# Performance Analysis of Cooperative Diversity in Multi-user Environments

24 Oct 2019-pp 1-4

TL;DR: The results revealed that increasing relays number on the network can improve the system performance and there was improvement in the performance when the number of users increased, however, the performance dropped when this number became close the relay number.

Abstract: The article studies the performance of cooperative multi-relay networks with random numbers of accessing users. A cooperative diversity is achieved at the destination nodes by receiving multiple independent copies of the same signal from M relays when all relays participate in the second phase of data transmission. The overall spectral efficiency (SE) of the considered system is investigated and accurate analytical expressions for it are developed. Furthermore, the article discusses how system performance is affected by its parameters. Monte Carlo simulations are used to validate the analytical results. The results revealed that increasing relays number on the network can improve the system performance. The results also indicated that there was improvement in the performance when the number of users increased. However, the performance dropped when this number became close the relays number.

## Summary (1 min read)

### Introduction

- This kind of cooperative technology has attracted the researchers‘ attention due to the dramatic performance gains that can be achieved in the case of the unavailability of the other types of diversity and when users share antennas and other resources to exchange channel information and transmitted symbols [1].
- Furthermore, the study investigated the achievable diversity orders of the network relay selection schemes.
- Further more, the ZF technique is applied at the relay nodes to tackle the interference.
- Such derivation, gives us the opportunities to explore the effect of various system parameters on its performance.

### II. SYSTEM MODEL

- The proposed system model is presented in Fig. 1. Ka represents the random active users number in the network and D is the destinations, it is assumed that there is no direct contact between the users and the destinations and communication occurs via Mr relays.
- Each node is equipped with A single antenna.
- For the proposed system model, the ZF technique is used at the relay nodes and assuming that there is a cooperation between the relay nodes, by this the authors mean that they have the ability of sharing the sent information from the source and transmitted data [12].
- The authors assumed that the channels are independently and identically distributed and subjected to complex Gaussian fading with mean equal to zero and variance equal to one ∼ CN (0, 1) .
- NDi, (2) where, g1i and g1k represent the i th and kth columns of G1, respectively, g2i indicates the i th column of G2, which is the channel matrix of the second phase of the communication.

### IV. NUMERICAL RESULTS

- The achievable overall SE with the use of ZF technique at the relay nodes is discussed and the numerical results are validated using computer simulations.
- Fast fading is considered represented by Rayleigh.
- In Fig. 2, the overall SE drawn with respect to the users number with different relays number.
- The analytical results which are obtained by (19) are validated using Monte Carlo simulations.
- For points on the plot for which M ≥ L, the SE increases with both the usage and number of users.

### V. CONCLUSIONS.

- The performance of the wireless system with a random number of active source nodes communicate with is provided with a single antenna.
- Analytical expressions for the overall SE are derived and the authors examined the effect of different system parameters on its performance.
- It was revealed that the analytical results and the computer simulations were in a perfect agreement.
- The results showed that the SE improves as the users number in the network increases.
- As the users number becomes close to the relays number, the SE starts decreasing.

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Gheth, W, Alﬁtouri, A, Rabie, Khaled ORCID logoORCID:

https://orcid.org/0000-0002-9784-3703, Adebisi, B ORCID logoORCID:

https://orcid.org/0000-0001-9071-9120 and Hamdi, Khairi Ashour (2019)

Performance Analysis of Cooperative Diversity in Multi-user Environments.

In: 8th International Conference on Modeling Simulation and Applied Op-

timization (ICMSAO), 15 April 2019 - 17 April 2019, Manama, Bahrain.

