This document summarizes a research paper on analyzing the achievable rate and power efficiency of massive MIMO in cooperative networks using zero-forcing receivers. It outlines the problem definition, system model, and simulation results. The system model considers uplink transmission from mobile users to a base station via relay stations. It analyzes the observed signal-to-noise ratio in direct and cooperative transmission and defines achievable rate metrics for direct, non-cooperative, and cooperative decoding schemes. Power efficiency is defined as the achievable rate divided by the total transmit power of all nodes.

1. Achievable Rate and Power Efficiency of Massive
MIMO in Cooperative Network with ZF Receivers
Varun Kumar
Prof Sarat Kumar Patra & Prof Poonam Singh
Department of Electronics and Communication Engineering
National Institute of Technology, Rourkela (India)
1

2. Outlines:
❏ Introduction
❏ Problem Definition
❏ System Model
❏ Simulation Results
❏ Conclusion
❏ References
2

3. Cooperative Communication
Definition:
In a cooperative communication system, each wireless entity is assumed to
transmit data as well as act as a cooperative agent for another entity.
Feature:
Cooperative communication is one of the fastest growing areas of research and it
is likely to be a key enabling technology for efficient energy and spectrum usage.
3

4. Different Types of Cooperative Scenario:
(A) Source-Relay-UT (B) Machine-to Machine(M2M) (C) Device-to-Device (D2D) 4
A
B
C

5. Signal Decoding Scheme:
5
● Direct Decoding Scheme
● Non-cooperative Decoding Scheme
● Cooperative Decoding Scheme

6. Massive MIMO: A Disruptive Research Direction for 5G
6
 Massive MIMO deals with the large
antenna array integration across 𝑇𝑋 and
𝑅 𝑋.
 Multiple-antenna (MIMO) technology is
becoming mature for wireless
communications and has been
incorporated into wireless broadband
standards like LTE and Wi-Fi.
 The more antennas across 𝑇𝑋/𝑅 𝑋
provides more possible signal paths and
the better performance in terms of data
rate and link reliability.

7. System Model
7
System Parameter
K=Total number of cell edge users
enabled with single antenna
𝑀𝑟=Total number relay antennas
𝑀𝑠=Total number of BS antennas
System Constraint
𝐾 < 𝑀𝑟 < 𝑀𝑠
• 𝑀𝑟 and 𝑀𝑠 are considered to
be very large.
• Analysis has been carried for
uplink scenario
Note: LTE Standard Maximum 8 antenna for 4G standard
Future Relay and BS
architecture (Dense
deployment of antenna)
Massive MIMO in Cooperative Scenario
How would be the
next generation
relay and BS ??

8. Channel Model:
8
Received signal at BS: (1 𝑠𝑡
time slot) (Uplink Scenario)
𝑌𝑏1
= 𝑝 𝑢 𝐻1 𝐷1
1
2
𝑋 + 𝑛 𝑢𝑏
Let 𝐺1 = 𝐻1 𝐷1
1
2
, 𝐻1 = 𝐶𝑁(0 𝑀𝑠×𝐾 , 𝐼 𝑀𝑠⊗𝐾) & 𝐷1 =
𝛽11 0
0 𝛽12
⋮
0
⋮
0
⋯ 0
⋯ 0
⋱
⋯
⋮
𝛽1𝐾
Theorem 1: For a central Whishart matrix 𝐺 ~𝐺 𝑁 𝑀, 𝐼 with M>N
𝑇𝑟 𝔼[(𝐺 𝐻
𝐺)−1
] =
𝑁
𝑀 − 𝑁
𝑇𝑟 𝔼[(𝐺1
𝐻
𝐺1)−1
] =
𝑘=1
𝐾
1
𝑀 − 𝐾 𝛽1𝑘
ZF Detection at BS receiver end
𝑌𝑏𝑑1
= 𝐴 𝑢𝑏 𝑌𝑏1
where 𝐴 𝑢𝑏 = (𝐺1
𝐻
𝐺1)−1
𝐺1
𝐻
(ZF Detector)
1. 1 𝑠𝑡
link: MU → BS, (Multiuser MIMO)
2. 2 𝑛𝑑
link: MU → RS, (Multiuser MIMO)
3. 3 𝑟𝑑
link: RS→BS, (Point-to-point (p2p) MIMO)

