν c Frequency-variations of h(t, f ) h(ν, τ) Coherence Bandwidth f c Delay Spread τ c s(f ) f h(t, f ) x(f ) f Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
34 Outline 1 Shannon Model of Communication 2 Overview of Linear Time Variant (LTV) Channels 3 System-level Parameters 4 MIMO Channel 5 Massive MIMO Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
35 MIMO System In MIMO, the BS antenna is highly non-isotropic. y(t) = s(t) Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
36 MIMO System In MIMO, the BS antenna is highly non-isotropic. We have an additional degree-of-freedom of arrival wave-number k R 3. y(t) = s(t) Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
37 MIMO System In MIMO, the BS antenna is highly non-isotropic. We have an additional degree-of-freedom of arrival wave-number k R 3. y(t) = s(t) f [f c W 2, f c + W 2 ]: negligible bandwidth W compared with f c, well-defined direction k(f ) = 2π λ = 2πf c 2πfc c. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
38 MIMO System In MIMO, the BS antenna is highly non-isotropic. We have an additional degree-of-freedom of arrival wave-number k R 3. y(t) = s(t) f [f c W 2, f c + W 2 ]: negligible bandwidth W compared with f c, well-defined direction k(f ) = 2π λ = 2πf c 2πfc c. E.g. f c = 3 GHz, and W = 20 MHz. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
39 Saeid Haghighatshoar (TUy(t) Berlin) = s(t) Massive MIMO I SPP 1798, December / 33 MIMO System The channel response is given by h(t, f, k): y(t, r) = Re[ ] h(t, f, k)x(t τ)e j k,r dτdk
40 MIMO System The channel response is given by h(t, f, k): y(t, r) = Re[ ] h(t, f, k)x(t τ)e j k,r dτdk = Re[ ] h(t, f, n)x(t τ)e j 2π λ n,r dτdn, where n {n : n = 1} denotes the unit sphere in 3D. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
41 MIMO System The channel response is given by h(t, f, k): y(t, r) = Re[ ] h(t, f, k)x(t τ)e j k,r dτdk = Re[ ] h(t, f, n)x(t τ)e j 2π λ n,r dτdn, where n {n : n = 1} denotes the unit sphere in 3D. The desired channel response is h(t, f, r) = h(t, f, n)e j 2π λ n,r dn Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
42 Outline 1 Shannon Model of Communication 2 Overview of Linear Time Variant (LTV) Channels 3 System-level Parameters 4 MIMO Channel 5 Massive MIMO Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
43 MIMO System The whole channel is represented by h(t, f, r). Space V h(t, f, r) Time T Bandwidth W Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
44 MIMO System The whole channel is represented by h(t, f, r). The 3D Communication Box! Space V h(t, f, r) Time T Bandwidth W Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
45 MIMO System The whole channel is represented by h(t, f, r). The 3D Communication Box! Some vocabulary: spatially correlated, fast fading, frequency dispersive,... Space V h(t, f, r) Time T Bandwidth W Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
46 Massive MIMO System Space V R 3 is typically sampled by antenna arrays (M antennas): Space V h(t, f, r) Time T Bandwidth W y(t) = s(t) Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
47 Massive MIMO System Space V R 3 is typically sampled by antenna arrays (M antennas): Space V h(t, f, r) Time T Bandwidth W We define channel vector y(t) = s(t) of a user as h(t, f, r 1 ) h(t, f, r 2 ) h(t, f ) =.. h(t, f, r M ) Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
48 Massive MIMO System Time is divided into several Coherence blocks over which h(t, f ) is almost constant. Time h s (f ) Frequency W t c Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
49 Massive MIMO System Time is divided into several Coherence blocks over which h(t, f ) is almost constant. Time h s (f ) Frequency W t c Several packets are transmitted over a coherence block. C M h s (f 1 ) f = 1 Ts... time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
50 Massive MIMO System H s = [h s (f 1 ),..., h s (f N )], N = W f = WT s is the channel matrix. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
51 Massive MIMO System H s = [h s (f 1 ),..., h s (f N )], N = W f h s (f i ) is the channel vector at f i. = WT s is the channel matrix. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
52 Massive MIMO System H s = [h s (f 1 ),..., h s (f N )], N = W f = WT s is the channel matrix. h s (f i ) is the channel vector at f i. {f 1,..., f N } are like N independent communication channels. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
53 Massive MIMO System H s = [h s (f 1 ),..., h s (f N )], N = W f = WT s is the channel matrix. h s (f i ) is the channel vector at f i. {f 1,..., f N } are like N independent communication channels. Variation in frequency is controlled by the delay-spread of the channel τ c : channel is constant over f c = 1 τ c. h s (f 1 ) h s (f N ) f = 1 T s... Bandwidth W T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
54 Massive MIMO System {f 1,..., f N } are like N independent communication channels. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
55 Massive MIMO System {f 1,..., f N } are like N independent communication channels. Uplink (UL) and Downlink (DL) signaling is as follows: h s (f 1 ) h s (f N ) f = 1 T s... Bandwidth W T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
56 Massive MIMO System {f 1,..., f N } are like N independent communication channels. Uplink (UL) and Downlink (DL) signaling is as follows: UL: User send m s(f i ) C BS receives y s(f i ) = h s(f i )m s(f i ) C M. h s (f 1 ) h s (f N ) f = 1 T s... Bandwidth W T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
