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CAPACITY ESTIMATION WAYS OF MASSIVE MIMO SYSTEMS
DOI 10.24411/2072-8735-2018-10159
Irina Stepanets,
Deutsche Telekom, Bonn, Germany, [email protected]
Grigoriy Fokin,
The Bonch-Bruevich St. Petersburg State University of Telecommunications, St. Petersburg, Russia
Andreas Mueller,
University of Applied Sciences Darmstadt, Darmstad, Germany
Keywords: massive M\MO, capacity, ergodic capacity, outage capacity, fast fading, slow fading.
In the course of the 5G development the massive multiple input multiple output (mMIMO) antenna technology offers big advantages over the conventional MIMO systems. In this paper a quantitative characteristic of the capacity rise was calculated for both antenna systems, conventional MIMO and massive MIMO, depending on the various fading types in the channel. For the fast fading channel, the capacity gain evaluation was done by ergodic capacity estimation. For the slow fading channel, the outage capacity method was applied. The obtained theoretical results of this work showed the capacity gain of massive MIMO with 64x64 antennas elements over the conventional MIMO with 4x4 antenna elements in the independent and identically-distributed (i.i.d.) channels, in which the growth of capacity gain has a linear dependence on the increase of the number of antenna elements. Thereby, massive MIMO systems can yield an essential capacity gain and its usage can be highly efficient for network deployment to cover the 5G requirements.
Information about authors:
Irina V. Stepanets, Project Manager "Deutsche Telekom", Bonn, Germany
Grigoriy A. Fokin, The Bonch-Bruevich St. Petersburg State University of Telecommunications, St. Petersburg, Russia Prof. Dr. Andreas Mueller, University of Applied Sciences Darmstadt, Darmstadt, Germany
Для цитирования:
Степанец И.В., Фокин Г.А., Мюллер А. Способы оценки пропускной способности систем massive MIMO // T-Comm: Телекоммуникации и транспорт. 2018. Том 12. №10. С. 64-69.
For citation:
Stepanets I.V., Fokin G.A., Mueller A. (2018). Capacity estimation ways of massive MIMO systems. T-Comm, vol. 12, no.10, pр. 64-69.
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1. Introduction
In the recent years the growth of the global mobile traffic was observed, according to Cisco statistics [1] it reaches in average over 70% traffic growth only in the one-year lime period. Wherein the same report is providing a forecast of the mobile data traffic till 2021, which shows an immense expansion of data usage on the threshold of fifth generation of mobile communication (5G). In connection with this it is of a big importance to accomplish a correct estimation of the mobile system capacity in order to be able to fulfill the capacity requirements dictated by 5G. The most efficacious approach to afford the high capacity in 5G is application of the massive multiple input multiple output (mMlMO) antenna systems. This work provides an analysis for different methods of capacity estimation in massive MIMO systems depending on the various fading types. In the first part of this paper the fading types and their properties are outlined. Further the different ways of the massive MIMO systems capacity estimation are described based on the known methodic for the conventional MIMO system and on the fading types. Next, the substantial influence of the fast and slow fading on the capacity estimation is demonstrated by means of MatLab simulations. At the end of this paper the conclusions of the application of two different ways for capacity estimation, namely ergodic and outage capacity estimation, are given.
2. Influence of different fading types
on the capacity estimation
As known, the wireless communication is subject to fading. Depending on the different propagation circumstances of the channel the signals will be influenced by the different types of fading. In turn the various fading types occurring in ihe channel have an impact on the individual way of the channel capacity estimation. That is why it is important to know the relation between the signal parameters and channel characteristics, or fading nature, to estimate the channel capacity correctly. There are two main fading types: large-scale fading and small-scale fading. The overview of the fading and their properties are presented on the figure I and described further.
I large-sea
ÜJ.M,
Att«nuitlon depend^ on
V
SftMkwlng: Var ai>;fu jtoji the fr)t*n
1AA
X
Wl-Kilt fading
on
rultizath
9
m
F»: Ulm pc nodfcnv
füTOßH
ppWtltv
StM po'mhüL,
Fig. 1. Fading types and their properties
Large-scale fading is caused by path loss and shadowing coming up between the transmitter and receiver and depends on location of the transmitted and received antennas (s. fig. 1).
