Mehdi M. Molu, Pei Xiao, Rahim Tafazolli 22 nd Feb, 2017

Transcription

1 , Pei Xiao, Rahim Tafazolli 22 nd Feb,

2 Outline Introduction and Problem Statement State of the Art Hybrid Beamformers Massive MIMO Millimetre Wave Proposed Solution (and Motivation) Sketch of the Proof Simulation Results Hardware Set up and Future Plan Conclusion Optimal 2/20

3 Introduction and Problem Statement Massive MIMO and millimetre wave communications are two potential candidate technologies for 5G. In fact, the concept of mmwave is already deployed in several standards (IEEE ad (ay), c). Large number of antennas in the system forces us to use hybrid (digital/analogue) beamforming techniques to i. avoid high costs of chains, ADC, DAC ii. reduce hardware operating costs (e.g., insertion loss). Base Band Precoder F BB Fully Connected F 3/20

4 Introduction and Problem Statement Massive MIMO and millimetre wave communications are two potential candidate technologies for 5G. In fact, the concept of mmwave is already deployed in several standards (IEEE ad (ay), c). Large number of antennas in the system forces us to use hybrid (digital/analogue) beamforming techniques to i. avoid high costs of chains, ADC, DAC ii. reduce hardware operating costs (e.g., insertion loss). Base Band Precoder F BB Fully Connected F Percentage of power consumed by F [1] S.Rangan et al. Energy efficient methods for millimetre wave picocellular systems, IEEE communications workshop, 2013 [2] R. Mendez-Rial et al. Channel estimation and hybrid combining for mmwave: phase shifters or switches Information theory and application /20

5 Introduction and Problem Statement Massive MIMO and millimetre wave communications are two potential candidate technologies for 5G. In fact, the concept of mmwave is already deployed in several standards (IEEE ad (ay), c). Large number of antennas in the system forces us to use hybrid (digital/analogue) beamforming techniques to i. avoid high costs of chains, ADC, DAC ii. reduce hardware operating costs (e.g., insertion loss). Base Band Precoder F BB Fully Connected F Percentage of power consumed by F Base Band Precoder F BB Partially Connected F [1] S.Rangan et al. Energy efficient methods for millimetre wave picocellular systems, IEEE communications workshop, 2013 [2] R. Mendez-Rial et al. Channel estimation and hybrid combining for mmwave: phase shifters or switches Information theory and application /20

6 Existing Solutions The idea is to maximise the transmission rate by properly designing F and F BB : C = max log det I + R 1 n H F F BB QF BB F H H. { F, F BB } Massive MIMO systems: Using law of large number H H H I. It can also be proved that F H F I. Given the assumptions, F BB I; F is calculated using some algorithms (e.g., F = (V) or (H) [1],[2] coordinate descent algorithm [3]). [1] L. Liang et al Low Complexity Hybrid precoding in Massive Multiuser MIMO Systems, IEEE Wireless Com Letters, 2016 [2] S. Payami et al, " for Large Antenna Arrays With Phase Shifter Selection," IEEE Trans Wireless [3] F. Sohrabi et al, Hybrid Digital and Analog Beamforming Design for Large-Scale MIMO Systems, IEEE JSTSP, /20

7 Existing Solutions The idea is to maximise the transmission rate by properly designing F and F BB : C = max log det I + R 1 n H F F BB QF BB F H H. { F, F BB } Massive MIMO systems: Using law of large number H H H I. It can also be proved that F H F I. Given the assumptions, F BB I; F is calculated using some algorithms (e.g., F = (V) or (H) [1],[2] coordinate descent algorithm [3]). Millimetre Wave Communication systems: Common assumptions i. only limited number of rays arrive at the transceiver (spatially sparse channel). ii. AoD/AoD and corresponding gains are estimated. Assuming H = UΣV H opt opt and F FBB V, (near-optimal) F is calculated by exhaustive search over codebook [4] [1] L. Liang et al Low Complexity Hybrid precoding in Massive Multiuser MIMO Systems, IEEE Wireless Com Letters, 2016 [2] S. Payami et al, " for Large Antenna Arrays With Phase Shifter Selection," IEEE Trans Wireless [3] F. Sohrabi et al, Hybrid Digital and Analog Beamforming Design for Large-Scale MIMO Systems, IEEE JSTSP, 2016 [4] Robert Heath et al, Spatially Sparse Precoding in Millimeter Wave MIMO Systems IEEE Trans Wireless, /20

