Millimeter Wave Hybrid Beamforming with DFT-MUB Aided Precoder Codebook Design K. Satyanarayana ∗ University of Southampton & † InterDigital Supervisors: Mohammed El-Hajjar ∗ , Ping-Heng Kuo † , Alain Mourad † , Lajos Hanzo ∗ ks1r15@soton.ac.uk www.satyanarayana.xyz 1 / 18
Overview mmWave Challenges 1 mmWave Architectures 2 Hybrid Architecture Conceived 3 DFT-MUB Precoder Codebook Design 4 Results 5 Conclusions 6 2 / 18
mmWave Challenges 10 2 5 Attenuation 2 10 Specific Attenuation (dB/km) 5 mmWave transmitter 2 1 5 2 10 -1 5 2 -2 10 5 Oxygen (O 2 ) 2 -3 10 -3 Water Vapour (H 2 O), = 7.5 g.m 5 Light Rain (2 mm/hr) Heavy Rain (50 mm/hr) 2 10 -4 50 100 150 200 250 300 Frequency (GHz) Receiver Wall mmWave transmitter Reflection Diffraction Blocked sub-3 GHz transmitter Transmitter I. A. Hemadeh, K. Satyanarayana , M. El-Hajjar, L. Hanzo “Millimeter-Wave Communications: Physical Channel Models, Design Considerations, Antenna Constructions and Link-Budget” IEEE Communications Surveys & Tutorials submitted. 3 / 18
mmWave Challenges Directional transmission is employed to mitigate the losses Conventional MIMO heavily relies on digital signal processing ◮ Dedicated RF chains (ADCs) for every antenna element Large number of antennas can be accommodate in compact space at mmWave frequencies ◮ Employing RF chains per antenna would incur more cost and complexity Analog signal processing combined with digital processing, termed hybrid beamforming is a plausible solution State-of-the-art hybrid beamforming designs include fully-connected architecture and sub-array-connected architecture 4 / 18
Fully-Connected Architecture + + � + + N r . . . . mmWave . . Channel N t F RF y s N s F BB H W RF W BB N RF N RF N c N ray t r . . . . . . + + The phase shifters of each RF chain are connected to all the transmit antennas Number of phase shifters required is equal to N t N RF t 5 / 18
Sub-Array-Connected Architecture λ/ 2 . . . . . λ/ 2 mmWave . N t N r . s y N s F BB . . Channel . W BB N c , N ray N RF N RF . t F RF H W RF . r . . . . . . . . The phase shifters of each RF chain are connected to only a subset of transmit antennas Number of phase shifters required is equal to N t Thus, the sub-array based architecture is more energy-efficient and cost-efficient than the fully-connected architecture 6 / 18
Hybrid Design Conceived mmWave Channel Cluster 1 N ray N t N sub H 1 d mmWave Channel . y . Cluster 2 N r . N ray s F BB Ns W BB Nt N RF W RF N sub H 2 r . . . F RF . . . . mmWave Channel N sub . Cluster . N ray . H N sub In contrast to state-of-the-art sub-array design, in this design, the sub-arrays are separated by a sufficiently large distance d, so that the they experience independent fading Thus, this design is capable of providing both diversity and BF gains K. Satyanarayana, et al. ”Dual-Function Hybrid Beamforming and Transmit Diversity Aided Millimeter Wave Architecture” in IEEE Trans. Veh. Technol. 2017 7 / 18
Hybrid Design Conceived 10 Full-connected 2 sub-arrays connected (proposed) 9 Parameters Values 4 sub-arrays connected (proposed) 8 sub-arrays connected (proposed) 8 N c 4 2 sub-arrays connected (state-of-the-art) Achievable Rate (bps/Hz) 7 N ray 6 6 N t 64 5 N r 32 N s 2 4 N RF 2 3 t N RF 2 2 r φ n ray ∼ U [0 , 2 π ) n c 1 0 -40 -35 -30 -25 -20 -15 -10 -5 0 SNR [dB] Proposed design performs superior to fully-connected design However, the performance begins to degrade when the number of sub-arrays is larger than 2 K. Satyanarayana, et al. ”Dual-Function Hybrid Beamforming and Transmit Diversity Aided Millimeter Wave Architecture” in IEEE Trans. Veh. Technol. 2017 8 / 18
Conceived Hybrid Design This result is independent of the precoder and the combiner used at the transmitter and the receiver, respectively! K. Satyanarayana, et al. ”Dual-Function Hybrid Beamforming and Transmit Diversity Aided Millimeter Wave Architecture” in IEEE Trans. Veh. Technol. 2017 9 / 18
