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Coverage Probability and Achievable Rate Analysis of FFR-Aided Multi-User OFDM-Based MIMO and SIMO Systems

TL;DR: The impact of frequency domain correlation amongst the OFDM sub-bands allocated to the FR1 and FR3 cell-regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the FFR network.
Abstract: Expressions are derived for the coverage probability and average rate of both multi-user multiple input multiple output (MU-MIMO) and single input multiple output (SIMO) systems in the context of a fractional frequency reuse (FFR) scheme. In particular, given a reuse region of $\frac{1}{3}$ (FR3) and a reuse region of 1 (FR1) as well as a signal-to-interference-plus-noise-ratio (SINR) threshold $S_{th}$ , which decides the user assignment to either the FR1 or FR3 regions, we theoretically show that: $1)$ the optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$ , where $T$ is the target SINR required for ensuring adequate coverage, and $2)$ the optimal choice of $S_{th}$ which maximizes the average rate is given by $S_{th}= T^{\prime}$ , where $T^{\prime}$ is a function of the path loss exponent, the number of antennas and of the fading parameters. The impact of frequency domain correlation amongst the OFDM sub-bands allocated to the FR1 and FR3 cell-regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the FFR network. Furthermore, the performance of our FFR-aided MU-MIMO and SIMO systems is compared. Our analysis shows that the (2 $\times$ 2) MU-MIMO system achieves 22.5% higher rate than the (1 $\times$ 3) SIMO system and for lower target SINRs, the coverage probability of a (2 $\times$ 2) MU-MIMO system is comparable to a (1 $\times$ 3) SIMO system. Hence the former one may be preferred over the latter. Our simulation results closely match the analytical results.

Summary (5 min read)

1 Introduction

  • Oil and gas prices have been fluctuating over the past two decades, but started declining in the 2010s.
  • In a 2014 report, the European Commission finds that energy retail prices have increased by 4% annually across all member states over the 2008-2012 period,1 and the average increase in electricity retail prices between 2008 and 2013 amounts to 28%.2.
  • This paper provides an empirical analysis of cost pass-through in the German retail market for electricity.
  • The independent firms, which the authors assume to be most competitive, exhibit 15-20% higher pass-through rates to the competitive market segment; the pass-through rates to baseline tariffs do not significantly differ across firms.
  • These dimensions of heterogeneity are key to go beyond the estimation of average pass-through rates and thus understand the sources of pass-through.

2 Literature

  • The literature on pass-through is quite extensive.
  • There is also a literature using reduced form approaches.
  • Deltas (2008) studies asymmetric pass-through in the US retail gasoline market and finds prices respond faster to wholesale price increases than decreases.
  • This asymmetric response, as well as the speed of adjustment, are shown to be a consequence of retail market power.
  • The authors study is therefore the first to estimate cost pass-through to electricity retail prices using a large and disaggregated panel dataset including both price and cost data, as well as distinguishing several dimensions of heterogeneity in pass-through rates.

3 The German electricity market

  • The German market is characterized by a vertical structure comprising a generation segment, a wholesale market, and retail markets (see figure 1).
  • The transmission network ensures that energy generated or imported is delivered to regional supply companies, which then distribute it via low or medium voltage distribution networks to energy re- tailers and final customers.
  • Finally, a parallel balancing market ensures that the necessary voltage is maintained in the network at any given time.

Insert Figure 1 here

  • The generation segment in Germany is dominated by three vertically integrated, although legally unbundled, utilities: E.ON, RWE, and Energie Baden-Württemberg (EnBW).
  • They jointly meet 2/3 - 3/4 of the total German electricity demand.
  • Other companies, including EWE and RheinEnergie, collectively represent [55-65 per cent] of this market."the authors.
  • All big players lost some market share over time, yet, at the national level, they continue to cover almost half of the market.
  • This rather aggregated picture is partially misleading.

Insert Figure 2 here

  • While several retailers offer different tariffs in each of these regions, incumbent providers are legally obliged to sell energy at a baseline tariff to all household customers who do not explicitly choose another provider.
  • Accordingly, this baseline tariff constitutes an upper bound for the energy retail prices in a given region because it is automatically chosen by customers unwilling or lacking the information to switch supplier.
  • The number of 8According to German law, the incumbent is the firm that serves the majority of household costumers in a local market at a given point in time.
  • The incumbent provider is newly defined every three years.
  • Households switching providers has grown at an increasing rate over time, yet incumbent providers have maintained a very strong customer base.

3.1 Retail price structure

  • The authors empirical analysis focuses on the evolution of retail prices, in particular on their relationship with wholesale prices and network charges.
  • On the one hand, they are affected by electricity wholesale prices that constitute the main essential input for retailers.
  • On the other hand, they are also strongly influenced by other factors, including the cost of transmission and distribution, concession fees, as well as taxes and other fees.
  • In its 2012 monitoring report (Bundesnetzagentur (2012)), the German regulator discusses the structure of retail tariffs in depth for household customers, whose national average composition for the 2006-2012 period is reported in figure 3.

Insert Figure 3 here

  • These average values are useful to understand the various components of retail tariffs.
  • Therefore, retail tariffs present a lot of cross-sectional variation across, as well as timeseries variation within regions.
  • The German regulator reports that the cost of energy purchase varies within different types of firms.
  • Since 2007, entrants achieved on average more favorable conditions mostly because they buy energy from the wholesale markets through shorter-term contracts and wholesale energy prices have decreased.
  • Customers living in urban areas tend to switch more because they tend to be better informed and because they face a larger set of available tariffs.

4 The data

  • The main data source for the analysis is the price comparison site Verivox, which provides highly disaggregated data on energy retail prices, specifically, monthly price data between January 2007 and August 2014 for 8,192 different postal codes (located in 6,205 cities across all 16 German states) from 893 different incumbent providers and 497 different non-incumbent providers.
  • In Table 1, the authors present summary statistics on retail prices in the data-set.
  • These bounds are used to define the variable ’price dispersion’ which represents the difference between the most and least expensive tariff in each postal code and period.
  • Thus, e67.1 per mWh or more than 25% could have been saved by switching from the baseline tariff to the least expensive tariff.
  • Municipal providers make up 19% of incumbents, while another 19% have a joint ownership structure.