Downloaded from:

https://e-space.mmu.ac.uk/622872/

Version: Accepted Version

Publisher: IEEE

DOI: https://doi.org/10.1109/ICMSAO.2019.8880443

Please cite the published version

https://e-space.mmu.ac.uk

Performance Analysis of Cooperative Diversity in

Multi-user Environments

Waled Gheth

1

, A. Alﬁtouri

2

, Khaled M. Rabie

1

, Bamidele Adebisi

1

and Khairi Ashour Hamdi

3

1

School of Engineering, Manchester Metropolitan University, Manchester, UK

2

School of Electrical and Electronic Engineering, Engineering Academy Tajoura, Tripoli, Libya

3

School of Electrical and Electronic Engineering,The University of Manchester, Manchester, UK

Emails:{w.gheth, k.rabie, b.adebisi}@mmu.ac.uk; a.alﬁtouri@hotmail.com; k.hamdi@manchester.ac.uk

Abstract—The article studies the performance of cooperative

multi-relay networks with random numbers of accessing users.

A cooperative diversity is achieved at the destination nodes by

receiving multiple independent copies of the same signal from

M relays when all relays participate in the second phase of

data transmission. The overall spectral efﬁciency (SE) of the

considered system is investigated and accurate analytical expres-

sions for it are developed. Furthermore, the article discusses

how system performance is affected by its parameters. Monte

Carlo simulations are used to validate the analytical results. The

results revealed that increasing relays number on the network can

improve the system performance. The results also indicated that

there was improvement in the performance when the number of

users increased. However, the performance dropped when this

number became close the relays number.

Index Terms—Cooperative communication, multi-relays sys-

tem, spectral efﬁciency, zero forcing.

I. INTRODUCTION

This kind of cooperative technology has attracted the re-

searchers‘ attention due to the dramatic performance gains

that can be achieved in the case of the unavailability of

the other types of diversity and when users share antennas

and other resources to exchange channel information and

transmitted symbols [1]. Transmission in wireless communi-

cation is mostly affected by shadowing, fading and distance

between the source and the end-users, particularly when the

communication is taking place between multiple-source nodes

and multiple-destinations. In such cases, relying protocols can

play a crucial role in aiding wireless communication by im-

proving the performance of the system [2]. Different relaying

protocols can be implemented, such as amplify-and-forward

(AF) and decode-and-forward (DF), in order to improve the

throughput and extend the coverage area without change the

source power, particularly for the users at edge of the cell

[3], [4]. There are some technical issues associated with the

implementation of relays in wireless communication systems,

which can degrade system performance. The most crucial one

is signals interference at the relay. However, zero forcing (ZF)

is one of the interference-cancellation techniques that can be

applied at the source, relay and/or destination nodes, or any

combinations of these to eliminate interference. This kind of

scheme is a multi-node ZF protocol, where the distributed

single antenna nodes can exchange channel information and

can be used to apply ZF processing [5]–[7].

Cooperative distributed multi-users relaying an ad-hoc wire-

less network are discussed in [8], where the gain factors of the

relays is derived to minimize the mean squared error (MSE) at

the destination. Multi-way relaying in Rician fading channels

is proposed in [9], where the authors reduced the transmission

time by applying random and semi-orthogonal relay selection

schemes. The study in [10] discussed the cooperative diver-

sity performance over Nakagami-m fading channels utilizing

equal gain combinations. The authors in [11] discussed the

selection schemes of wireless network relay. They introduced

different sub-optimal schemes with linear complexity for the

optimal relay selection. Furthermore, the study investigated

the achievable diversity orders of the network relay selection

schemes.

In this paper, the performance of an AF multi-relay system

is analyzed, where the communication between the random

users K and the destinations accrues via a number of re-

lays M . All nodes are provided with a single antenna. We

also discuss the effect of the users accessing number on

the proposed cooperative multi-relay networks performance,

where the relays communicate with several users in the same

time-frequency resource to achieve a higher data rate. At the

destination node we achieve cooperative diversity by receiving

multiple independent copies of the same signal from M

relays, where all relays cooperate in the second stage of the

communication process. Instead of adopting the best relay

selection to forward data, we sum all the signals that come

from all active relays.

Considering the fading and thermal noise effect at relays

and end-user nodes, novel and accurate expressions are de-

rived for multiple access interference at these nodes. So far,

however, there has been little discussion about considering

the communication between random users in wireless domain.