System Model + + � + + N r . . . . . mmWave . Channel N t F RF y s N s F BB W RF H W BB N RF N RF N c N ray t r . . . . . . + + The received signal vector y after hybrid precoding and combining is given by Received Signal Vector √ P W H BB W H RF HF RF F BB s + W H BB W H y = RF n (1) Channel Model N ray � N c N r N t α n ray n c a r ( φ n ray t ( φ n ray � � n c ) a T H = n c ) , (2) N c N ray n c =1 n ray =1 10 / 18
DFT-MUB Precoder Codebook Design We have H = U Σ V H RF Beamformer using Discrete Fourier Transform (DFT) at the Tx < DFT N t (: , i ) , v j >, 1 ≤ i ≤ N RF F RF (: , i ) = max t ; 1 ≤ j ≤ N t (3) i where v j is the j th vector of the right singular matrix of the channel matrix H and DFT N t (: , i ) is the i th column of the N t × N t DFT matrix. RF Combiner (DFT) at the Rx < DFT N r (: , i ) , u j >, 1 ≤ i ≤ N RF W RF (: , i ) = max , 1 ≤ j ≤ N t (4) r i where u j is the j th vector of the left singular matrix of the channel and DFT N r (: , i ) is the i th column of the N r × N r DFT matrix. 11 / 18
DFT-MUB Precoder Codebook Design The baseband precoder F BB is constructed from the mutually unbiased bases (MUBs). Motivation The motivation behind the choice of an MUB assisted codebook is that the entries of the matrix constructed from MUBs for powers of 2 are observed to be composed of finite alphabets i.e., { 1 , − 1 , i , − i } , which would significantly reduce the computational complexity. The total number of MUBs for a given dimension N is limited and is equal to N+1. 12 / 18
DFT-MUB Precoder Codebook Design For example, we consider the scenario where the transmitter is equipped with N RF t = 4 RF chains. For N RF = 4, the MUBs are given by t 1 1 1 1 1 1 1 1 A = 1 B = 1 1 1 − 1 − 1 − 1 − 1 1 1 , 1 − 1 − 1 1 − i − i 2 2 i i 1 − 1 1 − 1 − i i − i i 1 1 1 1 1 1 1 1 C = 1 , D = 1 − i − i i i i i − i − i . − i − i 1 − 1 − 1 1 2 i i 2 − 1 1 − 1 1 − i i − i i Thus 5 MUBs are obtained along with Identity matrix, which is also an MUB. 13 / 18
DFT-MUB Precoder Codebook Design Baseband Precoder F BB The baseband precoder F BB is chosen from the codebook F = { A 0 , A 1 , A 2 , A 3 , B 0 , B 1 , B 2 , B 3 , C 0 , C 1 , C 2 , C 3 , D 0 , D 1 , D 2 , D 3 } , which maximizes the minimum SNR and it is given by F desired = arg max F BB ∈F Λ min { H eff F BB } , (5) BB where H eff = W H RF HF RF . Baseband Combiner W BB The baseband combiner is chosen as the linear minimum mean squared error (LMMSE). 14 / 18
Simulation Results 7 Unconstrained Precoding (SVD) Orthogonal Matching Pursuit 6 DFT-MUB Codebook Parameters Values DFT-Identity Achievable Rate (bps/Hz) N c 4 5 Solid line: 32 16 MIMO Dashed line: 8 8 MIMO 6 N ray 4 N t 32, 8 32 16 MIMO 16, 8 N r 3 N s 2 N RF 4 t 2 N RF 2 r φ n ray ∼ U [0 , 2 π ) n c 8 8 MIMO 1 0 -40 -35 -30 -25 -20 -15 -10 -5 0 SNR [dB] Fig. Fully-connected architecture. DFT-MUB based codebook design with 4-bit feedback and different other methods relying on perfect CSI for 32 × 16 and 8 × 8 MIMO, and N s = 2 and N RF = 4 , N RF = 2. t r 15 / 18
Simulation Results 10 Optimal Unconstrained Precoding (SVD) 9 DFT-MUB Aided Codebook Unconstrained SIC-based Beamforming Achievable Rate (bps/Hz) Parameters Values 8 DFT-Identity Aided Beamforming 4 N c 7 N ray 6 6 64 N t 5 N r 32 2 N s 4 N RF 2 t 3 N RF 2 r φ n ray 2 ∼ U [0 , 2 π ) n c 1 0 -40 -35 -30 -25 -20 -15 -10 -5 0 SNR [dB] Fig. Proposed 2-sub-array-connected for 64 × 32 MIMO, using DFT-MUB based codebook design with 4-bit feedback using N s = 1 , N RF sub = 1, N sub = 2. 16 / 18
Conclusions Proposed a new architecture where we analyzed that 2-sub-array-connected design is the optimal in terms of achievable rate Further, we have proposed a low-complexity hybrid precoder codebook design that performs close to the optimal precoder K. Satyanarayana, et al. ”Dual-Function Hybrid Beamforming and Transmit Diversity Aided Millimeter Wave Architecture” in IEEE Trans. Veh. Technol. 2017 17 / 18
ks1r15@soton.ac.uk www.satyanarayana.xyz 18 / 18
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