Insert Table 2 here

  • The data on the costs of purchasing and transmitting electricity are obtained from EEX and ene‘t respectively.
  • The authors aggregate these cost factors (network charges, concession fees and wholesale energy) into a single cost variable, indicating the per-mWh cost of providing energy.
  • Note that while network charges and concessions fees are postal code-specific, thus varying across regions and time, wholesale prices are uniform across Germany and only vary over time.
  • 9All their findings are robust to using month-ahead, quarter-ahead or half-year ahead wholesale prices instead.
  • Finally, looking at the evolution of costs over time (figure 4, panel (c)) the authors see a significant peak in 2008, while costs mostly remain in the range of e 110 to e 120 per mWh in the years before and after.

Insert Figure 4 here

  • As discussed above, the heterogeneity in costs, demand, and competitive conditions at the regional level leads to significant retail price dispersion across local markets.
  • Figure 5 shows this geographical dispersion for one specific tariff – baseline tariff for a consumption of 2,800 kWh – for one particular point in time – the year 2010.
  • The different colors represent the quartiles of the price distribution.

Insert Figure 5 here

  • The authors observe significant differences in the level of the baseline tariffs across regions.
  • Baseline tariffs are highest in the north-eastern part of Germany, where the price of consuming one mWh of electricity lies in the (257, 302] interval in almost all regions.
  • In the southeastern part, this cost range is substantially lower with almost all regions belonging to the [207, 248] interval.
  • The west of Germany has more homogeneous prices, with most values lying in the second and third quartile.
  • The different colors represent the quartiles of the price-dispersion distribution.

Insert Figure 6 here

  • There is significant price dispersion in each area and significant cross-area differences in the size of this dispersion.
  • It varies between e26 (lowest value of the first quartile) and e107 (highest value of the fourth quartile) by mWh consumed.
  • This is quite substantial given that the average baseline tariff (best) price for consumption of one mWh is around e260 (e190).

Insert Table 3 here

  • Finally, the authors employ a large number of control variables at the postal code level which are also obtained from ene‘t.
  • The total population, the number of available distribution grids, their total length, the capacity of energy transformers, the total number of household connections (metering points), network losses in percent, cost of network losses in e, as well as total energy transmitted, also known as These include.
  • Table 3 contains summary statistics on network charges, wholesale prices and the control variables.

5 Model and estimation equation

  • The empirical model the authors apply to the data aims at estimating the pass-through rates of network charges and wholesale prices on retail tariffs, while at the same time controlling for local supply and demand conditions.
  • Even though electricity is a rather homogeneous good, contracts are perceived by costumer to be vertically differentiated, as the several tariffs of the different retailers in a given regional market are offered under different conditions (length of the contract, conventionally produced or ’green’ electricity, bonuses, quality of service, etc.).
  • The authors also add a large set of fixed-effects.
  • In a first step, the authors assume that β is common to all observations, thus reflecting the average pass-through of costs to retail prices in the whole sample.
  • Third, the authors estimate firm-type f specific pass-through rates so that they obtain separate pass-through rates for municipal, big-four, independent and other retailers as well as the different tariff types βi f .

6 Results

  • The authors discuss the main regression results.
  • In the first column, the authors look at the most aggregate specification where the tariffs are pooled.
  • Tariffs are positively related with demand drivers such as population and the number of connections as well as with costs drivers such as network loss and their costs.
  • 12This level of clustering aims at capturing that many providers – especially the big four – mostly offer tariffs that are homogenous across regions.
  • With measures of efficiency such as the number of grids, the total grid lengths, and the transformer capacity.

Insert Table 4 here

  • The authors then split the sample according to the two tariff types – ’incumbent base’ and ’overall best’– which allows us to estimate heterogeneous pass-through rates depending on the customers’ types.
  • The authors expect customer who buy the ’best’ tariff to be better informed and to have smaller switching costs.
  • Therefore, the authors expect these tariffs to be more competitive and to reflect more strongly changes in costs.
  • The coefficient estimate of the cost variable increases to 70% for the overall best tariff, while it drops to 49% for the baseline tariff.
  • In the next step the authors allow the pass-through to vary across firm types in an effort to analyze whether firms differ with respect to downstream market power.

Insert Table 5 here

  • The rate of cost pass-through to the incumbent base tariff is close to and not significantly different from 49% for all firm types, which is the same pass-through rate the authors found in the pooled specification (table 4, column 2).
  • In the more competitive market segment, the authors find that independent firms exhibit the highest degree of pass-through.
  • The next dimension of heterogeneity that the authors exploit in the econometric analysis is time.
  • In table 6 the authors report the results for the specifications where they estimate a time-dependent pass-through for the different tariffs.
  • In contrast, the best tariff passthrough rate, starts out at around 40% at the beginning of the sample period, increases in 2010 and, after a dip in 2011, becomes almost unity for the final years in the sample.

Insert Table 6 here

  • This result appears particularly interesting as it suggests that, after 2011, the passthrough rate for the most competitive part of the market, i.e., the best tariffs, is almost complete.
  • This is consistent with almost perfect competitive outcomes in this segment of the market.
  • The final step of their empirical analysis is to allow the maximum amount of heterogeneity in the pass-through rates, which are estimated to be tariff, firm, and time-specific.
  • Because of the large amount of estimated coefficients, the authors present the results graphically in figures 7 and 8 for the baseline and best tariffs respectively.

Insert Figure 8 here

  • While the authors see a different evolution of pass-through rates across tariffs, i.e., market segments, as before, they do not find significant differences across firms.
  • Thus, all types of firms in their data exhibit remarkably similar dynamics in their pass-through behavior over time.
  • For most time periods, the authors see that the pass-through rates of independent firms tend to be the highest, but not by a large margin.
  • Again, these results seem to suggest that the pass-through rate is mostly driven by consumer behavior as represented by the different tariff types rather than by firms’ characteristics.

7 Conclusion

  • In this paper the authors study the pass-through of cost shocks to household retail electricity tariffs in Germany.
  • The authors have precise information on the two major cost drivers for electricity retail prices – the regulated network fee and the wholesale electricity prices – which together constitute more than 2/3 of the cost of providing electricity to household customers and are able to control for most other cost factors through several time-varying drivers and numerous fixed effects.
  • They are significantly larger for those segments of the markets where demand is more elastic because consumers have lower switching costs and consider products to be less differentiated, while they are higher in market segments where the opposite is true.
  • The average pass-through of 60% decreases to around 50% for the incumbents’ baseline tariffs and increases to 70% for tariffs designed for the more mobile costumers.
  • The differences across different firm types appear to be limited: while the changes over time are substantial, the pass-through rates of different firm types tend to move in tandem and are not significantly different from each other.