The assumption of random users shows how the system

performance is affected by the user activity and makes the

derived expression more practicable than the existing ones.

Further more, the ZF technique is applied at the relay nodes to

tackle the interference. The derivation of the novel expressions

can be utilized in the throughput of the multi-relays technique

estimation in the considered channels. Such derivation, gives

R1

R2

D1

S1

SK

M Relays

K Users

K Destinations

DK

RM

.

.

.

.

.

.

.

.

.

.

.

Fig. 1: System Model

us the opportunities to explore the effect of various system

parameters on its performance. The analytical results of the

new expressions are validated by computer simulations.

The rest of this article is as follows. The system model under

consideration is presented in the following section. Section III

presents the analysis of the over all capacity. The discussions

of the numerical results are in Section IV. Finally, we present

our main conclusions in Section V.

II. S

YSTEM MODEL

The proposed system model is presented in Fig. 1. K

a

represents the random active users number in the network

and D is the destinations, it is assumed that there is no

direct contact between the users and the destinations and

communication occurs via M

r

relays. Each node is equipped

with A single antenna. K

a

is represented by a binomial

arbitrary variable and P

k

(K

a

0

= i) = (

L

i

)q

i

(1 − q)

L−i

is

its probability, q indicates the probability of the active state

a user and it should always be 0 ≤ q ≤ 1 and L denotes

the number of users. For the proposed system model, the ZF

technique is used at the relay nodes and assuming that there is

a cooperation between the relay nodes, by this we mean that

they have the ability of sharing the sent information from the

source and transmitted data [12]. The received signal at the

relays is as follows

y

r

=

√

p

t

G

1

x + n

g

, (1)

where

√

p

t

is the users transmit power, G

1

indicates the chan-

nel matrix of the ﬁrst phase of the communication process (i,e

users-to-relays links), this can be written as G

1

= H

1

D

1/2

1

,

where H

1

is the small-scale Rayleigh fading parameters ma-

trix, it is M ×L matrix, where M represents the relay receivers

antennas and L is the antennas of the user transmitters,

and large-scale of the Rayleigh fading is represented by the

diagonal matrix D

1

, which is L ×L matrix. The sent symbols

are represented by x = [x

1

, x

2

, . . . , x

L

]

T

and n

g

indicates

the noise at the relays, which is AWGN. We assumed that

the channels are independently and identically distributed and

subjected to complex Gaussian fading with mean equal to zero

and variance equal to one ∼ CN (0, 1) .

At the second stage of the communication, relays forward a

transformation of the received data from the users times the

transformation matrix V . The date at the end user is deﬁned

by

y

D

i

=

√

p

t

g

H

2i

V g

1i

x

i

+

√

p

t

K

X

k=1,k6=i

g

H

2i

V g

1k

x

k

+ g

H

2i

V n

g

+ n

D

i

,

(2)

where, g

1i

and g

1k

represent the i

th

and k

th

columns of G

1

,

respectively, g

2i

indicates the i

th

column of G

2

, which is the

channel matrix of the second phase of the communication.

n

D

i

denotes the destination noise i, which is AWGN. If

there is an available at the relay nodes between source and

destination, we can express the relays transformation matrix

as V = G

2

(G

H

2

G

2

)

−1

(G

H

1

G

1

)

−1

G

H

1

. In consonance with

the ZF concept that aimed to combat the users interference:

g

H

2i

V g

1k

= ψ

ki

, (3)

where ψ

ki

= 1 when k = i, and 0 otherwise [13]. Therefore,

we can rewrite (2) as

y

D

i

=

√

p

t

x

i

+ [(G

H

1

G

1

)

−1

G

H

1

]

i

n

g

+ n

D

i

, (4)

To simplify the equation, let G

†

1

= (G

H

1

G

1

)

−1

G

H

1

and we

obtain

y

D

i

=

√

p

t

x

i

+ [G

†

1

]

i

n

g

+ n

D

i

. (5)

