The DoF of the MIMO Y-channel Anas Chaaban, Karlheinz Ochs, and - PowerPoint PPT Presentation

RUB Chair of Communication Systems The DoF of the MIMO Y-channel Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin Chair of Digital Communication Systems RUB, Bochum Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 1

RUB Chair of Communication Systems Outline 1 Introduction and previous work 2 MIMO Y-channel 3 Transmission Strategy An Example Generalization 4 Upper Bounds 5 Conclusion Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 2

RUB Chair of Communication Systems The Y-channel Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 3

RUB Chair of Communication Systems The Y-channel Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 3

RUB Chair of Communication Systems The Y-channel Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 3

RUB Chair of Communication Systems The Y-channel Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 3

RUB Chair of Communication Systems The Y-channel Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 3

RUB Chair of Communication Systems The Y-channel Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 3

RUB Chair of Communication Systems The Y-channel Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 3

RUB Chair of Communication Systems The Y-channel Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 3

RUB Chair of Communication Systems 1 Introduction and previous work 2 MIMO Y-channel 3 Transmission Strategy An Example Generalization 4 Upper Bounds 5 Conclusion Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 4

RUB Chair of Communication Systems Two-way Communications • Bi-directional channel (Two-way channel) [Shannon 61] Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 5

RUB Chair of Communication Systems Two-way Communications • Bi-directional channel (Two-way channel) [Shannon 61] • Bi-directional relay channel (BRC) [Rankov et al. 05] Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 5

RUB Chair of Communication Systems Two-way Communications • Bi-directional channel (Two-way channel) [Shannon 61] • Bi-directional relay channel (BRC) [Rankov et al. 05] • Capacity of the BRC within 1/2 bit [G¨ und¨ uz et al. 08] Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 5

RUB Chair of Communication Systems Two-way Communications • Bi-directional channel (Two-way channel) [Shannon 61] • Bi-directional relay channel (BRC) [Rankov et al. 05] • Capacity of the BRC within 1/2 bit [G¨ und¨ uz et al. 08] • Deterministic BRC [Avestimehr et al. 09] Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 5

RUB Chair of Communication Systems Multi-way Communications • Approximate capacity of the multi-pair BRC [Sezgin et al. 09] Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 6

RUB Chair of Communication Systems Multi-way Communications • Approximate capacity of the multi-pair BRC [Sezgin et al. 09] • Approximate capacity of the multi-way relay channel (multicast) [G¨ und¨ uz et al. 09], [Ong et al. 10] Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 6

RUB Chair of Communication Systems Multi-way Communications • Approximate capacity of the multi-pair BRC [Sezgin et al. 09] • Approximate capacity of the multi-way relay channel (multicast) [G¨ und¨ uz et al. 09], [Ong et al. 10] • Capacity region of the Y-channel within 7/6 bit [Chaaban et al. 12] Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 6

RUB Chair of Communication Systems 1 Introduction and previous work 2 MIMO Y-channel 3 Transmission Strategy An Example Generalization 4 Upper Bounds 5 Conclusion Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 7

RUB Chair of Communication Systems The MIMO Y-channel Uplink: • Tx signals x j ( i ) ∈ R M j , power P Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 8

RUB Chair of Communication Systems The MIMO Y-channel Uplink: • Tx signals x j ( i ) ∈ R M j , power P • Uplink channels H j ∈ R N × M j , Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 8

RUB Chair of Communication Systems The MIMO Y-channel Uplink: Downlink: • Tx signals x j ( i ) ∈ R M j , power P • Uplink channels H j ∈ R N × M j , Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 8

RUB Chair of Communication Systems The MIMO Y-channel Uplink: Downlink: • Tx signals x j ( i ) ∈ R M j , power P • Relay signal x r ( i ) ∈ R N , power P • Uplink channels H j ∈ R N × M j , Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 8

RUB Chair of Communication Systems The MIMO Y-channel Uplink: Downlink: • Tx signals x j ( i ) ∈ R M j , power P • Relay signal x r ( i ) ∈ R N , power P • Uplink channels H j ∈ R N × M j , • Downlink channels D j ∈ R M j × N , Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 8