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Proof
IEEE TRANSACTIONS ON COMMUNICATIONS 1
Coverage Probability and Achievable Rate Analysis
of FFR-Aided Multi-User OFDM-Based
MIMO and SIMO Systems
1
2
3
Suman Kumar, Sheetal Kalyani, Lajos Hanzo, Fellow, IEEE, and K. Giridhar, Member, IEEE4
Abstract—Expressions are derived for the coverage probability5
and average rate of both multi-user multiple input multiple output6
(MU-MIMO) and single input multiple output (SIMO) systems7
in the context of a fractional frequency reuse (FFR) scheme. In8
particular, given a reuse region of
1
3
(FR3) and a reuse region of9
1 (FR1) as well as a signal-to-interference-plus-noise-ratio (SINR)10
threshold S
th
, which decides the user assignment to either the FR111
or FR3 regions, we theoretically show that: 1) the optimal choice12
of S
th
which maximizes the coverage probability is S
th
= T,where13
T is the target SINR required for ensuring adequate coverage, and14
2) the optimal choice of S
th
which maximizes the average rate is15
given by S
th
= T
,whereT
is a function of the path loss exponent,16
the number of antennas and of the fading parameters. The impact17
of frequency domain correlation amongst the OFDM sub-bands18
allocated to the FR1 and FR3 cell-regions is analysed and it is19
shown that the presence of correlation reduces both the coverage20
probability and the average throughput of the FFR network.21
Furthermore, the performance of our FFR-aided MU-MIMO and22
SIMO systems is compared. Our analysis shows that the (2 × 2)23
MU-MIMO system achieves 22.5% higher rate than the (1 × 3)24
SIMO system and for lower target SINRs, the coverage probability25
of a (2 × 2) MU-MIMO system is comparable to a (1 × 3) SIMO26
system. Hence the f ormer one may be preferred over the latter.27
Our simulation results closely match the analytical results.28
Index Terms—Author, please supply index terms/keywords for29
your paper. To download the IEEE Taxonomy go to http://www.30
ieee.org/documents/taxonomy_v101.pdf.31
I. INTRODUCTION32
O
RTHOGONAL frequency division multiple access
AQ1
33
(OFDMA) based systems maintain orthogonality among34
the intra-cell users, but the radical OFDMA system deploy-35
ments relying on a frequency reuse factor of unity suffer from36
inter-cell interference. As a remedy, inter-cell interference coor-37
dination (ICIC) schemes have been designed for minimizing the38
co-channel interference [1]. Fractional frequency reuse (FFR)39
[2] constitutes a low complexity ICIC scheme, which has been40
proposed for OFDMA based wireless networks such as IEEE41
WiMAX [3] and 3GPP LTE [4].42
Manuscript received January 18, 2015; revised June 5, 2015; accepted
August 1, 2015. The associate editor coordinating the re view of this paper and
approving it for publication was O. Oyman.
S. Kumar, S. Kalyani, and K. Giridhar are with the Indian Institute of
Technology Madras, Chennai 600 036, India (e-mail: ee10d040@ee.iitm.ac.in;
AQ2
skalyani@ee.iitm.ac.in; giri@ee.iitm.ac.in).
L. Hanzo is with the School of Electrical and Computer Science, University
of Southampton, Southampton SO17 1BJ, U.K. (e-mail: lh@ecs.soton.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TCOMM.2015.2465907
Fig. 1. Frequency allocation in FFR for three neighbouring cells with δ = 3.
The cell-centre users of all the cells rely on a common frequency band F
0
, while
the cell-edge users of the three cells occupy different frequency bands, namely
F
1
, F
2
and F
3
.
Explicitly, FFR is a combination of frequency reuse 1 (FR1) 43
and frequency reuse
1
δ
(FRδ). FR1 allocates all the frequencies 44
to each cell, leading to a unity spatial reuse, hence results in 45
a low-quality coverage due to the excessive inter-cell interfer- 46
ence. On the other hand, FRδ allocates a fraction of
1
δ
of the 47
frequencies to each cell and therefore reduces the area-spectral- 48
efficiency, but improves the SINR. FFR strikes an attractive 49
trade-off by exploiting the advantages of both FR1 and FRδ by 50
relying on FR1 for the cell-centre users i.e. for those users who 51
would experience less interference from the other cells, because 52
they are close to their serving base station (BS). By contrast, 53
FRδ is invoked for the cell-edge users i.e. for those users who 54
would experience high interference afflicted by the co-channel 55
signals emanating from the neighbouring cells in case of FR1, 56
because they are far from their serving BS. Typically, there 57
are two basic modes of FFR deployment: static and dynamic 58
FFR [1]. In this paper, we consider the more practical static 59
FFR scheme, where all the parameters are configured and kept 60
fixed over a certain period of time [5]. Fig. 1 depicts a typical 61
frequency allocation in the context of the FFR scheme for three 62
adjacent cells, where F
1
, F
2
and F
3
each use x% of the total 63
spectrum, hence F
0
uses (100 3x)% of the spectrum. 64
FFR schemes have been lavishly studied using both system 65
level simulations and theoretical analysis [6]–[11]. The optimiz- 66
ation of FFR relying on a distance threshold
1
or SINR threshold
2
67
1
Based on a pre-determined distance from the BS, the subscribers are divided
into cell-centre as well as cell-edge users and hence here the design parameter
is a distance threshold (R
th
).
2
Based on a pre-determined SINR, the subscribers are divided into cell-
centre as well as cell-edge users and here the design parameter is the SINR
threshold (S
th
).
0090-6778 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