The SINR

i

of the destination is expressed as

SINR

i

=

p

t

[G

†

1

]

i

2

N

g

+ N

D

, (6)

where N

g

represents the noise power at the relay nodes and N

D

the noise power at destination nodes. Hence,

SINR

i

=

[G

†

1

]

i

−2

1

γ

g

+

1

γ

D

[G

†

1

]

i

−2

, (7)

where

h

G

†

1

i

i

−2

is subjected to Erlang distribution, with

M − L + 1 shape parameter and ξ

k

scale parameter [14], γ

g

indicates the SNR at the relay nodes and γ

D

is the SNR at

destination nodes. It is assumed that γ

g

= γ

D

= γ.

III. S

PECTRAL EFFICIENCY ANALYSIS

The achievable SE of the two-way relay system is derived

in this section, and it written as

ζ =

1

2

E

K

a

X

k

a

=1

[log

2

(1 + SINR

k

a

)]

!

, (8)

where [log

2

(1 + SINR

k

a

)] denotes the instantaneous SE of a

user k

a

. The following equation represents the end-to-end SE

of the proposed system

ζ =

1

2

E {K

a

[log

2

(1 + SINR

1

)]}, (9)

where SINR

1

indicates the ﬁrst user SINR. The assumption

h

G

†

1

i

i

−2

= Y

k

, and by using the deﬁnition of the moment

generation function (MGF), the exact analytical expression of

the SE can be expressed as

Corollary 1. Let x

1

, ........, x

N

, y

1

, ......., y

M

be arbitrary ran-

dom variables >0. Then [15, eq. (5)]

E

(

ln

1 +

P

N

0

n

0

=1

x

n

0

P

M

0

m

0

=1

y

m

0

+ 1

!)

=

Z

∞

0

1

f

1 − e

−f

P

N

0

n

0

=1

x

n

0

e

−f

(

P

M

0

m

0

=1

y

m

0

+1

)

df. (10)

Now, we can re-write (9) as

ζ =

1

2

E[K

a

(log

2

e)

∞

Z

0

e

−f /γ

f

#

1 − e

−fY

k

e

−f Y

k

/γ

df]. (11)

which can be written as

ζ =

1

2

E[K

a

(log

2

e)

×

∞

Z

0

e

−f /γ

f

e

−fY

k

/γ

− e

−f Y

k

(1+

1

γ

)

df]. (12)

Let u =

Y

k

γ

, and v = Y

k

(1 +

1

γ

). Thus we obtain M

u

(f) =

E

e

−fY /γ

and M

v

(f) = E

h

e

−fY

k

(1+

1

γ

)

i

, where M

u

(f) =

E[e

−fu

] and M

v

(f) = E[e

−fv

] are the MGFs of u and v,

respectively. Hence,

M

u

(f | K

a

) = E

n

e

−fzY

k

/γ

| K

a

o

=

1

1 + f/γ

M−K

a

+1

.

(13)

and

M

v

(f | K

a

) =

E

n

e

−fY (1+

1

γ

)

| K

a

o

=

(

1

1 + f(1 +

1

γ

)

)

M−K

a

+1

. (14)

Substituting (13) and (14) into (12), the end-to-end SE is

expressed by

ζ =

1

2

E

(

K

a

(log

2

e)

∞

Z

0

e

−f /γ

f

(

1

1 + f/γ

M−K

a

+1

−

(

1

1 + f(1 +

1

γ

)

)

M−K

a

+1

)

df | K

a

)

. (15)

In order to ﬁgure-out the expected value of each part, Equation

(16) needs to be expanded and simpliﬁed as

ζ =

1

2

(log

2

e)

×

∞

Z

0

e

−f /γ

f

(

E

(

K

a

(1 + f/γ)

K

a

1

1 + f/γ

M +1

)

−E

K

a

1 + f (1 +

1

γ

)

K

a

(

1

1 + f (1 +

1

γ

)

)

M +1

)

df.

