Wideband Channel Tracking for mmWave MIMO
System with Hybrid Beamforming Architecture
Han Yan, Shailesh Chaudhari,
and Prof. Danijela Cabric
Dec. 13th 2017
D. Markovic / Slide 2
Intro: Tracking in mmW MIMO
MMW network features massive arrays– Beamforming gain in Tx & Rx to
compensate propagation loss
– Multiplexing gain for throughput boost
– Reduced interference
– Vulnerable to beam misalignment
2
BS sector
Fig. BS and UE needs to adaptively change beamformer for reliable communication in mmW MIMO system
t0
t1
Channel state information (CSI) is crucial in mmW MIMO – Channel estimation: training w/o using priori knowledge
● Widely used in sub-6GHz band
● High training overhead in mmW
– Channel tracking: updates CSI w/ priori knowledge
● Potentially reduce overhead
Rx beam
Tx beam
D. Markovic / Slide 3
Outlines
Mobile channel model for algorithm design & evaluation– 3GPP narrowband mobile model for above-6GHz band
– Wideband mmW mobile model
CSI tracking algorithm design– Propagation angle tracking
– Compressive sensing based narrow-band channel tracking
– Proposed wideband channel tracking
Performance-complexity study on tracking algorithms – SINR and achievable rate
– Training overhead
– Computational complexity
3
D. Markovic / Slide 4
DSP
...
mmW UE
ADCDSP
...
mmW BS
DAC
...
Rx ULATx ULA
System Model
Symbol Description Symbol Description
𝑁R, 𝑁T Rx/Tx antenna size𝐰𝑚, 𝐯𝑚
Beamformer of 𝑚𝑡ℎ channel probing in Tx and Rx𝜙, 𝜃 Angle of arrival (AOA); Angle of departure (AOD)
𝐚R(𝜙)𝐚T(𝜃)
Spatial response of ULA of specific angle;
𝑔𝑚
Post-Beamforming channel
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Precoder 𝐰𝑚 Combiner 𝐯𝑚MIMO
Channel 𝐇
2D narrow band mmW channel model (𝐿 paths)
Post-BF Channel 𝑔𝑚
D. Markovic / Slide 5
3GPP spatially-consistent UT mobility modelling [G17]
– Channel variation 𝐇(𝑛) determined by 𝛼𝑙(𝑛)
, 𝜃𝑙(𝑛)
, and 𝜙𝑙(𝑛)
– At 𝑡0: set BS, UE scatterer location; channel coefficient initialization
– At 𝑡𝑛: update channel coefficient from 𝑡𝑛−1
Narrowband Dynamic Channel Model
5
2D moving trajectory
UE Location
Speed: 𝑣[cos(𝛽) sin(𝛽)]T
BS Location
Channel coeff. at 𝑡𝑛−1{𝜙𝑙
𝑛−1, 𝜏𝑙
𝑛−1, 𝛼𝑙
(𝑛−1)}
Channel coeff. at 𝑡𝑛{𝜙𝑙
(𝑛), 𝜏𝑙
(𝑛), 𝛼𝑙
(𝑛)}
ScattererAOA
Gain (from delay)
Channel Coefficients updates (𝛥𝑡 = 𝑡𝑛-𝑡𝑛−1)
𝛽
𝝓𝒍
D. Markovic / Slide 6
Wideband Dynamic Channel Model
6
ScattererCluster
UE Location
Channel coeff. at 𝑡𝑛−1{𝜙𝑙,𝑟
𝑛−1, 𝜏𝑙,𝑟
𝑛−1, 𝛼𝑙,𝑟
(𝑛−1)}
Channel coeff. at 𝑡𝑛{𝜙𝑙,𝑟
(𝑛−1), 𝜏𝑙,𝑟
(𝑛−1), 𝛼𝑙,𝑟
(𝑛−1)}
Modified model for wideband channel– 𝑅 rays within each of 𝐿 multipath clusters
– Pulse shaping function 𝑝c(𝑡) due to band-limited nature in T/Rx
– UE 2D moving: channel parameters evolve with similar manner
– UE rotation: AOA of all rays incremented by 𝑣r ⋅ Δ𝑡
D. Markovic / Slide 7
Wideband Dynamic Channel Model
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Time & freq. domain WB mobile channel
Frequency Domain (subcarrier 𝑘)Discrete Time Domain (delay 𝑑)
[WSH+16] Y. Wang, Z. Shi, L. Huang, Z. Yu, and C.Cao, “An Extension of Spatial Channel Modelwith Spatial Consistency,” in Proc. IEEE 84thVehicular Technology Conference (VTC-Fall),2016, pp. 1–5.