The path loss leads to a consequent attenuation of the received signal power and depends on the distance between transmitted and received antennas. The shadowing leads to random changes of the signal power depending on the large obstacles compared to the wavelength between the antennas (building, trees, mountains, etc.) [2].
So these two effects are depending mostly on the space parameters such as distance or large obstacles and do not have any time dependences. In other words, the cannel with large fading is considered to be time-invariant, A representative example of a time-invariant channel is a channel with additive while Gaussian noise (AWGN) channel. The capacity of a time-invariant channel could be calculated according to the Shannon Theorem (I) [4]:
^ , m^IAI2
C,„™ = log3 l+-
[bits per transmission] (1)
Where P is a maximum transmit power, | /(is normalized channel coefficient, ¡-j; represents a noise power in form of the noise variance, thus the part of equation indicates a signal
to noise ratio (SNR),
The other type of fading is called small-scaled fading and occurs in the channel due to small scatters compared to wavelength (street signs, leaves, surface irregularities, etc.). This type of fading depends on time-variance in contrary to large scale fading and can be divided into two classes.
The first class of the small-scale fading is caused by multi-path propagation. This class can be further divided into the following two groups: flat fading and frequency selective fading. The explanation of this division is based on the fact that due to the multipath propagation the signal intervals Tsymb are coming to the receiver through the various paths with different delays. This leads to different time dispersions: signal delay spread ot can be much bigger or much smaller than the signal interval Ts)„,h. This time dispersion forces the channel to act as a pass filler in ihe frequency domain.
if the signal delay spread aT is much bigger than the symbol period Tsvmh, then the signal symbols transmitting in the different paths dramatically overlap and lose their initial sequence when coming to the receiver. This phenomenon is called frequency selective fading. Transforming the described situation into the frequency domain it can be observe that the coherence bandwidth is much smaller than the signal bandwidth. This means that the channel is not able to pass the whole signal bandwidth evenly. So there is no possibility to derive a signal from that channel at the receiver side. Therefore all mobile technologies are developed in such a way, where the frequency selective fading can be eliminated, for example by OFDMA in LTE, otherwise no communication can be organized. That is why there is no reason to make any capacity estimation in the case of frequency selectivity.
if the signal delay spread a, is smaller than the symbol period TSvmh, fhen the channel shows so call&A flat fading. Transforming this into the frequency domain it is obvious that the coherence bandwidth is equal or bigger than the signal bandwidth in contrary to the frequency selective fading. Hence, the signal can be easily derived from the channel. As a base condition for a successful telecommunication it is assumed that a channel has flat fading. Therefore, for the further computation in this paper a channel with a flat fading is considered.
The second class of small fading is caused by motion of the UE (user equipment) and has a considerable impact on the capacity estimation. This class is also divided into the two following groups:./cvs/ and slow fading. Due to the movement of the UE the transmitting frequency can be strongly influenced by the Doppler effect.
If the symbol interval is bigger than the coherence lime (coherence time means a time period during which the channel is considered to be constant), then the channel is changing very fast compared to the symbol duration (s. fig. !, part fast fading), in other words the symbol can span over many fades [3]. In the frequency domain it means that the signal bandwidth is narrower than the Doppler spread spectrum, and leads to a considerable influence of the Doppler effect on the carrier frequency. In ease of liie fast fading the channel has a behavior of an ergodic stationary random process, whose channel capacity can be averaged out and estimated by the mean value (2) of (I) [4j:
Fad [ne properties
C - F
^-'FaslFaUng
log J 1 +
P\h\2
[bits per transmission! (2)
where E indicates the mean value operator. The expression (2) is known in the communication theory by a term ergodic capacity.
From the other hand if the symbol interval is smaller than the coherence time, one can observe the slow fading process. In this case the channel stays constant during the symbol duration in contrary to the fast fading [4]. This refers to the bigger bandwidth pf the signal compared to the Doppler spread spectrum, so the Doppler effect has no significant influence on the carrier frequency. In case of the slow fading the channel can be modelled as stationary and ergodic. But the channel fades cannot be averaged out due to its rare periodicity over many symbols (s. fig. 1, part slow fading), so the capacity of such channel also cannot be averaged out. From this reason it is feasible to use another method of channel estimation for this case, for example a capacity estimation with outage. This method is based on the calculation of probability, that the outage of channel will occur.
log J 1
if the channel capacity
transmission rate R (3) [41, [5]:
is lower than a selected
/>,„„№ = Pr log.
