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Some Aspects on Hybrid Wideband Transceiver Design formmWave Communication Systems
Marcin Iwanow12, Nikola Vučić1, Mario H. Castañeda1, Jian Luo1, Wen Xu,1 and Wolfgang Utschick21Huawei Technologies Duesseldorf GmbH, Munich, Germany
2Associate Institute for Signal Processing, Technische Universität München, Germany
Introduction
mmWave frequency ranges are considered tobe a key enabler for extremely highthroughput in 5GPrincipal issues to solve on the PHY layer:transmit/receive strategy, channelestimation/tracking, multi-usercommunication, waveform design, etc.Our focus: Broadband transceiver design inthe hybrid beamforming architecture
Problem Description
Assuming perfect CSI, define the transmitand receive strategies for a multitap channel
Main issues:For practical solutions, the analogbeamformers Pk,A as well as combiners Gk,Aare constant across the subcarriersComputational complexity of solutions
Relevant Work in the Literature
Narrowband solutionsExploiting channel spatial sparsity aExploiting estimated channel subspaces b
Multicarrier solutionsCodebook-based approach with suboptimalsolutions more efficient than the exhaustivesearch.cSequential searching algorithm with limitedfeedback assumption. dSolution exploiting (slowly varying) secondorder statistics. e
aO. El Ayach et al. “Spatially Sparse Precoding in Millimeter Wave MIMO Systems”bH. Ghauch et al. “Subspace Estimation and Decomposition for Hybrid Analog-Digital Millimetre-Wave MIMO systems”cC. Kim et al. “Multi-beam transmission diversity with hybrid beamforming for MIMO-OFDM systems”dA. Alkhateeb et al. “Frequency Selective Hybrid Precoding for Limited Feedback Millimeter Wave Systems”eA. Adhikary et al. “Joint Spatial Division and Multiplexing for mm-Wave Channels”
System Model
DigitalTx
Precoder
OFDM Processing:IFFT,CP insertion
OFDM Processing:IFFT,CP insertion
...
RF chain# 1
...
RF chain# NRFtx
AnalogRFTx
Precoding
ChannelH [d]
AnalogRFRx
Equalizer
RF chain# 1
...
RF chain# NRFrx
OFDM Processing:CP deletion,FFT
...
OFDM Processing:CP deletion,FFT
DigitalRx
Equalizer
...
s1
sNsubc
...
Ntx Tx antennas
...
Nrx Rx antennas
...
s̃1
s̃Nsubc
Hk =1√
Nsubc
D−1∑d=0
H[d ] exp( j2πk
Nsubcd)
s̃k = GHk,DGHk,AHkPk,APk,Dsk + GHk,DGHk,Aηk
Channel Model
H[d ] = β
√NrxNtx
L
Ncl∑l=1
N lpath∑r=1
αr ,lp(dTs − τl − τr )arx(θr ,l )aHtx(φr ,l )
Assumptions:The number of paths is significantly lowerthan for the sub-6GHz frequency band.The paths propagate in space and timeclusters.
Proposed Solution
Based on the perfect (or estimated) CSI,design optimal linear precoders andcombinersDecompose the optimalprecoding/combining matrices jointly for aset of subcarriers Ω, such that the analogcomponents are equal for all the subcarriersin the setFor the decomposition, use the (heuristic)objective of minimizing the Frobenius normof the error matrix
(Brief) Description of the Algorithms
BCD:Optimize in each iteration either the digitalor analog part. Assume the other one fixedIn each step, project the analog matrix tothe nearest (in Euclidean sense) matrix ofthe required set
OMP:In each of the NRF steps, choose a vectorfrom the codebook that has the maximalprojection on the remains of the matrixbeing decomposed.In each step, project out the selected vector
BCD Decomposition, Measured Channels
−30 −25 −20 −15 −10 −5 0 5 100
2
4
6
8
10
12
14
16
18
20
SNR [dB]
Rate[bit/c.u.]