Top: Simulated results of delayprofile & AOA versus time 𝑡𝑛 usingproposed model
Bottom: Measured results in denseurban environment (at 73 GHz)[WSH+16]
Illustration of mobile channel simulation
D. Markovic / Slide 8
Problem Statement
Tracking procedure at 𝑡𝑛– BS sends 𝑀 beacons with
– UE measures post-BF channel
𝑔𝑚(𝑛)
[𝑘] with
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Update chan. parameters
{𝜶𝒍,𝒓(𝒏−𝟏)
, 𝝓𝒍,𝒓(𝒏−𝟏)
, 𝝉𝒍,𝒓(𝒏−𝟏)
}
Chan. measurement
using 𝐖𝒎(𝒏−𝟏)
and 𝐕𝒎(𝒏−𝟏)
Update chan. parameters
{𝜶𝒍,𝒓(𝒏), 𝝓𝒍,𝒓
(𝒏), 𝝉𝒍,𝒓
(𝒏)}
Chan. measurement
using 𝐖𝒎(𝒏)
and 𝐕𝒎(𝒏)
𝑡𝒏−𝟏 𝑡𝒏
𝑔𝑚(𝑛−1)
[𝑘] 𝑔𝑚(𝑛)
[𝑘]
Rx ULATx ULA
DSP
...
mmW UE
ADCDSP
...
mmW BS
DAC
... ..
.
...
𝐯𝑚(𝑛)
𝐇f(𝑛)
[𝑘]
𝒈𝒎(𝒏)[𝒌]
𝐰𝑚(𝑛)
Tracking objective– Given probing beamformer 𝐖 𝑛 and 𝐕 𝑛 , design tracking algorithm to
update channel parameters
D. Markovic / Slide 9
Prior-Art: AOA Tracking
Tracking via angle refinement – Probing beams: narrow beams
– Previous CSI*: 𝜃 and 𝜙(𝑛−1)
– Algorithm: RSS measurement into neighbor angles
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Fig. UE refines steer angle based on pointing direction from previous time slot
Steering angle at 𝑡𝑛−1
Neighbor steering angle trial at tn
Adopted in IEEE802.11ad (Beam Refinement Protocol) [NCF+14]– Low computational complexity: energy measurement & comparison
* Dominant propagation angle is tracked and subscription 𝑙 is omitted; Can be extension to all angles[NCF+14] Nitsche et al, “IEEE 802.11ad: directional 60 GHz communication for multi-Gigabit-per-second Wi-Fi [Invited Paper],” IEEE Commun. Mag., vol. 52, no. 12, p. 132, 2014.
D. Markovic / Slide 10
Compressive narrowband (NB) chan. probing procedure – Probing beams: quasi-omni beams
● Fixed over 𝑛
● Pseudorandom value {±1 ± 1𝑗} in elements of 𝐖 and 𝐕
● Probe all angles in a compressed manner
– Previous CSI: መ𝜃𝑙, 𝜙𝑙(𝑛−1)
and ො𝛼𝑙(𝑛−1)
– Measured post-BF channel
Prior-Art: NB Channel Tracking
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[MRM16] Z. Marzi, D. Ramasamy, and U. Madhow, “Compressive Channel Estimation and Tracking for Large Arrays in mm-Wave Picocells,” IEEE J. Sel. Topics Signal Process., vol. 10, no. 3, pp. 514–527, Apr. 2016.
