The document discusses intelligent reflecting surfaces (IRS) which consist of passive elements that can reflect signals with adjustable phase shifts. This allows IRS to maximize SNR by passive beamforming. The key points are: 1. An IRS-assisted wireless network model is presented with an IRS containing N reflecting elements, a base station with M antennas, and K users. 2. The mathematical model expresses the received signal at each user as the direct path plus the IRS-aided path, with the reflection coefficient matrix at the IRS adjusting the phase shifts. 3. Design aspects of IRS include estimating the channel state information between the base station/IRS and IRS/users to optimize active/passive beamforming for maximizing

1. Intelligent Reflecting Surface Aided Wireless Network
Domain: 5G Beyond Wireless Communication Research
Dr. Varun Kumar
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2. Outlines
1 Introduction to Intelligent Reflecting Surface (IRS)
2 Mathematical Model for IRS Assisted Wireless Network
3 Important Design Aspects for Making IRS-aided Wireless Network
4 References
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3. Intelligent Reflecting Surface (IRS):
Intelligent Reflecting Surface (IRS)
⇒ Intelligent reflecting surface (IRS) is a cost-effective solution for
achieving high spectrum and energy efficiency.
⇒ It consists of massive low-cost passive elements that are able to
reflect the signals with adjustable phase shifts.
⇒ It minimize the transmit power at the access point (AP).
⇒ SNR is maximized by passive beamforming through the IRS.
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4. Current research direction
1 IRSs for secure communication
Secure signal reception across dedicated user is the prime objective.
2 Deep learning based design for IRS-aided communications
3 Channel estimation for IRS-aided communications
4 Getting power and spectral efficiency through IRS-assisted wireless
network.
5 Practical implementation of IRS
6 Massive MIMO and massive IRS: which one is good ?
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5. System Model for IRS Assisted Wireless Network
Let a IRS assisted wireless network has N reflecting surface element, whereas
base station (BS) has M antenna. This BS assist K users and analysis is done for
the downlink scenario.
System Model:
1 BS to users links are supposed to be in deep fade.
2 BS to users link experience the active beamforming.
3 IRS unit to users link experience the passive beamforming.
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6. Continued–
4 IRS may have the capability for changing the rotational displacement.
5 Phase shifter is an essential hardware circuitry for IRS.
6 There may be two possibility for end-to-end communication
BS transmit stronger beam towards the IRS and fractional energy goes
in the direction of user equipment.
BS transmit weaker beam towards the IRS and fractional energy goes
in the direction of IRS unit.
7 If line of sight path dominates (in the absence of obstacle) then IRS
improvise the capacity/data rate significantly, when the links between BS to
IRS unit and IRS unit to user equipment are in the free space.
8 If line of sight path dominates (in the absence of obstacle) then IRS does
not improvise the capacity/data rate significantly, when there are obstacles
between BS to IRS unit and IRS unit to user equipment.
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7. Mathematical model for IRS assisted wireless network
⇒ hd,k → Direct channel gain vector of size 1 × M from BS to kth user
equipment, ∀ k = 1, 2, ...K.
⇒ hr,k → Channel gain vector of size 1 × N from IRS to kth user
equipment, ∀ k = 1, 2, ...K
⇒ G → Channel matrix of size N × M from BS to IRS unit.
⇒ θn → Angular shift of the incident EM wave from the nth IRS
reflecting surface element.
Received signal by kth user in IRS aided wireless network
yk = hH
d,kx
Direct−link
+ hH
r,kΘH
Gx
IRS−aided−link
+ nk (1)
⇒ nk is the additive noise experienced by kth user.
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8. Continued–
⇒ Θ is the reflection coefficient matrix of size N × N.
⇒ The composite transmit data symbol can be expressed as
x =
K
k=1
wksk (2)
⇒ The size of x is M × 1.
⇒ xk → Transmit symbol for kth user (size 1 × 1)
⇒ wk → Beamforming vector of size M × 1.
⇒ Using (2), the eqn (1) can also be expressed as
yk = hH
d,k + hH
r,kΘH
G
K
k=1
wksk + nk (3)
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9. Details about Θ
⇒ Θ is the reflection coefficient matrix of size N × N.
⇒ IRS will calculate this Θ matrix, so that the received SNR across UE
could be maximized.
⇒ Let the Θk is diagonal phase matrix of size N × N.
Θk =





ejφ1,k , 0, 0, ....., 0
0, ejφ2,k , 0, ....., 0
0, 0, ....,
... , 0
0, ................ ejφN,k





where ejφ1,k → Angle between 1st IRS element and kth user.
⇒ Similarly for jth user, the phase matrix should be
Θj = diag(eφ1,j , eφ2,j , ...., eφN,j )
⇒ Theoretically, NK number of phase needs for doing the passive beam
formation.
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10. Continued–
⇒ During reflection, total N suitable reflection coefficient is required out
of the NK phase elements.
⇒ Composite phase matrix Θ is the function of Θ1, Θ2, ....., ΘK .
Mathematically, we can express as
Θ = f Θ1, Θ2, ............., ΘK
⇒ Here, N >> K. For numerical simplicity we can assume N
K =
Constant
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11. Continued–
⇒ From above figure, it is clear
Incident and reflected angle = θ → Snail’s law →
At θ angle of reflection UE is not present.
UE is present, when the projection of reflected beam is at an angle of
θ + θ0
⇒ Projection or reflecting wave in 3D co-ordinate system requires three
components
IRS surface element to UE radial separation → r
Angle of elevation → θ
Azimuth angle → α
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12. Important facts for analytical simplification
⇒ Active beamforming vector is made with the help of channel matrix
between BS and user equipment (UE).
⇒ Two links should be precisely known in term CSI for better beam
formation.
BS to IRS link
IRS to users equipment link
⇒ If BS knows the co-ordinates of IRS then BS can estimates its angle
of incidence, so that a good amount of signal could reach at the UE
side.
⇒ BS is more intelligent than the IRS.
⇒ BS does the precoding operation in DL scenario. Based on the BS to
UEs and IRS to UEs link knowledge, BS should precode the signal in
such a way that the received SNR at UE could be maximized.
⇒ Novelty of the work based on the finding the CSI for IRS to UEs and
BS to UEs link jointly and accordingly designing a low complex
precder by the BS.
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13. Continued–
⇒ BS can communicate to the IRS regarding the location of UEs.
⇒ IRS has to adjust or estimate the angle of projection towards the UEs.
⇒ Users are either static or pedestrian.
⇒ BS and IRS are supposed to static, hence the channel coefficient is
also known between them.
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14. References
M. Di Renzo, M. Debbah, D.-T. Phan-Huy, A. Zappone, M.-S. Alouini, C. Yuen,
V. Sciancalepore, G. C. Alexandropoulos, J. Hoydis, H. Gacanin et al., “Smart
radio environments empowered by reconfigurable ai meta-surfaces: An idea whose
time has come,” EURASIP Journal on Wireless Communications and Networking,
vol. 2019, no. 1, pp. 1–20, 2019.
H. Guo, Y.-C. Liang, J. Chen, and E. G. Larsson, “Weighted sum-rate optimization
for intelligent reflecting surface enhanced wireless networks,” arXiv preprint
arXiv:1905.07920, 2019.
Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wireless network via
joint active and passive beamforming,” IEEE Transactions on Wireless
Communications, vol. 18, no. 11, pp. 5394–5409, 2019.
J.-P. Niu and G. Y. Li, “An overview on backscatter communications,” 2019.
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