IEEE
Proof
2 IEEE TRANSACTIONS ON COMM UNICATIONS
has been studied using graph theory in [6] and convex optimiza-68
tion in [7]. Specifically, it h as been shown in [7] that the optimal69
frequency reuse factor is FR3 for the cell-edge users. The av-70
erage cell throughput of an FFR system was derived in [8] as a71
function of the distance threshold. It was shown in [9] that there72
exists an optimal radius threshold for which the average rate be-73
comes maximum. The performance of FFR and soft frequency74
reuse (SFR) has been studied in [12] under both fully loaded75
and partially loaded scenarios. An algorithm was proposed76
in [13] for enhancing the network capacity and the cell-edge77
performance for a dynamic SFR deployment relying on re-78
alistic irregularly shaped cells. A fuzzy logic based generic79
model was proposed for deriving different frequency reuse80
schemes in [14]. As a further development, an FFR based 3-cell81
network-MIMO based tri-sector BS architecture was presented82
in [15]. FFR and SFR are compared in the presence of corre-83
lated interferers in [16]. The optimal configuration o f FFR is84
determined in [17] for a high-density wireless cellular network.85
The authors of [18] have proposed a distributed and adaptive86
solution for interference coordination based on the center of87
gravity of users in each sector. An optimal FFR and power88
control scheme which can coordinate the interference among89
the heterogeneous nodes is proposed in [19].90
An analytical framework of calculating both the coverage91
probability (CP
r
) and the average rate of FFR schemes was92
presented in [10] and [11] for homogeneous single input single93
output (SISO) and MIMO heterogeneous networks, respec-94
tively, using a Poisson point process (PPP). However, the au-95
thors of [10], [11] assumed having an unplanned FFR network,96
where the cells using the same frequency set are randomly97
allocated. Hence, two cells using the same frequency for the98
cell-edge users may in fact be co-located [10], [11]. However,99
in case of FFR based deployments the regions using the same100
frequency are typically planned to be as far apart as possible101
and our focus is on these types of deployments. An FFR-aided102
distributed antenna system (DAS) and an FFR-aided picocell103
was studied in [20] and [21]. While, an FFR-aided femtocell104
has been extensively studied in [22]–[26].105
However, most of the work based on FFR has considered the106
conventional SISO case. To the best of our knowledge, no prior107
work has analytically derived the optimal SINR threshold for108
FFR, when the number of antennas is high at the transmitter109
and/or at the receiver. Hence, in this work, we derive both the110
CP
r
and the average achievable rate expressions of FFR in the111
presence of both MU-MIMO as well as of SIMO systems and112
derive the optimal SINR threshold corresponding to the desired113
CP
r
and throughput. Furthermore, the performance of FFR-114
aided MU-MIMOs is compared to that of FFR in the presence115
of a SIMO system.116
The key benefit of MU-MIMO is their ab ility to improve117
the spectral efficiency, which has b een extensively studied in118
a single-cell context in the presence of AWGN [27]–[29].119
However, it has been shown in [30], [31] with the h elp of120
simulation, that the efficiency of MU-MIMOs is significan tly121
eroded in a multi-cell environment due to interference, es-122
pecially in the cell-edge region. FFR is capable of signifi-123
cantly improving the cell-edge coverage since it uses FR3 for124
the cell-edge users. Hence we study FFR-aided MU-MIMOs125
and quantify their average throughput as well as coverage 126
probability. 127
Furthermore, we carefully examine the correlation of the sub- 128
bands F
0
, F
1
, F
2
and F
3
in Fig. 1 used in the FFR system 129
considered. All prior work on FFR has assumed that the sub- 130
bands experience independent fading, which is mathematically 131
convenient, but practically not realisable. Indeed, when we 132
consider practical transmission block based modulation such as 133
OFDM, the channel’s delay spread is assumed to b e confined to 134
the cyclic prefix of the OFDM symbol. Such a limited-duration 135
(typically less than 20% of the useful OFDM symbol duration) 136
impulse response will result in correlation amongst the adjacent 137
freque ncy domain OFDM sub-channels. More explicitly, unless 138
the sub-bands F
0
···F
3
are spaced apart by more than the recip- 139
rocal of the delay spread, correlation will exist. Since the delay 140
spread experienced in the downlink is user-dependent, it is vir- 141
tually impossible to ensure that the sub-bands F
i
in Fig. 1 are in- 142
dependent for each user scheduled in the downlink. Therefore, 143
in our analysis we will specifically take into account the corre- 144
lation of the sub-bands. For FFR-aided MU-MIMO and SIMO 145
systems, the expressions of CP
r
and average rate are derived 146
and the following new results are presented: 147
(a) The optimal SINR threshold that m aximizes th e CP
r
of 148
FFR is derived for a given T. We show that the optimal 149
S
th
(denoted by S
opt,C
)isS
th
= T for both the MU-MIMO 150
and SIMO system, and if we choose the SINR threshold 151
to be S
opt,C
, then the achievable CP
r
of FFR is higher 152
than that of FR3. The improvement of the FFR CP
r
over 153
that of FR3 is due to the resultant sub-band diversity gain 154
achieved by the systems when a user is classified as either 155
a cell-centre or a cell-edge user. 156
(b) The optimal SINR threshold that maximizes the average 157
rate of FFR is derived. We show that the optimal S
th
(de- 158
noted by S
opt,R
) is equal to T
for both MU-MIMO and 159
SIMO systems, where T
is a fixed SINR value, which de- 160
pends on the system p arameters such as the path loss expo- 161
nent, the number of antennas, the fading parameters, etc. 162
(c) The correlation of the sub-bands always degrades both the 163
CP
r
and the average rate of the FFR-aided MU-MIMO 164
and SIMO systems. 165
(d) The performance of FFR-aided MU-MIMO and SIMO 166
systems is compared. It is shown that system designer 167
may choose the (2 × 2) MU-MIMO system over (1 × 3) 168
SIMO system of FFR scheme as MU-MIMO achieves 169
significant gain in average rate over SIMO. 170
We will demonstrate that our analytical results are in close 171
agreement with the simulation results. Moreover, it is shown 172
that at optimal S
th
, the FFR achieves significantly high gain in 173
CP
r
than that of average rate with respect to FR1 and hence this 174
scheme would be more useful when coverage gain is essentially 175
required. Therefore, FFR-aided MU-MIMO provides both high 176
average rate and satisfactory CP
r
foralowervalueofN
a
. 177
II. SYSTEM MODEL 178
A homogeneous macrocell network relying on hexagonal 179
tessellation and on an inter cell site distance of 2R is considered, 180