1 +
P\k I
<R
(3)
Urge-scale
fading
Attenuation depending on distance
Shadowing: Variations about
IM
Small-scale fading
n
\ Flat fading
Based OA UE motions
• F»t fading J
1 H#L
Symbol» periodicity Fan radlni pertMleftr
k fading j
MUL
Symbcii periodic^
Slew fading penodkity
Capacity estimation
Time-invariant channel:
Cawgn = log2 (l + ^r)
Flat fading channel;
Considered for successful communication. Frequency selectivity:
No communication is possible.
Fast fading channel; Slow fading channel:
Fig. 2. Influence of different fading type on the capacity estimation
3.1. Ergodic capacity estimation for fast fading MIMO and massive MIMO systems
With the assumption of the fast fading channel in the MIMO wireless system the equation (1) can be also represented as follows (4), where the Shannon part of expression for the MIMO
channel is depicted in a matrix form
C - E
^ Ff Mim
log, det
I MT a, J
4], [6]: [bits per transmission] (4)
Keeping in mind probability (3), its PDF (probability density function) and consequently CDF (cumulative distribution function) of the process can be calculated as a guaranteed channel capacity, which provides a reliable communication with predc-lined outage.
The relationship between channel capacity estimation and fading types is presented in the figure 2.
3. Examples of the different ways of capacity estimation for MIMO and massive MIMO systems depending on fading types
In this part the examples of the different ways of capacity estimation are discussed for MIMO and massive MIMO systems. Two fading groups, which are relevant for mobile systems, were taken into account below: fast and slow fading. The capacity of these two fading channels were calculated and investigated by means of MATLAB simulations.
where I is the identity matrix, H is the channel matrix consisting of the channel attenuation coefficients hy, H" is a Hermitian transformed channel matrix, is the number of transmitting antenna elements, which means that the transmitted power is equally shared between the transmitting antenna ports. The matrix entities hjj are complex random values which real as well as imaginary parts are normal distributed. Thus, the magnitude of h^ is a Rayleigh distributed random number. That is to be noted thai the random numbers hy are independently generated. Consequently, the MIMO transmission capacity will increase linearly with the number of antenna ports respectively with the number of transmission and receiving chains at eNodeB and user equipment.
Figure 2 shows the simulation algorithm in MATLAB, which computes the ergodic capacity estimation for the fast fading channel as a function of antenna number and SNR. For the calculation of the output values of this function the two cycles were implemented into the algorithm: antenna-number cycle and SNR cycle.
The results of the MATLAB simulation for ergodic capacity of MIMO channels are presented in the figure 4. To provide an actual view with respect on 5G requirements, the SNR=35 dB was chosen, which is supposed in 5G to support extremely high throughput and high reliability [7]. The results show, thai the average capacity of the fast fading channel with MIMO 4x4 system is 41.86 bits/transmission. Whereby the achievable capacity of massive MIMO system with configuration of 64x64 antenna elements at the same SNR value can reach
T
4, Conclusions
The obtained results allow to draw the following conclusions.
The calculated capacity by means of both methods, ergodic estimation for fast fading channel and outage estimation for slow fading channel for an outage probability of 50%, converge roughly to the similar values. This means that the estimation methods were correct for both fading types. The computed capacity of 64x64 M1MO is 16 times higher than for 4x4 Ml MO which corresponds with the expectation for a MIMO channel matrix with i.i.d. coefficients. This further confirms both ways of capacity computations.
However, these high massive MIMO gains represent theoretical values. In the reality such many independent propagation paths with i.i.d. channel coefficients cannot be achieved for a 64x64 system. But otherwise the assumption of this paper is correct if the 64 antennas at user equipment (UE) side belong to several sufficiently separated UEs and not to a single UE. Thereby, massive MIMO systems can yield an essential capacity gain and its usage what is highly efficient for network deployment to cover the 5G requirements.
References
1. Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update, 2016-2021, https://www.cisco.eom/c/en/us/solutions/ collate ra I /serv i ee- pro v i der/v i s u a I -net working- i ndex- vn 1/m o b i le-w h i te -paper-c 1 l-520862.pdf.
2. Sklar B. (1997). Rayleigh lading channels in mobile digital communication systems. 1. Characterization. IEEE Communications magazine, 15(9), pp.136-146.