8 Existing Solutions The idea is to maximise the transmission rate by properly designing F and F BB : C = max log det I + R 1 n H F F BB QF BB F H H. { F, F BB } Massive MIMO systems: Using law of large number H H H I. It can also be proved that F H F I. Given the assumptions, F BB I; F is calculated using some algorithms (e.g., F = (V) or (H) [1],[2] coordinate descent algorithm [3]). Millimetre Wave Communication systems: Common assumptions i. only limited number of rays arrive at the transceiver (spatially sparse channel). ii. AoD/AoD and corresponding gains are estimated. Assuming H = UΣV H opt opt and F FBB V, (near-optimal) F is calculated by exhaustive search over codebook [4] [1] L. Liang et al Low Complexity Hybrid precoding in Massive Multiuser MIMO Systems, IEEE Wireless Com Letters, 2016 [2] S. Payami et al, " for Large Antenna Arrays With Phase Shifter Selection," IEEE Trans Wireless [3] F. Sohrabi et al, Hybrid Digital and Analog Beamforming Design for Large-Scale MIMO Systems, IEEE JSTSP, 2016 [4] Robert Heath et al, Spatially Sparse Precoding in Millimeter Wave MIMO Systems IEEE Trans Wireless, 2014 Note: The solutions are (i) system/channel specific and (ii) sub/near optimal if not used in the specific scenario. 8/20

9 Proposed Hybrid Beamformer Define transmission rate as follows C = max log det I + R 1 n H F F BB QF BB F H H. { F, F BB } Proposed Algorithm for Designing F : Assuming H = UΣV H Step I: - set r 21 = sign{im v 11 v 21 } v 11 v 21 - set δ 21 = Arccos ( Re(v 11 v 21 ) ) r 21 V = F = exp(j v 11 v 12 v 13 v 21 v 22 v 23 v 31 v 32 v θ 21 ) 9/20

10 Proposed Hybrid Beamformer Define transmission rate as follows C = max log det I + R 1 n H F F BB QF BB F H H. { F, F BB } Proposed Algorithm for Designing F : Assuming H = UΣV H Step I: - set r 21 = sign{im v 11 v 21 } v 11 v 21 V = v 11 v 12 v 13 v 21 v 22 v 23 v 31 v 32 v 33 Step II: - set δ 21 = Arccos ( Re(v 11 v 21 ) ) r 21 if (r 21 > 0) => θ 21 = δ 21 F = exp(j 0 0 θ 21 ) else θ 21 = δ 21 + π 10/20

11 Proposed Hybrid Beamformer Define transmission rate as follows C = max log det I + R 1 n H F F BB QF BB F H H. { F, F BB } Proposed Algorithm for Designing F : Assuming H = UΣV H Step I: - set r 31 = sign{im v 11 v 31 } v 11 v 31 V = v 11 v 12 v 13 v 21 v 22 v 23 v 31 v 32 v 33 - set δ 31 = Arccos ( Re(v 11 v 31 ) ) r 31 F = exp(j 0 0 θ 21 θ 31 ) Optimal 11/20

12 Proposed Hybrid Beamformer Define transmission rate as follows C = max log det I + R 1 n H F F BB QF BB F H H. { F, F BB } Proposed Algorithm for Designing F : Assuming H = UΣV H Step I: - set r 32 = sign{im v 12 v 32 } v 12 v 32 V = v 11 v 12 v 13 v 21 v 22 v 23 v 31 v 32 v 33 Step II: - set δ 32 = Arccos ( Re(v 12 v 32 ) ) r 32 if (r 32 > 0) => θ 32 = δ 32 F = exp(j 0 0 θ 21 θ 22 θ 31 θ 32 ) else θ 32 = δ 32 + π 12/20