57 Massive MIMO System {f 1,..., f N } are like N independent communication channels. Uplink (UL) and Downlink (DL) signaling is as follows: UL: User send m s(f i ) C BS receives y s(f i ) = h s(f i )m s(f i ) C M. DL: BS sends m s(f i ) C M User receives y s(f i ) = h s(f i ) H m s(f i ) C. h s (f 1 ) h s (f N ) f = 1 T s... Bandwidth W T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
58 Multiuser Massive MIMO System At each degree-of-freedom (DoF) (frequency f i ), we have y s = ( ) h (1) s, h (2) s, h (3) s, h (4) s = H s x s + n s. x s (1) x s (2) x s (3) x s (4) + n s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
59 Multiuser Massive MIMO System The BS decoder (e.g. ZFBF) to compensates the channel x s = H 1 s y s x s (k) = α (k) x (k) s + n (k) for k = 1, 2, 3, 4. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
60 Multiuser Massive MIMO System The BS decoder (e.g. ZFBF) to compensates the channel x s = H 1 s y s x s (k) = α (k) x (k) s + n (k) for k = 1, 2, 3, 4. The achievable Sum-Rate is C sum = 4 N log 2 (1 + α (k) 2 SNR) 4N log 2 (1 + α 2 SNR). k=1 Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
61 Multiuser Massive MIMO System The BS decoder (e.g. ZFBF) to compensates the channel x s = H 1 s y s x s (k) = α (k) x (k) s + n (k) for k = 1, 2, 3, 4. The achievable Sum-Rate is 4 C sum = N log 2 (1 + α (k) 2 SNR) 4N log 2 (1 + α 2 SNR). k=1 SDMA C sum =4 Blog P N Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
62 Channel State Computing the decoder or beamformer requires H s at each slot s. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
63 Channel State Computing the decoder or beamformer requires H s at each slot s. In many communication scenarios, training the channel state is considered as overhead. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
64 Channel State Computing the decoder or beamformer requires H s at each slot s. In many communication scenarios, training the channel state is considered as overhead. In massive MIMO, training is part of the game! SDMA C sum =4 Blog P N Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
65 Channel State Computing the decoder or beamformer requires H s at each slot s. In many communication scenarios, training the channel state is considered as overhead. In massive MIMO, training is part of the game! If we point at a random direction, the signal is attenuated by 1 M. SDMA C sum =4 Blog P N Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
66 Channel State Computing the decoder or beamformer requires H s at each slot s. In many communication scenarios, training the channel state is considered as overhead. In massive MIMO, training is part of the game! If we point at a random direction, the signal is attenuated by 1 M. For massive MIMO M SDMA C sum =4 Blog P N Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
67 Channel State Computing the decoder or beamformer requires H s at each slot s. In many communication scenarios, training the channel state is considered as overhead. In massive MIMO, training is part of the game! If we point at a random direction, the signal is attenuated by 1 M. For massive MIMO M, Communication completely fails. SDMA C sum =4 Blog P N Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
68 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Fast Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
69 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Fast Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
70 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Fast Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
71 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Fast Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
72 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Fast Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
73 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Fast Variations in Frequency f = 1 Ts... Time h s (f ) Frequency Only one user can be trained! T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
74 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Slow Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
75 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Slow Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
76 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Slow Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
77 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Slow Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
78 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Slow Variations in Frequency f = 1 Ts... Time h s (f ) Frequency T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
79 Training and Pilot Dimension Pilot Dimension refers to number of users trainable over a symbol. h s (f 1 ) Slow Variations in Frequency f = 1 Ts... Time h s (f ) Frequency Several users can be trained simultaneously! T s Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
80 System Throughput A fraction of γ (0, 1) for training and 1 γ for data transmission. Training Time t c Data Frequency W Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
81 System Throughput A fraction of γ (0, 1) for training and 1 γ for data transmission. Throughput: Number of users Number of data blocks γ(1 γ). Training Time t c Data Frequency W Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
82 System Throughput A fraction of γ (0, 1) for training and 1 γ for data transmission. Throughput: Number of users Number of data blocks γ(1 γ). Maximum Throughput for γ = 1 2. Training Time t c Data Frequency W Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
