i i TITOLO 2017/9/22 16:42 page 1 #1 i i i i University of Pisa
Department of Information Engineering
Master's Thesis in Telecomunications Engineering
Design and performance evaluation
of a UFMC waveform in 5G NOMA
communications
Author
Francesca Baldon
Supervisors :
Prof. Filippo Giannetti Ing. Carmine Vitiello Prof. Marco Luise Ing. Vincenzo Lottici
Pisa, September 2017 2016-17
Contents
Abstract 1
1 Introduction 3
2 Multiple access techniques 5
2.1 TDMA . . . 6 2.2 FDMA . . . 8 2.3 OFDMA . . . 11 2.3.1 SC-FDMA . . . 15 2.4 CDMA . . . 18 2.5 NOMA . . . 23 2.5.1 NOMA downlink . . . 24 2.5.2 NOMA uplink . . . 26
2.5.3 Advantages and disadvantages of NOMA . . . 27
2.6 Channel capacity of Multiple Access Techniques . . . 28
3 System Model: UFMC 31 3.1 UFMC single-user . . . 32
3.2 UFMC multi-users . . . 36
3.2.1 SIC receiver in UFMC multi-users . . . 38
3.3 UFMC in presence of a carrier frequency offset . . . 40
3.3.1 UFMC in presence of a channel perturbation . . . 43
4 Simulation Results 44 4.1 UFMC single-user . . . 44
4.1.1 Simulation results under the presence of CFO . . . 48
4.3 Simulation results using convolutional encoding . . . 68
5 Conclusions 71
Abstract
The actual LTE technology, based on OFDM architecture, does not satisfy the requirements of the 5G communication systems. Especially, the advent of Inter-net of Things (IoT) communications leads to a boundless growth of the number of users. As a consequence, current channel access techniques are not able to man-age such a large amount of users. This results in the need to use non-orthogonal channel access techniques. Moreover, since the most of these users will be sensors or autonomous entities, there is the problem of increasing the battery lifetime of these devices up to 5-10 years at least. Given that the synchronization procedure required by OFDM waveform, in order to keep orthogonality between signals, is computationally heavy and is not energy efficient, new types of waveform have been introduced. In this thesis, we propose a Universal Filtered Multi-Carrier (UFMC) system by applying it for the first time in a Non-Orthogonal Multiple Access (NOMA) multi-user scenario for the future generation of mobile com-munications (5G). After a brief overview on the most important channel access techniques and on the UFMC waveform, we design and implement a NOMA UFMC communication scenario, dwelling upon the successive interference can-cellation (SIC) process exploited in the receiver. Then, we evaluate the Bit Error performance of our system by considering different channels, varying the number of users and the power allocation to each of them. We focus on perfect and imper-fect synchronization, compared with the current OFDMA transmission system, highlighting the benefits provided this method. In conclusion, the proposed sys-tem yields better results in term of BER and as such it could be a valid candidate for the 5G communications.
Chapter 1
Introduction
Nowadays, recently emerging trends of the new fifth-generation (5G) are changing traffic characteristics of the mobile communication technology. In order to ensure the sustainability of mobile communication services over the next decade, new technology solutions that can respond to future challenges need to be identified and developed.
The main aim of 5G development is to support the advent of the Internet of Things (IoT), where devices will be able to transfer data without requiring a human interaction. IoT entities will be everywhere improving our everyday life, starting from the simplest applications such as home automation, up to the most now unthinkable applications like intelligent vehicular communications and telemedicine.
In this scenario, the main considerations are twofold: i) the number of users involved in the communication will considerably increase; ii) the communication entities, such as sensors, require a very low energy consumption in order to pre-serve the battery life time (even more than 10 years).
The current OFDM modulation, which is at the base of the LTE technology, presents some limitations for satisfying the above-mentioned 5G requirements. The spectrum is characterized by high out-of-band emissions which show an in-efficient frequency localization and lead to introduce guard intervals for avoiding interference between adjacent users, reducing the number of the possible contem-porary communications. Moreover, OFDM requires a complex synchronization procedure to preserve the orthogonality between signals in the time and in the frequency domain, which is computationally heavy and increases the end-to-end
latency between the transmission and the reception. This procedure is quite ex-pensive from the energy consumption point of view and therefore it is in contrast with the energy saving principle of the IoT.
The non-orthogonal multiple access (NOMA) technique is proposed as an alternative to the orthogonal access approach in order to increase the number of users involved in the communication. NOMA allows the overlapping of the signal coming from different users providing a more efficient transmission.