9. 9
𝑌𝑏𝑑1
= 𝑝 𝑢 𝑋 + 𝐷1 𝑑
𝑛 𝑢𝑏𝑑
Where 𝐷1𝑑 =
1
𝑀𝑠−𝐾 𝛽11
0
0
1
𝑀𝑠−𝐾 𝛽12
⋮
0
⋮
0
⋯ 0
⋯ 0
⋱
⋯
⋮
1
𝑀𝑠−𝐾 𝛽1𝐾
& nubd = 𝐶𝑁(0 𝐾×1 , 𝐼 𝐾)
Received signal at relay station: (1 𝑠𝑡
time slot)
𝑌𝑢𝑟 = 𝑝 𝑢 𝐻2 𝐷2
1
2
𝑋 + 𝑛 𝑢𝑟
𝐻2 = 𝐶𝑁(0 𝑀 𝑟×𝐾 , 𝐼 𝑀 𝑟⊗𝐾) & 𝐷2 =
𝛽21 0
0 𝛽22
⋮
0
⋮
0
⋯ 0
⋯ 0
⋱
⋯
⋮
𝛽2𝐾
Detected Signal
𝑌𝑢𝑟 𝑑
= 𝐴 𝑢𝑟 𝑌𝑢𝑟 ⇒ 𝐺2= 𝐻2 𝐷2
1
2
& 𝐴 𝑢𝑟 = (𝐺2
𝐻
𝐺2)−1
𝐺2
𝐻
𝑌𝑢𝑟 𝑑
= 𝑝 𝑢 𝑋 + 𝐷2 𝑑
𝑛 𝑢𝑟𝑑
Where 𝐷1𝑑 =
1
𝑀𝑠−𝐾 𝛽11
0
0
1
𝑀𝑠−𝐾 𝛽12
⋮
0
⋮
0
⋯ 0
⋯ 0
⋱
⋯
⋮
1
𝑀𝑠−𝐾 𝛽1𝐾
& nubd = 𝐶𝑁(0 𝐾×1 , 𝐼 𝐾)

10. 10
AF Relaying Strategy: (2 𝑛𝑑
time slot operation)
𝑌𝑏2
=
1
𝑀 𝑟
𝜒 𝑟𝑏 𝐻3 𝐷3
1
2
𝑊𝑌𝑢𝑟 𝑑
+ 𝑛 𝑟𝑑 (W is the 𝑀𝑟 × 𝐾 Precoding matrix such that 𝑊𝑊 𝐻
= 𝐼 𝑀 𝑟
)
⇒
1
𝑀𝑟
𝜒 𝑟𝑏 𝐻3 𝐷3
1
2
𝑊 ( 𝑝 𝑢 𝑋 + 𝐷2 𝑑
𝑛 𝑢𝑟𝑑) + 𝑛 𝑟𝑏
𝐻3 = 𝐶𝑁(0 𝑀𝑠×𝑀 𝑟
, 𝐼 𝑀𝑠⊗𝑀 𝑟
) & 𝐷3 =
𝛽31 0
0 𝛽32
⋮
0
⋮
0
⋯ 0
⋯ 0
⋱
⋯
⋮
𝛽3𝑀 𝑟
Here 𝛽31 = 𝛽32 = ⋯ = 𝛽3𝐾 ≈ 𝛽𝑟 or 𝐷3 ≈ 𝛽𝑟 𝐼 𝑀 𝑟
Amplification Factor:
𝜒 𝑟𝑏 =
𝑝 𝑟
𝐾𝑝 𝑢
𝑇𝑟 𝔼 𝐷2 𝑑
𝐻 𝐷2 𝑑
−1 +
1
𝐾
𝔼[𝑇𝑟(𝑛 𝑢𝑟𝑑 𝑛 𝑢𝑟𝑑
𝐻 )]
𝑝 𝑟= Total transmit power by relay terminal
Theorem 2 : If 𝑈~𝐶𝑁 0,1 𝑀×𝑁
and 𝑉~𝐶𝑁 0,1 𝑁×𝑃
are two random matrices and Z is the another
random matrix such that 𝑍 = 𝑈𝑉, where 𝑀 > 𝑁 > 𝑃. In such a scenario
𝑇𝑟(𝔼 (𝑍 𝐻
𝑍 −1
]) ≈
𝑃
(𝑀 − 𝑃)(𝑁 − 𝑃)

11. Continued--
11
𝑇𝑟 𝔼 𝐺 𝑑
𝐻
𝐺 𝑑
−1
) ≈
𝐾
𝑀𝑠 − 𝐾 𝑀𝑟 − 𝐾 𝛽𝑟
𝑌𝑏𝑑2
=
1
𝑀𝑟
𝜒 𝑟𝑏 𝑝 𝑢 𝑋 + 𝜒 𝑟𝑏 𝐺 𝑑
𝐻
𝐺 𝑑
−1
𝐺 𝑑
𝐻
𝐷2 𝑑
𝑛 𝑢𝑟𝑑 + 𝐺 𝑑
𝐻
𝐺 𝑑
−1
𝐺 𝑑 𝑛 𝑟𝑏
Detected Signal at BS in two time slot
𝑌𝑑 = 𝑌𝑏𝑑1
𝑌𝑏𝑑2 𝐾×2
Achievable Rate Analysis Under Different Cooperation Protocol
Observed SNR in 1 𝑠𝑡
time slot :
𝑃𝑑1 = 𝑝 𝑢 𝐼 𝐾 𝔼 𝑋 𝐻
𝑋 + 𝐷1𝑑
𝐻
𝐷1𝑑 𝔼(𝑛 𝑢𝑏
𝐻
𝑛 𝑢𝑏)
Signal Power Matrix Noise Power matrix
Observed co-variance matrix of SNR
𝛾 = 𝑝 𝑢 𝐼 𝐾 𝔼 𝑋 𝐻
𝑋 𝐷1𝑑
𝐻
𝐷1𝑑 𝔼(𝑛 𝑢𝑏
𝐻
𝑛 𝑢𝑏)
−1

