Analysis and Optimization of an Intelligent Reflecting Surface-assisted System With Interference Ying Cui Department of Electrical Engineering Shanghai Jiao Tong University Sept. 2020 SJTU Ying Cui 1 / 56
Outline Introduction System model Rate analysis Rate optimization Comparision with system without IRS Numerical results Conclusion SJTU Ying Cui 2 / 56
Outline Introduction System model Rate analysis Rate optimization Comparision with system without IRS Numerical results Conclusion SJTU Ying Cui 3 / 56
Background ◮ Current 5G solutions require high hardware cost and energy consumption ◮ Finding spectral and energy efficient, and yet cost-effective solutions for 6G wireless networks is still imperative ◮ Intelligent Reflecting Surface (IRS) is envisioned to be a promising solution ◮ An IRS consists of nearly passive, low-cost and reflecting elements whose phase shifts can be adjusted independently by smart switches ◮ Signals reflected by an IRS can add constructively with those from the other paths to enhance the desired signal power, or destructively to cancel the interference ◮ IRSs can be practically deployed and integrated in wireless networks with low cost ◮ low profile, light weight, conformal geometry, and easy to mount/remove them on/from the wall, ceiling, building, etc SJTU Ying Cui 4 / 56
Typical IRS applications (a) User at dead (b) Physical layer zone. security. (c) User at cel- (d) Massive D2D l edge. communications. Figure: Typical IRS applications [Wu & Zhang (2020)] SJTU Ying Cui 5 / 56
Previous work ◮ Consider optimal phase shift (and beamforming) design for IRS-assisted systems where one BS serves one or multiple users with the help of one or multiple IRSs ◮ Instantaneous CSI-adaptive phase shift design: phase shifts are adjusted based on instantaneous CSI (assumed known) ◮ Maximize the weighted sum rate [Nadeem et al. (2019); Yang et al. (2019); Guo et al. (2019); Wu & Zhang (2019)], and energy efficiency [Yu et al. (2019b,a); Huang et al. (2019)] ◮ Minimize the transmission power [Wu & Zhang (2019); Jiang & Shi (2019)] ◮ Quasi-static phase shift design: phase shifts are determined by CSI statistics (Line-of-Sight (LoS) components and distributions of Non-Line-of-Sight (NLoS) components) and do not change with instantaneous CSI (assumed unknown) ◮ Consider slowly varying Non-line-of sight (NLoS) components, and minimize the outage probability [Zhang et al. (2019),Guo et al. (2020)] ◮ Consider fast varying NLoS components, and maximize the ergodic rate [Han et al. (2019); Nadeem et al. (2020)], [Hu et al. (2020)] SJTU Ying Cui 6 / 56
Previous work ◮ Quasi-static phase shift design has less frequent phase adjustment than instantaneous CSI-adaptive phase shift design ◮ All the aforementioned works ignore interference from other transmitters ◮ However, interference usually has a severe impact, especially in dense networks or for cell-edge users ◮ Consider optimal phase shift and beamforming design for IRS-assisted systems where multiple BSs serve their own users with the help of one IRS ◮ Instantaneous CSI-adaptive phase shift design in the presence of interference ◮ Consider fast varying NLoS components and maximize the weighted sum average rate [Pan et al. (2020)], [Xie et al. (2020); Ni et al. (2020)] ◮ It is highly desirable to obtain cost-efficient quasi-static design for IRS-assisted systems with interference SJTU Ying Cui 7 / 56
Outline Introduction System model Rate analysis Rate optimization Comparision with system without IRS Numerical results Conclusion SJTU Ying Cui 8 / 56
� �� � �� ������������� ��������������� �� � �� � � �� � �� ������ � ��������������� � �� ��������� ��� ������ Network model ◮ A multi-antenna signal BS S , equipped with a URA of M S × N S antennas, serves a single-antenna user U ◮ A multi-antenna interference BS I , equipped with a URA of M I × N I antennas, serves a single-antenna user U ′ ◮ A multi-element IRS, equipped with a URA of M R × N R antennas, is installed on the wall of a high-rise building ◮ Channels between the BSs and users follow Rayleigh fading ◮ scattering is often rich near the ground ◮ Channels between the IRS and BSs/user follow Rician fading ◮ scattering is much weaker far from the ground SJTU Ying Cui 9 / 56