(16)

Corollary 2. The expected value of E

K

a

(A)

K

a

−1

, where

K

a

is a binomial random variable with probability P

r

(K

a

=

i) = (

L

i

)q

i

(1 − q)

L−i

can be found as [16, Eq. (28)]

E

K

a

(A)

K

a

−1

= qL(1 − q + qA)

L−1

. (17)

Therefore, the ﬁnal expression for overall SE can be expressed

as

ζ =

qL

2

(log

2

e)

∞

Z

0

e

−z /γ

z

((

(1 + qf/γ)

L−1

(1 + f/γ)

M

)

−

1 + qf(1 +

1

γ

)

L−1

1 + f (1 +

1

γ

)

M

)

df. (18)

Now, (18) can be expressed in terms of the weights and

abscissas of a Laguerre orthogonal polynomial

ζ =

qL

2

(log

2

e)

N

0

X

n

0

=1

α

n

0

β

n

0

((

(1 + qµ

n

0

/γ)

L−1

(1 + µ

n

0

/γ)

M

)

−

1 + qµ

n

0

(1 +

1

γ

)

L−1

1 + µ

n

0

(1 +

1

γ

)

M

)

+ R

N

0

, (19)

where µ

n

0

= β

n

0

γ, β

n

0

are Laguerre polynomial sample

points factor and α

n

0

is the weights factor of it, tabulated

in [17, Eq. (25.4.45)], and the remainder R

N

0

, is small for

N

0

≥ 15. Thus, (19) an effective numerical valuation for the

overall SE.

1 2 3 4 5 6 7 8 9 10

Number of Users (S)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

R (bits/s/Hz)

Simulation

Analytical

N = 9, 10, 11

Fig. 2: SE versus different number

of users.

10 20 30 40 50 60 70 80 90 100

Number of Relays (N)

2.5

3

3.5

4

4.5

5

5.5

6

R (bits/s/Hz)

Simulation

Analytical

= 0.5, 0.8, 1

Fig. 3: SE versus different number

of relays.

-10 -5 0 5 10 15 20

dB

0

5

10

15

20

25

30

35

R (bits/s/Hz)

Simulation

Analytical

N = 80, 20, 10

Fig. 4: SE with respect to SNR.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

2

4

6

8

10

12

14

16

18

R (bits/s/Hz)

Simulation

Analytical

= 10, 12,

15

Fig. 5: SE with respect to user

activity.

IV. NUMERICAL RESULTS

In this section, the achievable overall SE with the use of ZF

technique at the relay nodes is discussed and the numerical

results are validated using computer simulations. Fast fading

is considered represented by Rayleigh.

In Fig. 2, the overall SE drawn with respect to the users

number with different relays number. The analytical results

which are obtained by (19) are validated using Monte Carlo

simulations. It is clear that the overall SE dramatically in-

creases as the users number increases from 0 to 7. Neverthe-

less, for more users, the value of the overall SE relies on the

number of relays as seen when M increases from 9 to 11.

When the number of users is higher than the relays number,

this will result in a signiﬁcant degradation in spatial diversity

and increasing of interference at relay nodes, which will have

an adverse effect on the performance of the system.

Fig. 3, presents the SE as a function of M with different values

of q and 10 users. For points on the plot for which M ≥ L,

the SE increases with both the usage and number of users.

It can be seen that when M is considerably higher than the

users number (M >> L, that is M > 30) all curves have a

very slow increasing with further increase in M. However,

as the user activity becomes higher, the overall SE of the

proposed system enhances substantially. This is due to the

spatial diversity remains high if M > 30 regardless of the users

activity level, which can be used to determine the maximum

number of antennas required for a given application.

Fig. 4 presents the SE as a function in SNR (γ) with different

relays numbers and 10 users. The results were expected, SE

enhances for any increase of γ. It is noticeable that there is

clear enhancement in the SE of the system when L = 10

users, and M changes from 10 to 20. However, there is small

improvement in SE when M is changing from 20 to 80 with

same value of L.