IEEE
Proof
KUMAR et al.: COVER AGE PROBABILITY AND ACHIEVABLE RATE ANALYSIS OF MU-MIMO AND SIMO SYSTEMS 3
Fig. 2. Hexagonal structure of 2-tier macrocell. Interference for 0th cell in
FR1 system is contributed form all the neighbouring 18 cells, while in a FR3
system it is contributed only from the shaded cells.
as shown in Fig. 2. Both a MU-MIMO and a SIMO system is181
considered. We assume that in the MU-MIMO case each user182
is equipped with N
r
receive antennas, while the BS is equipped183
with N
t
transmit antennas and that N
t
= N
r
. Our focus is on the184
downlink and hence N
t
transmit antennas are used for transmis-185
sion, while the N
r
receive antennas at the UE are u sed for re-186
ception. We also assume that all N
t
transmit antennas at the BS187
are u tilized to transmit N
t
independent data steams to its own N
t
188
users. A linear minimum mean-square-error (LMMSE) receiver189
[32] is considered. In order to calculate the p ost-processing190
SINR of this LMMSE r eceiver, it is assumed that the (N
r
1)191
closest interferers can be completely cancelled using the anten-192
nas at the receiver.
3
For example, in the MU-MIMO case, the193
user will not experience any intra-tier interference emanating194
from the serving BS as N
t
= N
r
. In the SIMO case each user195
is equipped with N
r
antennas. The SINR η
t
(r) of a user in the196
MU-MIMO system and the SINR η
r
(r) of a user in the SIMO197
system located at r meters from its serving BS are given by198
η
t
(r) =
gr
α
σ
2
P
+ I
t
, I
t
=
iψ
N
t
j=1
h
ij
d
α
i
(1)
and
199
η
r
(r) =
gr
α
σ
2
P
+ I
r
, I
r
=
iψ
r
h
ij
d
α
i
, (2)
respectively, where the transmit power of a BS is denoted by P.
200
Here ψ is the set of interfering BSs in the FR1 network and ψ
r
201
denotes all the interfering BSs, excluding the nearest (N
r
1)202
interferers, while N
t
denotes the number of transmit antennas.203
The standard path loss model of x
α
is assumed, where204
α 2 is the path loss exponent and x is the distance of a user205
from the BS. We assumed that the users are at least at a distance206
of d away from the BS.
4
The noise power is d enoted by σ
2
.207
Here, r and d
i
are the distances from the user to the serving BS208
andtothei
th
interfering BS, respectively, while g and h
i
denote209
3
It is widely exploited that using the LMMSE receiver (N
r
1) interferers
can be mitigated, where N
r
is the number of receive antennas [32]. Ho wever,
for simplicity, we assume that the N
r
1 closest interferers can be completely
cancelled.
4
Typically , the path loss model is assumed to be max{d, x}
α
.
the corresponding channel fading power, which are independent 210
and identically exponentially distributed (i.i.d.) with a unit 211
mean, i.e., g exp(1) and h
i
exp(1) i. In MU-MIMO case, 212
h
ij
is the channel’s fading power from the j
th
antenna of the 213
i
th
interfering BS to the user and it is i.i.d. with a unit mean. 214
Without loss of generality we have considered a user in the 0
th
215
cell of Fig. 2 in our analysis. 216
Similar to [10], the subscribers are classified as cell-centre 217
users and cell-edge users based on the SINR at the mobile sta- 218
tion. If the calculated SINR of a user is lower than the specified 219
SINR threshold S
th
, the user is classified as a cell-edge user. 220
Otherwise, the user is classified as a cell-centre user. Typically, 221
FFR divides the whole frequency band into a total of (1 + δ) 222
parts, where F
0
is allocated to all the cells for the cell-centre 223
users, as seen in Fig. 1. One of the {1 , ··· } parts is assigned 224
to the cell-edge users in each cell in a planned fashion. The 225
users are assumed to be uniformly distributed in a cell and all r e- 226
source blocks are uniformly shared among the users. The trans- 227
mit power is assumed to b e fixed. If we have η
t
(r)(or η
r
(r)) 228
S
th
for a user, then the user will continue to experience the same 229
fading power, i.e., g and h
i
from the user to the serving BS 230
andtothei
th
interfering BS, respectively. However, if we have 231
η
t
(r)(or η
r
(r)) < S
th
for a user, the user is allocated another 232
sub-band (from the set of sub-bands assigned to cell-edge users) 233
and it experiences a new fading power, i.e., ˆg and
ˆ
h
i
from the 234
user to the serving BS and to the i
th
interfering BS, respectively. 235
Based on the coherence bandwidth of the OFDM system, and 236
the bands associated with F
0
to F
3
in Fig. 1 is is possible that ˆg 237
and
ˆ
h
i
are either correlated with or independent of g and h
i
,re-238
spectively. Note that g, ˆg, h
i
,and
ˆ
h
i
are the channel gains in the 239
frequency domain and the term correlation is used for referring 240
to frequency domain correlation in this paper. The correlation 241
depends both on the particular user’s channel conditions and 242
on the instantaneous coherence bandwidth with respect to the 243
FFR frequency bands. To better understand the impact of corre- 244
lation among the sub-bands on the FFR system’s performance, 245
in this paper, we consider the following two extreme cases: 246
Case 1: g and ˆg are independent and also h
i
as well as
ˆ
h
i
,are247
independent for all i. 248
Case 2: g and ˆg are fully correlated and also h
i
as well as
ˆ
h
i
, 249
are fully correlated for all i. 250
In reality these channel output powers may be partially corre- 251
lated, but the analysis of partial (arbitrary) corr e lation is quite 252
complicated and hence it is beyond the scope of this work. 253
However, the analysis of the above two extreme cases we be- 254
lieve, is sufficient for understanding the impact of correlation 255
among the sub-bands. 256
III. COVERAGE PROBABILITY ANA LY S I S O F FFR 257
In this section, we first derive the CP
r
of both the 258
MU-MIMO and SIMO system considered, which is defined 259
as the probability that a randomly chosen user’s instantaneous 260
SINR η
t
(r) is higher than T. This defines, the average fraction 261
of users are having an SINR higher than the target SINR. The 262
coverage prob ability is determined by the complementry cumu- 263
lative distribution function of the SINR over the network. The 264