RUB Chair of Communication Systems The MIMO Y-channel Uplink: Downlink: • Tx signals x j ( i ) ∈ R M j , power P • Relay signal x r ( i ) ∈ R N , power P • Uplink channels H j ∈ R N × M j , • Downlink channels D j ∈ R M j × N , DoF R jk The DoF per message is defined as d jk = lim P →∞ 2 log( P ) , and the sum DoF 1 is d = � d jk . Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 8

RUB Chair of Communication Systems MIMO Y-channel If the MIMO Y-channel has M 1 = M 2 = M 3 = M and N ≥ ⌈ 3 M/ 2 ⌉ , then the cut-set bound is achievable, i.e., d = 3 M [Lee et al. 10]. Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 9

RUB Chair of Communication Systems MIMO Y-channel If the MIMO Y-channel has M 1 = M 2 = M 3 = M and N ≥ ⌈ 3 M/ 2 ⌉ , then the cut-set bound is achievable, i.e., d = 3 M [Lee et al. 10]. Question 1: What is the DoF of the MIMO Y-channel in general? Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 9

RUB Chair of Communication Systems MIMO Y-channel If the MIMO Y-channel has M 1 = M 2 = M 3 = M and N ≥ ⌈ 3 M/ 2 ⌉ , then the cut-set bound is achievable, i.e., d = 3 M [Lee et al. 10]. Question 1: What is the DoF of the MIMO Y-channel in general? Question 2: Is the DoF characterized by the cut-set bounds? Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 9

RUB Chair of Communication Systems MIMO Y-channel If the MIMO Y-channel has M 1 = M 2 = M 3 = M and N ≥ ⌈ 3 M/ 2 ⌉ , then the cut-set bound is achievable, i.e., d = 3 M [Lee et al. 10]. Question 1: What is the DoF of the MIMO Y-channel in general? Question 2: Is the DoF characterized by the cut-set bounds? Theorem The DoF of the MIMO Y-channel with M 1 ≥ M 2 ≥ M 3 (wlog) is given by d = min { M 1 + M 2 + M 3 , } . � �� � Cut-set bound Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 9

RUB Chair of Communication Systems MIMO Y-channel If the MIMO Y-channel has M 1 = M 2 = M 3 = M and N ≥ ⌈ 3 M/ 2 ⌉ , then the cut-set bound is achievable, i.e., d = 3 M [Lee et al. 10]. Question 1: What is the DoF of the MIMO Y-channel in general? Question 2: Is the DoF characterized by the cut-set bounds? Theorem The DoF of the MIMO Y-channel with M 1 ≥ M 2 ≥ M 3 (wlog) is given by d = min { M 1 + M 2 + M 3 , 2 M 2 + 2 M 3 , 2 N } . � �� � � �� � Cut-set bound New bounds Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 9

RUB Chair of Communication Systems 1 Introduction and previous work 2 MIMO Y-channel 3 Transmission Strategy An Example Generalization 4 Upper Bounds 5 Conclusion Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 10

RUB Chair of Communication Systems Transmission Strategy Transmission strategy is signal-space alignment for network-coding [Lee et al. 10] with asymmetric DoF allocation • The signals H 1 x 1 , H 2 x 2 , and H 3 x 3 fill the entire space at the relay Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 11

RUB Chair of Communication Systems Transmission Strategy Transmission strategy is signal-space alignment for network-coding [Lee et al. 10] with asymmetric DoF allocation • The signals H 1 x 1 , H 2 x 2 , and H 3 x 3 fill the entire space at the relay • Relay zero-forces H 2 x 2 using N 13 and H 3 x 3 using N 12 Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 11

RUB Chair of Communication Systems Transmission Strategy Transmission strategy is signal-space alignment for network-coding [Lee et al. 10] with asymmetric DoF allocation • The signals H 1 x 1 , H 2 x 2 , and H 3 x 3 fill the entire space at the relay • Relay zero-forces H 2 x 2 using N 13 and H 3 x 3 using N 12 • Result: N 12 H 1 x 1 + N 12 H 2 x 2 (2D) and N 13 H 1 x 1 + N 13 H 3 x 3 (1D) Anas Chaaban, Karlheinz Ochs, and Aydin Sezgin DoF of the MIMO Y-Channel 11