𝜃𝑙 is assumed to be known and constant; Such constant (Tx gain) is absorbed in 𝛼𝑙
Post beamforming noise
– Adapted from [MRM16]
D. Markovic / Slide 11
Prior-Art: NB Channel Tracking
Parameter updating algorithm for NB channel
– Alternative update estimated path gain 𝛼𝑙(𝑛)
and AOA 𝜙𝑙(𝑛)
based on 𝐠(𝑛)
– Each step can be approximately solved by LS
– Moderate complexity: pseudo-inverse of a 𝑀 ×𝑁t matrix
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Gain update step for all 𝑙
AOA update step for all 𝑙
next tracking slot
D. Markovic / Slide 12
Proposed wideband (WB) channel probing procedure – Probing beams: 𝐿 narrow beams for each of the cluster
– Previous CSI*: 𝜃𝑙,𝑟, 𝜙𝑙,𝑟(𝑛−1)
, 𝜏𝑙,𝑟(𝑛−1)
, and 𝛼𝑙,𝑟(𝑛−1)
– Measured effective channel (1st probing beam for example)
WB Channel Tracking Procedure
𝐚T( ഥ𝜃𝑙) 𝐚R ത𝜙𝑙(𝑛−1)
𝑙 ≤ 𝐿
ഥ𝜃𝑙 ത𝜙𝑙(𝑛−1)
𝑙
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From other multipath cluster & AWGN; Treated as effective noise
D. Markovic / Slide 13
WB Channel Tracking Algorithm
Channel coefficients update algorithm
13
Delay Refinement: update delay coeff. via
where and is the post-BF channel w/ estimated channel coeff at 𝑡𝑛−1
Angle Refinement: updates AOA coeff. via
where with other coeff. at 𝑡𝑛−1
Gain Refinement: solve for
where and is matrix with other coeff. at 𝑡𝑛−1
D. Markovic / Slide 14
Channel Parameter Initialization
Tracking requires channel coeff. estimation at 𝑡0– Assuming rough angle estimation ҧ𝜃1 and ത𝜙1 are reached
– Use 𝐚T(𝜃1) and 𝐚R ത𝜙1(𝑛−1)
for post-BF channel probing 𝐠1(0)
– Orthogonal matching pursuit (OMP) based initialization
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Dictionary
The 𝑝th column contains freq-domain support due to delay pΔ𝜏
The post-BF channel probing results
𝒈1(0)
consists of up to 𝑅 supports
Set of selected index 𝒯
Contains selected 𝜏1,𝑟 items
D. Markovic / Slide 15
Metric: spectral efficiency (SE) after beamforming– Scenario of transmission 1 stream
Performance Metrics
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𝐰data[𝑘] 𝐯data[𝑘]
𝒂t(𝜃) 𝒂r(𝜙) 𝜃 𝜙
𝐇
𝐇f[𝑘]𝑘th
𝐇f[𝑘]𝑘th
𝑡0
𝐇f[𝑘]𝑘th 𝑡0
– SVD based beamforming 𝐰data and 𝐯data as primary eigenvector of MIMO channel
– As SE upper bound for actual hybrid architecture
– BF w/ NB CSI: same BF for all sub-carriers
– BF w/ WB CSI: unique BF for each sub-carrier
D. Markovic / Slide 16
Simulation: SE v.s. Time
16
Fig. spectral efficiency over time with CSI from tracking;
𝑁T = 𝑁R = 16
• 𝐿• 𝑅
•
•
• 𝐾
• 𝑁s
D. Markovic / Slide 17
Training Overhead
Re-estimation
(w/o Tracking)
Prop. Angle
Tracking
NB Channel
Tracking
WB Channel
Tracking
Interval btw
Channel Est. 100 ms 500 ms* 500 ms 500 ms
Channel Est.
Frame Num.256** 256 256 256
Interval btw
Tracking- 10 ms 10 ms 4 ms
Tracking Frame
Num.- 6 10 2
Overhead*** 3.84% 1.67% 2.23% 1.52%
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Overhead
* Multipath scatterers may significantly change after moving beyond coherence distance, which is assumed to be 10m (1 s w/ 10m/s speed)** Advanced channel estimation approach may significantly reduces required channel estimation frames*** A frame length is assumed to be 15𝜇𝑠; Results are conservative since additional higher layer overheads are not considered
D. Markovic / Slide 18
Conclusions & Future Works
We have proposed a wideband mmWave mobile channel model– Facilitate tracking algorithm evaluating
We have proposed a wideband channel tracking algorithm– Improved performance over narrowband tracking approach by using lower
training overhead
Future works– Study the impact of probing beamformer in tracking performance
– Study the overhead & capacity trade-off in channel tracking
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D. Markovic / Slide 19
Thanks for your attention!
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D. Markovic / Slide 20
References
[G17] 3GPP, “TR38.900 Study on channel model for frequency spectrum above 6 GHz (Release 14),” Jul. 2017 [online available] http://www.3gpp.org/DynaReport/38-series.htm
[M17] 5GPPP, “mmMAGIC project D2.2 Measurement Results and Final mmMAGIC Channel Models,” May. 2017 [online available] https://5g-mmmagic.eu/results/#deliverables
[NCF+14] Nitsche et al, “IEEE 802.11ad: directional 60 GHz communication for multi-Gigabit-per-second Wi-Fi [Invited Paper],” IEEE Commun. Mag., vol. 52, no. 12, p. 132, 2014.
[WSH+16] Y. Wang, Z. Shi, L. Huang, Z. Yu, and C. Cao, “An Extension of Spatial Channel Model with Spatial Consistency,” in Proc. IEEE 84th Vehicular Technology Conference (VTC-Fall), 2016, pp. 1–5.
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