IEEE
Proof
4 IEEE TRANSACTIONS ON COMM UNICATIONS
CP
r
of a user who is at a distanc e of r meters from the BS in a265
FR1-aided MU-MIMO scenario is given by266
P
1
(T, r) = P [η
t
(r)>T] = P
g > Tr
α
I
t
+ Tr
α
σ
2
P
, (3)
where I
t
is defined in (2). Since g exp(1), h
ij
exp(1),and267
h
ij
are i.i.d., P
1
(T, r) is given by268
P
1
(T, r) = E
h
ij
e
Tr
α
I
t
Tr
α
σ
2
P
=
iψ
N
t
j=1
E
h
ij
e
Tr
α
h
ij
d
α
i
× e
Tr
α
σ
2
P
=
iψ
1
1 + Tr
α
d
α
i
N
t
e
Tr
α
σ
2
P
, (4)
where ψ is the set of interfering BSs in a FR1 network.
269
Similarly, the CP
r
of a user located at a distance of r meters270
from the BS in a FR3 network can be formulated as271
P
3
(T, r) =
iφ
1
1 + Tr
α
d
α
i
N
t
e
Tr
α
σ
2
P
(5)
where φ is the set of interfering cells in the FR3 scheme, w hich
272
is a function of the frequency reuse plan. Also, the CP
r
of a user273
in the SIMO-based FR1 network and in a FR3 network can be274
expressed as275
P
1
(T, r) =
iψ
r
1
1 + Tr
α
d
α
i
e
Tr
α
σ
2
P
and
P
3
(T, r) =
iφ
r
1
1 + Tr
α
d
α
i
e
Tr
α
σ
2
P
. (6)
Here φ
r
denotes the set of interfering cells in the FR3 scheme276
excluding the nearest (N
r
1) interferers. Let us now derive277
the CP
r
of FFR for both the independent and correlated cases.278
A. Case 1: g and ˆg are Independent as Well as h
i
and
ˆ
h
i
are279
Also Independent for all i280
The CP
r
P
F,c
(r) of a cell-centre user who is at a distance of281
r meters from the 0
th
BS in a FFR-aided MU-MIMO scenario282
is given by283
P
F,c
(r)
(a)
= P [η
t
(r)>T|η
t
(r)>S
th
]
= P
gr
α
I
t
+
σ
2
P
> T
gr
α
I
t
+
σ
2
P
> S
th
,
where (a) follows from the fact that a cell-centre user has SINR
284
S
th
. Upon applying Bayes’ rule, one can rewrite P
F,c
(r) as285
P
F,c
(r) =
P
gr
α
I
t
+
σ
2
P
> T,
gr
α
I
t
+
σ
2
P
> S
th
P
gr
α
I
t
+
σ
2
P
> S
th
=
iψ
1
1+max{T,S
th
}r
α
d
α
i
N
t
e
max{T,S
th
}r
α
σ
2
P
jψ
1
1+S
th
r
α
d
α
j
N
t
e
S
th
r
α
σ
2
P
. (7)
Similarly, the CP
r
of a cell-edge user who is at a distance of r 286
meters from the BS in the FFR-aided MU-MIMO case P
F,e
(r) 287
is given by 288
P
F,e
(r) = P
ˆη
t
(r)>T|η
t
(r)<S
th
=
P
ˆgr
α
ˆ
I
t
+
σ
2
P
> T,
gr
α
I
t
+
σ
2
P
< S
th
P
gr
α
I
t
+
σ
2
P
< S
th
.
Here, the cell-edge user will experien ce the new interference
289
term of
ˆ
I
t
=
iφ
N
t
j=1
ˆ
h
ij
d
α
i
and the new channel power ˆg,i.e.a290
new SINR ˆη(r) due to the fact that th e cell-edge user is now a 291
FR3 user. Basically, ˆη(r) denotes the SINR experienced by the 292
user at a distance of r meters from the BS in a FR3 system and 293
is given by 294
ˆη(r) =
ˆgr
α
ˆ
I
t
+
σ
2
P
,
ˆ
I
t
=
iφ
N
t
j=1
ˆ
h
ij
d
α
i
. (8)
Since both g and ˆg as well as h
i
and
ˆ
h
i
areassumedtobei.i.d,295
P
F,e
(r) can be simplified to 296
P
F,e
(r) = P
ˆgr
α
ˆ
I
t
+
σ
2
P
> T
= P
3
(T, r). (9)
Let us now derive the CP
r
P
f
(r) of a user in the FFR-aided 297
MU-MIMO system, which can be written as 298
P
F
(r) =P
F,c
(r)P [η
t
(r)>S
th
] + P
F,e
(r)P [η
t
(r)<S
th
] . (10)
Here, the first term denotes the CP
r
contributed by the cell- 299
centre users, while the seco nd term denotes the contribution of 300
the cell-edge users. By using the expression in (7) for P
F,c
(r) 301
and the expression in (9) for P
F,e
(r), (10) can be simpli- 302
fied to 303
P
F
(r) =
iψ
1
1 + max{T, S
th
}r
α
d
α
i
N
t
e
max{T,S
th
}r
α
σ
2
P
+ P
3
(T, r) P
3
(T, r)P
1
(S
th
, r). (11)
Lemma 1: The optimum S
th
(denoted by S
opt,C
)thatmaxi-304
mizes the FFR-aided coverage probability is S
th
= T,andwhen305
the SINR threshold is set to S
opt,c
, the coverage probability of 306
FFR becomes higher than that of FR3. 307
Proof: See Appendix A for the proof. 308
B. Case 2: g and ˆg are Completely Correlated as Well as h
i
309
and
ˆ
h
i
are Also Completely Correlated for all i 310
Note th at the centre CP
r
is the same for both the above 311
Case 1 and for this case, since a user does not change its sub- 312
band, when it becomes a cell-centre user because if η
t
(r) S
th
313
for a user, then it will continue to experience the same fading 314
power. However, the edge CP
r
is different in Case 1 as well as 315
Case 2, and in this scenario the CP
r
P
F,e
(r) of a cell-edge user, 316