Fig. 5 illustrates the effect of the activity on the SE for

different values of SNR when L = 11 and M = 10. It is clear

that the SE initially increases until the user activity reaches

about 0.8 for all SNR curves then it starts decreasing until it

becomes 0 at q = 1 where the active users number is more than

the relay nodes number, which leads to more interference.

the destination nodes through multi-relays when every node

V. C

ONCLUSIONS.

In this paper, the performance of the wireless system with

a random number of active source nodes communicate with

is provided with a single antenna. In order to combat the

interference, a ZF technique is implemented at the relay nodes.

Analytical expressions for the overall SE are derived and

we examined the effect of different system parameters on its

performance. It was revealed that the analytical results and

the computer simulations were in a perfect agreement. The

results showed that the SE improves as the users number in

the network increases. However, as the users number becomes

close to the relays number, the SE starts decreasing. Further-

more, increasing the total relays number in the system can

positively affect the system performance. The ZF technique,

which is implemented at the relay nodes, can effectively be

utilized to combat the users interference.

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Abstract: To address the explosive traffic demands, the capacity of the fading channel is increasingly becoming a prime concern in the designing of the wireless communication system. The channel capacity is an extremely important quantity, since it allows the transmission of the data through the channel with an arbitrarily small probability of error. In other words, capacity dictates the maximum rate of information transmission, called as ‘capacity’ of channel, determined by the intrinsic properties of the channel and is independent of the content of the transmitted information. In this paper, we present a comprehensive survey of the existing work related to the channel capacity model over various fading channels. With an elaborated explanation of the theory of channel capacity, definitions of channel capacity based on the channel state information are reviewed. To compliment this, review of the technique to enhance the channel capacity is discussed and reviewed. An effective capacity model to overcome the channel capacity limitation is also explained. Furthermore, as the secure transmission of data is of utmost importance, to address this physical layer security model is also reviewed. We also summarize the work related to channel capacity in various types of wireless networks. We finally cover the future research directions, including less explored aspects of the channel capacity that can be studied to design efficient communication systems.

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04 Aug 2021TL;DR: In this article, the authors present a survey of the existing work related to the channel capacity (CC) model over various fading channels, including the diversity combining technique to enhance the CC, and the future research directions including less explored aspects of the CC that can be studied to design efficient communication systems.

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##### References

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TL;DR: Several SNR-suboptimal multiple relay selection schemes are proposed, whose complexity is linear in the number of relays and are proved to achieve full diversity.

Abstract: This paper is on relay selection schemes for wireless relay networks. First, we derive the diversity of many single-relay selection schemes in the literature. Then, we generalize the idea of relay selection by allowing more than one relay to cooperate. The SNR-optimal multiple relay selection scheme can be achieved by exhaustive search, whose complexity increases exponentially in the network size. To reduce the complexity, several SNR-suboptimal multiple relay selection schemes are proposed, whose complexity is linear in the number of relays. They are proved to achieve full diversity. Simulation shows that they perform much better than the corresponding single relay selection methods and very close to the SNR-optimal multiple relay selection scheme. In addition, for large networks, these multiple relay selection schemes require the same amount of feedback bits from the receiver as single relay selection schemes.

739 citations

### "Performance Analysis of Cooperative..." refers background in this paper

...The authors in [11] discussed the selection schemes of wireless network relay....

[...]

••

01 Feb 2010TL;DR: This paper presents a simple new expression for the exact evaluation of averages of the form E, where x, y, N, y are arbitrary non-negative random variables, in terms of the joint moment generating functions of these random variables.

Abstract: This paper presents a simple new expression for the exact evaluation of averages of the form E [ln (1+x1+...xN/y1+...+yM+1)], where x1,..., xN, y1..., yM are arbitrary non-negative random variables, in terms of the joint moment generating functions of these random variables. Application examples are given for the ergodic capacity evaluation of some multiuser wireless communication systems which are difficult to solve by the known classical methods.