3. Rappaport T.S. (1996). Wireless communications: principles and practice (Vol. 2). New Jersey: prentice hall PTR.
4. Brown T., Kyritsi P, and De Carvalho E. (2012). Practical guide to MIMO radio channel: With MATLAB examples. John Wiley & Sons.
5. Cho Y.S., Kim J„ Yang W.Y. and Kang C.G. (2010). MI MO-OFDM wireless communications with MATLAB. John Wiley & Sons.
6. Marzetta T.L., Larsson E.G., Yang H„ & Ngo H.Q. (2016). Fundamentals of Massive MIMO. Cambridge University Press.
7. Tuovinen T., Tervo N. and Parssinen A. (2017). Analyzing 5G RF System Performance and Relation to Link Budget for Directive MIMO. IEEE Transactions on Antennas and Propagation, 65(12), pp.6636-6645,
СПОСОБЫ ОЦЕНКИ ПРОПУСКНОЙ СПОСОБНОСТИ СИСТЕМ MASSIVE MIMO
Степанец Ирина Валерьевна, Дойче Телеком, Бонн, Германия. Фокин Григорий Алексеевич, СПб ГУТ им. М.А. Бонч-Бруевича, Санкт-Петербург, Россия. Мюллер Андреас, Дармштадтский университет прикладных наук, Дармштадт, Германия
Аннотация
Увеличение пропускной способности канала связи - одна из задач, стоящих на этапе развития технологий подвижной связи пятого поколения 5G. Антенные системы massive MIMO (massive Multiple Input Multiple Output) представляют собой эффективное решение этой задачи и в разы превосходят показатели пропускной способности классических систем MIMO (Multiple Input Multiple Output). Приводятся различные методы количественной оценки пропускной способности в зависимости от различных типов замирания в канале для обеих антенных систем: классического MIMO и massive MIMO. Для канала связи с быстрыми замираниями выполнена оценка шенноновской (эргодической) пропускной способности. Для канала связи с медленными замираниями выполнена оценка пропускной способности для заданной вероятности отказа. Оценка пропускной способности выполнена средствами статистического имитационного моделирования с допущением, что канал связи имеет независимые и одинаково распределенные коэффициенты канальной матрицы. Полученные результаты показали повышение пропускной способности с увеличением количества антенных элементов. Были исследованы и сопоставлены параметры пропускной способности систем massive MIMO с антенной решеткой 64x64 и MIMO 4x4. Таким образом, системы massive MIMO способны обеспечить существенно большую емкости сети, и их применение является эффективным для выполнения требований по развертыванию сети 5G.
Ключевые слова: massive MIMO, пропускная способность, шенноновскую ёмкость канала, гарантированная пропускная способность при заданной вероятности отказа, быстрые замирания, медленные замирания.
Литература
1. Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update, 2016-2021, https://www.cisco.com/c/en/us/solutions/col-lateral/service-provider/visual-networking-index-vni/mobile-white-paper-cll-520862.pdf.
2. Sklar B. Rayleigh fading channels in mobile digital communication systems. I. Characterization // IEEE Communications magazine. 1997. Т. 35. № 7. С. 90-100.
3. Rappaport T.S. et al. Wireless communications: principles and practice. New Jersey: prentice hall PTR, 1996. Т. 2.
4. Brown T., Kyritsi P., De Carvalho E. Practical guide to MIMO radio channel: With MATLAB examples. John Wiley & Sons, 2012.
5. Cho Y.S. et al. MIMO-OFDM wireless communications with MATLAB. John Wiley & Sons, 2010.
6. Marzetta T.L. et al. Fundamentals of massive MIMO. Cambridge University Press, 2016.
7. Tuovinen T., Tervo N., Pаrssinen A. Analyzing 5G RF System Performance and Relation to Link Budget for Directive MIMO //IEEE Transactions on Antennas and Propagation. 2017. Т. 65. № 12. С. 6636-6645.
Информация об авторах:
Степанец Ирина Валерьевна, проект-менеджер "Дойче Телеком", Бонн, Германия
Фокин Григорий Алексеевич, к.т.н., доцент кафедры радиосвязи и вещания (РС и В) СПб ГУТ им. М.А. Бонч-Бруевича, Санкт-Петербург, Россия
Мюллер Андреас, Dr. rer. nat., профессор кафедры информатики, Дармштадтский университет прикладных наук, Дармштадт, Германия
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