IEEE
Proof
KUMAR et al.: COVER AGE PROBABILITY AND ACHIEVABLE RATE ANALYSIS OF MU-MIMO AND SIMO SYSTEMS 5
who is at a distance of r meters from the BS in our FFR network317
is given by318
P
F,e
(r) =P
ˆη
t
(r)>T|η
t
(r)<S
th
=
P
ˆη
t
(r)>T
t
(r)<S
th
P [η
t
(r)<S
th
]
.
(12)
Substituting the value of P
F,c
and P
F,e
from (7) and (12) into319
Eq. (10), the CP
r
P
f
(r) in our FFR network can be written as320
P
F
(r) =
iψ
1
1 + max{T, S
th
}r
α
d
α
i
N
t
e
max{T,S
th
}r
α
σ
2
P
+ P
ˆη
t
(r)>T
t
(r)<S
th
. (13)
Recall that η
t
(r) and ˆη
t
(r) represent the SINR experienced by a321
user in an FR1 and an FR3 system, respectively. Note that even322
though g and ˆg as well as h
i
and
ˆ
h
i
are completely correlated,323
η
t
(r) is not the same as ˆη
t
(r), because the set of interferers are324
different in the denominator of the η
t
(r) and ˆη
t
(r) expressions325
given in (2) and (8), respectively, i.e., ψ corresponds to the326
set of interferers in the FR1 network, while φ corresponds to327
the set of interferers in the FR3 network. Since g and ˆg are328
completely correlated and h
i
and
ˆ
h
i
are also completely corre-329
lated for all i, we use the following transformation to further330
simplify P
F
(r):331
P
ˆη
t
(r)>T
t
(r)<S
th
=P
ˆη
t
(r)>T, ˆη
t
(r)<
ˆ
S
th
. (14)
Basically instead of marking a user as a cell-edge user based
332
on the FR1 SINR η
t
(r), we mark them on the basis of the FR3333
SINR ˆη
t
(r) by introducing a new SINR threshold
ˆ
S
th
.Inother334
words, we introduce a new SINR threshold
ˆ
S
th
for ensuring that335
if for any user we have η
t
(r)<S
th
, then for the same user we336
have ˆη
t
(r)<
ˆ
S
th
and vice-versa. The threshold
ˆ
S
th
is computed337
using the relationship of P[η
t
(r)<S
th
]=Pη
t
(r)<
ˆ
S
th
].This338
ensures that the same user is marked as a cell-edge user for both339
reuse patterns FR1 and FR3. Now, using the transformation340
given in (14), P
F
(r) can be simplified to341
P
F
(r) =
iψ
1
1 + max{T, S
th
}r
α
d
α
i
N
t
e
max{T,S
th
}r
α
σ
2
P
+ P
ˆη(r)>T
P
ˆη(r)>max{
ˆ
S
th
, T}
. (15)
In this case, to obtain the optimum S
opt,C
, we co nsider the342
following two possibilities: (i) S
th
T, (ii) S
th
< T.343
(i) S
th
T: In this scenario, CP
f
(r) can be expressed in344
terms of T as:345
P
F
(r, S
th
T) =
iψ
1
1 + S
th
r
α
d
α
i
e
S
th
r
α
σ
2
P
+ P
3
(T, r) P
3
(
ˆ
S
th
, r). (16)
Since we have P
3
(
ˆ
S
th
, r) = P
1
(S
th
, r) and P
1
(S
th
, r) =346
iψ
1
1+S
th
r
α
d
α
i
N
t
e
S
th
r
α
σ
2
P
, hence347
P
F
(r, S
th
T) = P
3
(T, r). (17)
(ii) S
th
< T: In this case P
f
(r) can be formulated in terms 348
of T as: 349
P
F
(r, S
th
< T) =
iψ
1
1 + Tr
α
d
α
i
N
t
e
Tr
α
σ
2
P
+ P
3
(T, r) P
3
max{
ˆ
S
th
, T}, r
. (18)
Note that when S
th
< T,
ˆ
S
th
may be higher or lower than T. 350
When
ˆ
S
th
> T, 351
P
3
max{
ˆ
S
th
, T}, r
=P
3
(
ˆ
S
th
, r) =P
1
(S
th
, r)>P
1
(T, r) (19)
since S
th
< T.Andwhen
ˆ
S
th
< T,wehave: 352
P
3
max{
ˆ
S
th
, T}, r
= P
3
(T, r)>P
1
(T, r). (20)
Hence, we arrive at:
353
P
F
(r, S
th
< T) =
iψ
1
1 + Tr
α
d
α
i
N
t
e
Tr
α
σ
2
P
+ P
3
(T, r) P
3
max{
ˆ
S
th
, T}, r
< P
3
(T, r). (21)
Comparing the FFR CP
r
for S
th
T and S
th
< T given by (17) 354
and (21), respectively, it becomes apparent that P
F
(r, S
th
355
T)>P
F
(r, S
th
< T). I n other words, when the fading is fully 356
correlated across the sub-bands, the optimal choice of the SINR 357
threshold is S
th
T and at the optimal SINR threshold the FFR 358
scheme succeeds in achieving the FR3 CP
r
. Unlike for Case 1, 359
the FFR CP
r
is not better than the FR3 CP
r
since there is no sub- 360
band diversity gain, when a user moves from the cell-centre to 361
the cell-edge region. 362
In order to find the CP
r
for a typical user, we have to calculate 363
the probability density function (pdf) of r, which is the distanc e 364
between the 0
th
BS (serving BS) and the desired user. To 365
calculate this pdf, we model the cell shape by an inner circle 366
within a hexagonal cell [33], and assume that the users are 367
uniformly distribu ted. Therefore, the pdf f
R
(r) of r is given by 368
f
R
(r) =
2r
R
2
, r R
0, r > R.
(22)
IV. A
VERAGE RATE 369
In this section, we derive the average rate of both the FFR- 370
aided MU-MIMO as well as of its SIMO counterpart and find 371
the optimum value of S
th
(denoted by S
opt,R
) for which the 372
average rate is maximum. The average rate of the system is 373
given by R = E[ln(1 + SINR)]. In order to derive the average 374
rate
5
for the FFR system, we have to consider its sub-band al- 375
location. Since the users are uniformly distributed, the specific 376
sub-band allocated to the cell-centre users and cell-edge users 377
are given by [9], [10] N
c
= N
t
P
F,c
and N
e
=
N
t
N
c
3
,whereP
F,c
378
denotes the specific fraction of cell-centre users, while N
t
, N
c
379
and N
e
denote the total band, cell-centre sub-band and cell-edge 380
5
An interference limited system is assumed for simplicity, which implies
ignoring the effects of noise. However, the derivation of the average rate can be
readily e xtended to the case, where the thermal noise is also considered.