Channel model ◮ Rayleigh channels between the BSs and the users: i = √ α i ˜ h H h H i , i = SU , IU , IU ′ ◮ α i > 0 is the distance-dependent path losses ◮ The elements of ˜ h H i are i.i.d. according to C N (0 , 1) ◮ Rician channels between the IRS and the BSs (users): �� � � H cR = √ α cR 1 K cR ¯ ˜ H cR + H cR , c = S , I K cR + 1 K cR + 1 �� � � h RU = √ α RU K RU 1 ¯ ˜ h RU + h RU K RU + 1 K RU + 1 ◮ α cR , α RU > 0 denote the distance-dependent path losses and K cR , K RU ≥ 0 denote the Rician factors, where i = S , I ◮ ¯ H cR , ¯ h RU represent the deterministic normalized LoS components, with unit-modulus elements ◮ ˜ H cR , ˜ h RU represent the normalized NLoS components, with elements i.i.d. according to C N (0 , 1) SJTU Ying Cui 10 / 56
Channel model ◮ Define: f ( θ ( h ) , θ ( v ) , m , n ) � 2 π d λ sin θ ( v ) (( m − 1) cos θ ( h ) + ( n − 1) sin θ ( h ) ) � e jf ( θ ( h ) ,θ ( v ) , m , n ) � A m , n ( θ ( h ) , θ ( v ) , M , N ) � m =1 ,..., M , n =1 ,..., N � � a ( θ ( h ) , θ ( v ) , M , N ) � rvec A m , n ( θ ( h ) , θ ( v ) , M , N ) ◮ λ denotes the wavelength of transmission signals ◮ d ( ≤ λ 2 ) denotes the distance between adjacent elements or antennas in each row and each column of the URAs ◮ ¯ H cR and ¯ h H RU are modeled as: H cR = a H ( δ ( h ) ¯ cR , δ ( v ) cR , M R , N R ) a ( ϕ ( h ) cR , ϕ ( v ) cR , M c , N c ) , c = S , I ¯ RU = a ( ϕ ( h ) RU , ϕ ( v ) h H RU , M R , N R ) � � � � � � ◮ δ ( h ) δ ( v ) , ϕ ( h ) ϕ ( v ) and ϕ ( h ) ϕ ( v ) represent the cR cR cR cR RU RU corresponding azimuth (elevation) angles SJTU Ying Cui 11 / 56
Quasi-static phase shift design ◮ Phase shifts of the IRS φ � ( φ m , n ) m ∈M R , n ∈N R with φ m , n ∈ [0 , 2 π ) is fixed, where M R � { 1 , 2 , ..., M R } , N R � { 1 , 2 , ..., N R } � �� �� e j φ m , n � ◮ Define Φ( φ ) � diag ∈ C M R N R × M R N R rvec m ∈M R , n ∈N R ◮ Considering linear beamforming at BSs S , I , the signal received at user U : � � � � P S ( h H RU Φ( φ ) H SR + h H h H RU Φ( φ ) H IR + h H Y � SU ) w S X S + P I w I X I + Z IU ◮ w S ∈ C M S N S × 1 and w I ∈ C M I N I × 1 denote the normalized beamforming vectors at BS S and BS I , where || w S || 2 2 = 1 and || w I || 2 2 = 1 ◮ X S and X I are the information symbols for user U and user U ′ , � | X S | 2 � � | X I | 2 � respectively, with E = 1 and E = 1, and Z ∼ C N (0 , σ 2 ) is the additive white gaussian noise (AWGN) ◮ h H RU Φ( φ ) H cR + h H cU represents the equivalent channel between BS c and user U via the IRS ◮ Assume that user U knows ( h H RU Φ( φ ) H SR + h H SU ) w S , but does not know � � h H RU Φ( φ ) H IR + h H w I IU SJTU Ying Cui 12 / 56
Instantaneous CSI case ◮ Assumptions: ◮ CSI of the equivalent channel between BS S and user U , i.e., h H RU Φ( φ ) H SR + h H SU , is known at BS S ◮ CSI of the channel between BS I and user U ′ , i.e., h IU ′ , is known at BS I ◮ Consider instantaneous CSI-adaptive MRT beamformers: � � H h H RU Φ( φ ) H SR + h H h IU ′ w ( instant ) w ( instant ) SU = , = �� � � �� S � h H RU Φ( φ ) H SR + h H I || h IU ′ || 2 � SU 2 ◮ w ( instant ) and w ( instant ) are chosen to enhance the signals S I received at user U and user U ′ ◮ w ( instant ) is optimal for the average rate maximization S SJTU Ying Cui 13 / 56
Instantaneous CSI case ◮ The SINR at user U : 1 � �� � �� � 2 � h H RU Φ( φ ) H SR + h H P S SU γ ( instant ) ( φ ) = 2 �� 2 � � h IU ′ � ( h H � RU Φ( φ ) H IR + h H � + σ 2 P I E IU ) � || h IU ′ || 2 ◮ The average rate for the IRS-assisted system with interference: � � �� C ( instant ) ( φ ) = E 1 + γ ( instant ) ( φ ) log 2 � � ◮ log 2 1 + γ ( instant ) ( φ ) can be achieved by coding over one coherence time interval ◮ C ( instant ) ( φ ) with P I = 0 reduces to the average rate in [Han et al. (2019)] � �� � 2 �� � � � �� � 1 Treat h H RU Φ( φ ) H IR + h H h H RU Φ( φ ) H IR + h H w I X I ∼ C N 0 , E , w I IU IU which corresponds to the worst-case noise. SJTU Ying Cui 14 / 56
Statistic CSI case ◮ Assumptions: ◮ Only the CSI of the LoS components h H RU , H SR are known at BS S ◮ No channel knowledge is known at BS I ◮ Consider statistical CSI-adaptive MRT beamformers: � ¯ � H RU Φ( φ )¯ h H H SR 1 w ( statistic ) w ( statistic ) √ M I N I = , = 1 M I N I � �� �� � S � ¯ RU Φ( φ )¯ I h H H SR � 2 ◮ w ( statistic ) is approximately optimal for the ergodic rate S maximization (optimal for maximizing an upper bound) ◮ Any w I with || w I || 2 2 = 1 achieves the same ergodic rate for user U ′ ◮ Have lower costs on channel estimation and beamforming adjustment SJTU Ying Cui 15 / 56
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