12. Continued--
12
𝛾1 =
𝑝 𝑢 𝑀𝑠 − 𝐾 𝛽11 𝜖12
𝜖21 𝑝 𝑢 𝑀𝑠 − 𝐾 𝛽12
⋮
𝜖 𝐾1
⋮
…
⋯ 𝜖1𝐾
⋯ 𝜖2𝐾
⋱
⋯
⋮
𝑝 𝑢 𝑀𝑠 − 𝐾 𝛽1𝐾 K×𝐾
where 𝜖𝑖𝑗 → 0 ∀ 𝑖, 𝑗 & 𝑖 ≠ 𝑗
From Jensen’s inequality
𝔼 𝐶 𝛾 ≤ log2(1 + 𝛾)
Note: 𝛾1 =
𝛾11+𝛾12+⋯+𝛾1𝐾
K
∀ 𝛾1𝑗 = 𝑝 𝑢 𝑀𝑠 − 𝐾 𝛽1𝑗

13. Continued--
13
Observed SINR 𝛾2 in 2 𝑛𝑑
time slot
𝑆𝑖𝑔𝑛𝑎𝑙 𝑃𝑜𝑤𝑒𝑟 𝑆 =
𝑝 𝑢 𝜒 𝑟𝑏
2
𝑀𝑟
𝐼 𝐾
𝐼𝑛𝑡𝑒𝑟𝑓𝑒𝑟𝑛𝑐𝑒 𝐼 =
𝜒 𝑟𝑏
2
𝑀𝑟 𝑀𝑟 − 𝐾
𝐷2𝑑
𝐻
𝐷2𝑑 𝔼(𝑛 𝑢𝑟𝑑 𝑛 𝑢𝑟𝑑
𝐻
)
𝑁𝑜𝑖𝑠𝑒 𝑁 =
1
𝑀𝑟 − 𝐾 𝑀𝑠 − 𝐾 𝛽𝑟
𝔼(𝑛 𝑟𝑏 𝑛 𝑟𝑏
𝐻
)
Hence 𝛾2 =
𝑆
𝐼+𝑁
𝛾2 =
𝑝 𝑢 𝜒 𝑟𝑏
2
𝑀𝑟
𝐼 𝐾
𝜒 𝑟𝑏
2
𝑀𝑟 𝑀𝑟 − 𝐾
𝐷2𝑑
𝐻
𝐷2𝑑 𝔼 𝑛 𝑢𝑟𝑑 𝑛 𝑢𝑟𝑑
𝐻
+
1
𝑀𝑠 − 𝐾 𝑀𝑟 − 𝐾 𝛽𝑟
𝔼 𝑛 𝑟𝑏 𝑛 𝑟𝑏
𝐻
−1

14. 14
𝛾2𝑘 =
𝑝 𝑢 𝜒 𝑟𝑏
2
𝑀𝑟
𝜒 𝑟𝑏
2
𝑀𝑟 𝑀𝑟 − 𝐾 𝛽2𝑘
+
1
𝑀𝑠 − 𝐾 𝑀𝑟 − 𝐾 𝛽𝑟
So average SNR can be expressed as
𝛾2 =
𝛾21 + 𝛾22 + ⋯ + 𝛾2𝐾
𝐾
Achievable Rate Analysis:
𝐶 𝐷𝑖𝑟𝑒𝑐𝑡 =
𝑖=1
𝐾
log2(1 + 𝑝 𝑢 𝑀𝑠 − 𝐾 𝛽1𝑖)
𝐶 𝑛𝑜𝑛−𝑐𝑜𝑜𝑝 =
1
2
𝑘=1
𝐾
log2(1 + 𝛾2𝑘)
𝐶𝑐𝑜𝑜𝑝 =
1
2
𝑘=1
𝐾
log2(1 + 𝛾1𝑘 + 𝛾2𝑘)
𝐶 𝑢𝑝𝑝𝑒𝑟 =
𝐾
2
log2(1 + 𝛾1 + 𝛾2)

15. 15

16. Continued--
16

17. Power Efficiency
17
𝜂 𝑒𝑒 =
𝐶𝐵
𝐾𝑝 𝑢+𝑝 𝑟
C= Observed capacity in bps/Hz
B= Occupied Bandwidth

18. EE vs total transmit power in dB (𝑀𝑠 is fixed)
18

19. EE vs total transmit power in dB (𝑀𝑟 is fixed)
19

20. Conclusion:
20
1. As like non-cooperative scenario [2], massive MIMO is also viable in cooperative
networks.
2. We first derived the tight lower bound of the achievable rate and also the power
efficiency using ZF precoder as well as detector and compared with Monte Carlo
simulation result.
3. In such a scenario more number of relay antenna drives the system performance with
faster rate comparing to BS antenna.
4. There may be some practical difficulty to accommodate large number of antenna
across relay in such a scenario we may opt multiple relay but there may arise some
signal synchronization issue along with computation complexity.

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21
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22. 22