Full digitalHybrid str., separate analog part ∀ subc.Hybrid str., |Ω| = 1Hybrid str., |Ω| = 3Hybrid str., |Ω| = 10Hybrid str., |Ω| = Nsubc
Formal Description
(P?Ω,A,P?Ω,D
)= arg min
PΩ,A,PΩ,D‖P?Ω − PΩ,APΩ,D‖F
s.t. ‖PΩ,APΩ,D‖2F ≤ |Ω|Ptx
Nsubc, PΩ,A ∈ PA
where
P?Ω =[P?ω1 , . . . ,P
?ω|Ω|
]∈ CNrx×(|Ω|Ns),
PΩ,D =[Pω1,D, . . . ,Pω|Ω|,D
]∈ CNRFtx ×(|Ω|Ns),
PΩ,A ∈ CNtx×NRFtx
Ω ⊂ {1, . . . ,Nsubc}ωl ∈ Ω, ∀l ∈ {1, . . . , |Ω|}
BCD Decomposition, Statistical Channel Model
−30 −25 −20 −15 −10 −5 0 5 100
2
4
6
8
10
12
14
16
18
20
SNR [dB]
Rate[bit/c.u.]
Full digitalHybrid str., separate analog part ∀ subc.Hybrid str., |Ω| = 1Hybrid str., |Ω| = 3Hybrid str., |Ω| = Nsubc
−30 −25 −20 −15 −10 −5 0 5 100
2
4
6
8
10
12
14
16
18
20
SNR [dB]
Rate[bit/c.u.]
Full digitalHybrid str., separate analog part ∀ subc.Hybrid str., |Ω| = 1Hybrid str., |Ω| = 3Hybrid str., |Ω| = Nsubc
OMP Decomposition, Measured Channels
−30 −25 −20 −15 −10 −5 0 5 100
2
4
6
8
10
12
14
16
18
20
SNR [dB]
Rate[bit/c.u.]
Full digitalHybrid str., separate analog part ∀ subc.Hybrid str., |Ω| = 1Hybrid str., |Ω| = 3Hybrid str., |Ω| = Nsubc
−30 −25 −20 −15 −10 −5 0 5 100
2
4
6
8
10
12
14
16
18
20
SNR [dB]
Rate[bit/c.u.]
Full digitalHybrid str., separate analog part ∀ subc.Hybrid str., |Ω| = 1Hybrid str., |Ω| = 3Hybrid str., |Ω| = Nsubc
Solutions
Considered strategies:
Full digital setup. Linear precoding withP?k and linear combining with G?k for eachsubcarrier kFull hybrid transceiver. Linear precodingwith P?k,AP?k,D and linear combining with(G?k,AG?k,D
)Hat each subcarrier.
Full hybrid transceiver. Linear precodingwith P?Ω,AP?k,D and linear combining with(G?Ω,AG?k,D
)Hat each subcarrier.
For solving the optimization problem, we useeither the Orthogonal Matching Pursuit (OMP)or the Block Coordinate Descent (BCD)algorithm
OMP Decomposition, Statistical Channel Model
−30 −25 −20 −15 −10 −5 0 5 100
2
4
6
8
10
12
14
16
18
20
SNR [dB]
Rate[bit/c.u.]
Full digitalHybrid str., separate analog part ∀ subc.Hybrid str., |Ω| = 1Hybrid str., |Ω| = 3Hybrid str., |Ω| = Nsubc
−30 −25 −20 −15 −10 −5 0 5 100
2
4
6
8
10
12
14
16
18
20
SNR [dB]
Rate[bit/c.u.]
Full digitalHybrid str., separate analog part ∀ subc.Hybrid str., |Ω| = 1Hybrid str., |Ω| = 3Hybrid str., |Ω| = Nsubc
Discussion
A practical solution for wideband linearprecoding/combining has been presentedA reduced set of subcarriers can be used fordesigning the analog transmit/receivestrategy → reduction of complexityThe choice of the decomposition algorithmis remarkably importantFuture work should consider channelestimation
Associate Institute forSignal Processing Technische Universität München