277 citations

••

09 Jun 2013

TL;DR: This work considers a multi-pair relay channel where multiple sources simultaneously communicate with destinations using a relay, and shows that when the number of antennas grows to infinity, the asymptotic achievable rates of MRC/MRT and ZF are the same if the authors scale the power at the sources.

Abstract: We consider a multi-pair relay channel where multiple sources simultaneously communicate with destinations using a relay. Each source or destination has only a single antenna, while the relay is equipped with a very large antenna array. We investigate the power efficiency of this system when maximum ratio combining/maximal ratio transmission (MRC/MRT) or zero-forcing (ZF) processing is used at the relay. Using a very large array, the transmit power of each source or relay (or both) can be made inversely proportional to the number of relay antennas while maintaining a given quality-of-service. At the same time, the achievable sum rate can be increased by a factor of the number of source-destination pairs. We show that when the number of antennas grows to infinity, the asymptotic achievable rates of MRC/MRT and ZF are the same if we scale the power at the sources. Depending on the large scale fading effect, MRC/MRT can outperform ZF or vice versa if we scale the power at the relay.

160 citations

### "Performance Analysis of Cooperative..." refers background in this paper

...In consonance with the ZF concept that aimed to combat the users interference: g2iV g1k = ψki, (3) where ψki = 1 when k = i, and 0 otherwise [13]....

[...]

••

TL;DR: In this paper, the uplink performance of a multicell multiuser single-input multiple-output (SIMO) system with both small-and large-scale fading was investigated.

Abstract: We consider the uplink of a multicell multiuser single-input multiple-output system (MU-SIMO), where the channel experiences both small- and large-scale fading. The data detection is done by using the linear zero-forcing technique, assuming the base station (BS) has perfect channel state information of all users in its cell. We derive new exact analytical expressions for the uplink rate, the symbol error rate (SER), and the outage probability per user, as well as a lower bound on the achievable rate. This bound is very tight and becomes exact in the large-number-of-antenna limit. We further study the asymptotic system performance in the regimes of high signal-to-noise ratio (SNR), large number of antennas, and large number of users per cell. We show that, at high SNRs, the system is interference limited, and hence, we cannot improve the system performance by increasing the transmit power of each user. Instead, by increasing the number of BS antennas, the effects of interference and noise can be reduced, thereby improving system performance. We demonstrate that, with very large antenna arrays at the BS, the transmit power of each user can be made inversely proportional to the number of BS antennas while maintaining a desired quality of service. Numerical results are presented to verify our analysis.

144 citations

••

01 Jan 2005

TL;DR: A wireless ad-hoc network with single antenna nodes under a two-hop traffic pattern is considered and the relaying scheme can outperform the latter in terms of average sum rate and diversity gain and the derivation of the MMSE gain factors is derived.

Abstract: We consider a wireless ad-hoc network with single antenna nodes under a two-hop traffic pattern. Two system architectures are investigated in this paper: Either linear amplify-and-forward relays (LinRel) or a distributed antenna system with linear processing (LDAS) serve as repeaters. The gain factors of the repeaters are assigned such that the mean squared error (MSE) of the signal at the destinations is minimised (multiuser MMSE relaying). A scalar multiplier γm ∈ C at each destination m allows for received signals that are scaled and rotated versions of the transmitted symbols. We distinguish two cases: 1) The factors are equal for all destinations: γm = γ. 2) An individual factor γm is chosen for each destination m. Multiuser MMSE relaying essentially realizes a distributed spatial multiplexing gain with single antenna nodes as all source/destination pairs can communicate concurrently over the same physical channel. The main contribution of this paper is the derivation of the MMSE gain factors. We evaluate the relaying scheme in comparison to multiuser zero forcing (ZF) (1) and show that it can outperform the latter in terms of average sum rate and diversity gain. Keywords - cooperative relaying, ad-hoc networks, distributed spatial multiplexing, minimum mean squared error (MMSE)

91 citations