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References
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Book
01 Jan 2005
TL;DR: In this paper, the authors propose a multiuser communication architecture for point-to-point wireless networks with additive Gaussian noise detection and estimation in the context of MIMO networks.
Abstract: 1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background.

8,084 citations

Book
29 Aug 2011
TL;DR: Scrase et al. as discussed by the authors provide a comprehensive system-level understanding of LTE, built on explanations of the theories which underlie it, and provide a broad, balanced and reliable perspective on this important technology Lucid yet thorough, the book devotes particular effort to explaining the theoretical concepts in an accessible way.
Abstract: Where this book is exceptional is that the reader will not just learn how LTE works but why it works Adrian Scrase, ETSI Vice-President, International Partnership Projects LTE - The UMTS Long Term Evolution: From Theory to Practice provides the reader with a comprehensive system-level understanding of LTE, built on explanations of the theories which underlie it The book is the product of a collaborative effort of key experts representing a wide range of companies actively participating in the development of LTE, as well as academia This gives the book a broad, balanced and reliable perspective on this important technology Lucid yet thorough, the book devotes particular effort to explaining the theoretical concepts in an accessible way, while retaining scientific rigour It highlights practical implications and draws comparisons with the well-known WCDMA/HSPA standards The authors not only pay special attention to the physical layer, giving insight into the fundamental concepts of OFDMA, SC-FDMA and MIMO, but also cover the higher protocol layers and system architecture to enable the reader to gain an overall understanding of the system Key Features: Draws on the breadth of experience of a wide range of key experts from both industry and academia, giving the book a balanced and broad perspective on LTE Provides a detailed description and analysis of the complete LTE system, especially the ground-breaking new physical layer Offers a solid treatment of the underlying advances in fundamental communications and information theory on which LTE is based Addresses practical issues and implementation challenges related to the deployment of LTE as a cellular system Includes an accompanying website containing a complete list of acronyms related to LTE, with a brief description of each (http://wwwwileycom/go/sesia_theumts) This book is an invaluable reference for all research and development engineers involved in LTE implementation, as well as graduate and PhD students in wireless communications Network operators, service providers and R&D managers will also find this book insightful

3,452 citations

Journal ArticleDOI
TL;DR: While the proposed algorithms are suboptimal, they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity.
Abstract: The use of space-division multiple access (SDMA) in the downlink of a multiuser multiple-input, multiple-output (MIMO) wireless communications network can provide a substantial gain in system throughput. The challenge in such multiuser systems is designing transmit vectors while considering the co-channel interference of other users. Typical optimization problems of interest include the capacity problem - maximizing the sum information rate subject to a power constraint-or the power control problem-minimizing transmitted power such that a certain quality-of-service metric for each user is met. Neither of these problems possess closed-form solutions for the general multiuser MIMO channel, but the imposition of certain constraints can lead to closed-form solutions. This paper presents two such constrained solutions. The first, referred to as "block-diagonalization," is a generalization of channel inversion when there are multiple antennas at each receiver. It is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high SNR. The second, known as "successive optimization," is an alternative method for solving the power minimization problem one user at a time, and it yields superior results in some (e.g., low SNR) situations. Both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined. In order to accommodate more general scenarios, we also propose a framework for coordinated transmitter-receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas. While the proposed algorithms are suboptimal, they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity.

3,291 citations


"Coverage Probability and Achievable..." refers background in this paper

  • ...The key benefit of MU-MIMO is their ability to improve the spectral efficiency, which has been extensively studied in a single-cell context in the presence of AWGN [27]–[29]....

    [...]

Journal ArticleDOI
TL;DR: Multi-user MIMO (MU-MIMO) networks reveal the unique opportunities arising from a joint optimization of antenna combining techniques with resource allocation protocols, and brings robustness with respect to multipath richness, yielding the diversity and multiplexing gains without the need for multiple antenna user terminals.
Abstract: Multi-user MIMO (MU-MIMO) networks reveal the unique opportunities arising from a joint optimization of antenna combining techniques with resource allocation protocols. Furthermore, it brings robustness with respect to multipath richness, allowing for compact antenna spacing at the BS and, crucially, yielding the diversity and multiplexing gains without the need for multiple antenna user terminals. To realize these gains, however, the BS should be informed with the user's channel coefficients, which may limit practical application to TDD or low-mobility settings. To circumvent this problem and reduce feedback load, combining MU-MIMO with opportunistic scheduling seems a promising direction. The success for this type of scheduler is strongly traffic and QoS-dependent, however.

1,097 citations

Journal ArticleDOI
TL;DR: An overview of the LTE radio interface, recently approved by the 3GPP, together with a more in-depth description of its features such as spectrum flexibility, multi-antenna transmission, and inter-cell interference control are provided.
Abstract: This article provides an overview of the LTE radio interface, recently approved by the 3GPP, together with a more in-depth description of its features such as spectrum flexibility, multi-antenna transmission, and inter-cell interference control. The performance of LTE and some of its key features is illustrated with simulation results. The article is concluded with an outlook into the future evolution of LTE.

886 citations


"Coverage Probability and Achievable..." refers background in this paper

  • ...A LTE system having a 10 MHz bandwidth, 50 physical resource blocks (PRB) and 25 users is considered for each cell....

    [...]

  • ...Fractional frequency reuse (FFR) [2] constitutes a low complexity ICIC scheme, which has been proposed for OFDMA based wireless networks such as IEEE WiMAX [3] and 3GPP LTE [4]....

    [...]

Frequently Asked Questions (1)
Q1. What are the contributions in "Coverage probability and achievable rate analysis of ffr-aided multi-user ofdm-based mimo and simo systems" ?

In 8 particular, given a reuse region of 3 ( FR3 ) and a reuse region of 9 1 ( FR1 ) as well as a signal-to-interference-plus-noise-ratio ( SINR ) 10 threshold Sth, which decides the user assignment to either the FR1 11 or FR3 regions, the authors theoretically show that: 1 ) the optimal choice 12 of Sth which maximizes the coverage probability is Sth = T, where 13 T is the target SINR required for ensuring adequate coverage, and 14 2 ) the optimal choice of Sth which maximizes the average rate is 15 given by Sth = 21 Furthermore, the performance of their FFR-aided MU-MIMO and 22 SIMO systems is compared.