83 System Throughput A fraction of γ (0, 1) for training and 1 γ for data transmission. Throughput: Number of users Number of data blocks γ(1 γ). Maximum Throughput for γ = 1 2. Training Time t c Data Frequency W Here we have a fading channel Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
84 System Throughput A fraction of γ (0, 1) for training and 1 γ for data transmission. Throughput: Number of users Number of data blocks γ(1 γ). Maximum Throughput for γ = 1 2. Training Time t c Data Frequency W Here we have a fading channel with no channel state at transmitter or receiver. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
85 System Throughput A fraction of γ (0, 1) for training and 1 γ for data transmission. Throughput: Number of users Number of data blocks γ(1 γ). Maximum Throughput for γ = 1 2. Training Time t c Data Frequency W Here we have a fading channel with no channel state at transmitter or receiver. Is this pilot training optimal? Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
86 Information-theoretic Optimality Grassmannian Packing for i.i.d. fading in the high-snr regime 1 : M antennas, K users, T length of coherence block where C sum M (1 M ) log SNR + O(1) T M = min{m, K, T 2 } 1 Lizhong Zheng and David NC Tse. Communication on the Grassmann manifold: A geometric approach to the noncoherent multiple-antenna channel. In: Information Theory, IEEE Transactions on 48.2 (2002), pp Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
87 Information-theoretic Optimality Grassmannian Packing for i.i.d. fading in the high-snr regime 1 : M antennas, K users, T length of coherence block where C sum M (1 M ) log SNR + O(1) T M = min{m, K, T 2 } For massive MIMO M, this bound is tight for K = T 2 : use UL training and DL precoding (e.g., ZFBF), with M orthogonal pilots per coherence block. 1 Lizhong Zheng and David NC Tse. Communication on the Grassmann manifold: A geometric approach to the noncoherent multiple-antenna channel. In: Information Theory, IEEE Transactions on 48.2 (2002), pp Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
88 Why Massive MIMO? By increasing the number of antennas M, the effect of noise and interference disappears 2 y = hx + K h k x k + n. k=2 2 Thomas L Marzetta. Noncooperative cellular wireless with unlimited numbers of base station antennas. In: IEEE Transactions on Wireless Communications 9.11 (2010), pp Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
89 Why Massive MIMO? By increasing the number of antennas M, the effect of noise and interference disappears 2 Even for a simple decoding y = hx + K h k x k + n. k=2 x = hh y K h 2 = x + h H h k h 2 x k + hh n h 2, k=2 the effect of noise+interference decays proportionally to K M Gaussian channel vector model. under i.i.d. 2 Thomas L Marzetta. Noncooperative cellular wireless with unlimited numbers of base station antennas. In: IEEE Transactions on Wireless Communications 9.11 (2010), pp Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
90 Challenges in Massive MIMO In practice, synchronous sampling of M antennas is challenging. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
91 Challenges in Massive MIMO In practice, synchronous sampling of M antennas is challenging. Massive MIMO gain appears around M 64. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
92 Challenges in Massive MIMO In practice, synchronous sampling of M antennas is challenging. Massive MIMO gain appears around M 64. The channel vectors are not fully i.i.d. but spatially correlated M K larger. must be Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
93 Challenges in Massive MIMO In practice, synchronous sampling of M antennas is challenging. Massive MIMO gain appears around M 64. The channel vectors are not fully i.i.d. but spatially correlated M K larger. There are other problems such as pilot contamination. must be Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
94 Summary and Conclusion We discussed the mathematical and system-level aspects of: single-antenna time-variant wireless channels, MIMO wireless channels, massive MIMO wireless channels. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
95 Summary and Conclusion We discussed the mathematical and system-level aspects of: single-antenna time-variant wireless channels, MIMO wireless channels, massive MIMO wireless channels. Although the signal in a massive MIMO is high-dim it has low-dim structures in practice. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
96 Summary and Conclusion We discussed the mathematical and system-level aspects of: single-antenna time-variant wireless channels, MIMO wireless channels, massive MIMO wireless channels. Although the signal in a massive MIMO is high-dim it has low-dim structures in practice. Compressed sensing techniques are applied in almost all applications. Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
97 Summary and Conclusion We discussed the mathematical and system-level aspects of: single-antenna time-variant wireless channels, MIMO wireless channels, massive MIMO wireless channels. Although the signal in a massive MIMO is high-dim it has low-dim structures in practice. Compressed sensing techniques are applied in almost all applications. To be discussed in the next talk... Saeid Haghighatshoar (TU Berlin) Massive MIMO I SPP 1798, December / 33
98 Questions?
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