13 (Sketch of) Proof Received signal at the receiver is y = H F F BB X = UΣV H F S Now, let us define new parameter T= V H F S t 1 t 2 t 3 = v 11 v 21 v 31 v 12 v 22 v 32 v 13 v 23 v 33 a 11 a 12 s a 21 a 1 22 s2 = a 31 a s 1 s 2 t 1 = (a 11 v 11 + a 21 v 21 + a 31 v 31 )s 1 + (a 12 v 11 + a 22 v 21 + a 32 v 31 )s 2 = s 1 t 2 = (a 11 v 12 + a 21 v 22 + a 31 v 32 )s 1 + (a 12 v 12 + a 22 v 22 + a 32 v 32 )s 2 = s 2 t 3 = (a 11 v 13 + a 21 v 23 + a 31 v 33 )s 1 + (a 12 v 13 + a 22 v 23 + a 32 v 33 )s 2 = 0 13/20

14 Simulation Results Mutual Information: R = log det I + R 1 n H F F BB Q F H BB F H H H Sparse Channel Rich Scattering Channel (Rayleigh) State-of-the-Art: Robert Heath et al, Spatially Sparse Precoding in Millimeter Wave MIMO Systems IEEE Trans Wireless, /20

15 Simulation Results Mutual Information: R = log det I + R 1 n H F F BB Q F H BB F H H H Channel: Rayleigh (unit mean) State-of-the-Art: Sohail Payami et al, "Hybrid Beamforming for Large Antenna Arrays With Phase Shifter Selection," IEEE Trans Wireless, 2016 (Lemma 2) 15/20

16 Simulation Results Mutual Information: R = log det I + R 1 n H F F BB Q F H BB F H H H Channel: Rayleigh (unit mean) State-of-the-Art: Foad Sohrabi et al, Hybrid Digital and Analog Beamforming Design for Large-Scale MIMO Systems, IEEE JSTSP, /20

17 Simulation Results (Complexity) n T : number of antennas n S : number of data streams L: 2 n Qbits Assumption n S = n Assumption A m n B n p : m p(2n 1) e.g., 4X A (ns 1)n T B nt n T + 2X A nt n T B nt n T Algorithms State-of-the-Art [1] State-of-the-Art [2] Proposed and State-of-the-Art [3] # of Operations (+,x) 2n T (2n T 1)(2n S + n T ) L(2n S 1)(L n S ) + 2 L + 1 n T n S 2n T 1 + Ln T [1] F. Sohrabi et al, Hybrid Digital and Analog Beamforming Design for Large-Scale MIMO Systems, IEEE JSTSP, 2016 [2] Robert Heath et al, Spatially Sparse Precoding in Millimeter Wave MIMO Systems IEEE Trans Wireless, 2014 [3] S. Payami et al, " for Large Antenna Arrays With Phase Shifter Selection," IEEE Trans Wireless, /20

18 Hardware Set up and Future Plan Verification: Emulation of proposed algorithm in baseband (Antenna array: 8x1) Future Plan: Prototyping a testbed with phased-array antennas in 26 GHz 18/20

19 Conclusion Advantages: F is calculated using simple functions derived in this work. Only H is required for implementing the algorithm. The proposed algorithm is generally applicable to a wide range of channels and systems, regardless the number of data streams, e.g., mm-wave, massive MIMO, fully or partially-connected. State of the art is system and/or channel specific. Low complexity and comparable performance compared to the state of the art. Disadvantages: Any disadvantage of analogue phase shifters Challenges (and future work): Regardless of the type of beamforming algorithm, initialisation (including synchronization and channel estimation) seems to be a major challenge for hybrid MIMO architectures. 19/20

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