The universal-filtered multi-carrier (UFMC) modulation has been introduced in order to overcome the OFDM limitations. Indeed, it reduces the out of band emissions caused by high sidelobe levels by applying a filtering operation to a group of consecutive subcarriers. In this way, the potential interference between adjacent users is minimized. In the same time, the filtering increases the ro-bustness against both time and frequency misalignment due to an imperfect syn-chronization. In this thesis, the UFMC system is applied in a non-orthogonal multiple access (NOMA) multi-user scenario in order to manage a large amount of users. In Chapter 2, we start presenting an overview of the most important channel access techniques focusing on the advantages and disadvantages of each one. Chapter 3 introduces the main purpose of this thesis: the design and the implementation of the NOMA UFMC communication system and the successive interference cancellation (SIC) process exploited in the receiver. Finally, Chapter 4 shows the simulation results in terms of BER of the proposed system compared with the current OFDMA system in both perfect and imperfect synchronization, coded and uncoded.
Chapter 2
Multiple access techniques
The multiple access techniques are the basis of the multi-user communications. ”Multiple access” means the common use of the medium by many users in most efficient manner, allowing the transmission of several signals and several data streams.
In wireless communication systems, it is often necessary to allow the users to send simultaneously information to the base station while other user are receiving information from the base station, on the same available band.
There are different multiple access techniques to allow access to the chan-nel that can be generally divided into orthogonal (OMA) and non-orthogonal (NOMA) approaches. In OMA technique, radio resources are orthogonally di-vided between devices, where the signals from different devices are not overlapped with each other respect to a certain domain [9]. The most significant OMA tech-niques are the time division multiple access (TDMA) and the frequency division multiple access (FDMA).
In spite of OMA, non-orthogonal multiple access (NOMA) allows overlapping among the signals from different devices by exploiting code domain (CDMA) or power domain (NOMA), to correctly decode the signal [9].
The Fig. 2.1 shows the differences in the use of radio resources in OMA ap-proach, TDMA and FDMA, and in NOMA apap-proach, CDMA and NOMA.
TDMA, FDMA, and CDMA are the three major multiple access techniques that are used to share the available bandwidth in a wireless communication sys-tem. They will be described in this chapter, focusing on the characteristics and describes the pros and cons of them, with a particular attention to the new NOMA
Fig. 2.1: Representation of user alloca-tion with respect to different domain.
technique.
2.1
TDMA
In TDMA (Time Division Multiple Access), the transmission of different users happen in different time interval, called time slots, with duration Ts.
TDMA provides different time-slots to different transmitters: only one user can use one time-slot to transmit by using the total available band W ; the others users have to wait for a free slot [1]. For example, if two users transmit a signal, the user u1 will take the slot s1 and the user u2 will take the slot s2. The
transmission scheme will perform again in a cyclically repetitive frame structure unless one of the users concludes the transmission and that time-slot becomes free or assigned to another user [1].
The orthogonality between signals is guaranteed because signals occupy dif-ferent slots without any kind of overlapping between adjacent signals, as shown in Fig. 2.2.
2.1 TDMA
Fig. 2.2: TDMA time-frequency diagram.
As a matter of fact, the signals transmitted from users must be orthogonal in order to avoid interference. This implies that the correlation of two signals is null:
Z +∞
−∞
si(t)sj(t)dt = 0, (2.1)
where si(t) and sj(t) are respectively the signals transmitted by user i and by
user j. It is easy to verify that the correlation is null if the two users transmit on different slots, as it happens to TDMA [1].
The TDMA technique is typically used in the satellite communications to enable earth stations to transmit intermittently on the same frequency, but in different time-slots, so that the signals are not overlapped when arrive at the satellite [11].
Another example is the 2G cellular system: GSM (Global System for Mobile Communications) is based on a combination of TDMA and FDMA. Each sub-band is divided into eight time-slots: seven time-slots are used for seven phone calls, and one for signalling communications [1]. The GSM will be explained better in the following paragraph, after the introduction of the FDMA technique. There are important advantages in the use of TDMA technique. First of all, the resource allocation is easy and flexible. For example, there is the possibility to set priority between users by extending the duration of a slot. Moreover, data transmission in TDMA is not continuous but occurs in bursts: this leads to a low
battery consumption because the transmitter can be turned off when it is not in use. Finally, TDMA uses different time slots for transmission and reception thus duplexers are not required [1], [11].
Despite these advantages, the TDMA technique shows a disadvantage that can’t be neglected: the synchronization between the receiver and the transmitter is very difficult to realize because, for example, in a wireless communication system, the users are not typically at the same distance from the base station and so the signals have different propagation delay from user to user. This involves the ”dead time” between time-slots, which limits the potential number of users which share the temporal axis of a TDMA channel. This also means that for example in cellular communications, TDMA systems have limits on cell sizes in terms of range because if the user is too far from the BS the ”dead time” will be too large [1], [11]. Furthermore, the other disadvantage is that the user has to transmit at a high-rate because the time-slot is limited. In a frequency-selective channel, the condition for finding a frequency flat channel is given by:
Ts >> τmax− τmin, (2.2)
where Ts is the transmission interval and τmax− τmin represents the delay spread,
defined as the difference between the maximum delay and the minimum delay due to multipath. It means that the transmission interval must be much bigger than the delay spread and in TDMA this condition might not be respected. Thus, a fast transmission, like TDMA, may require more complex and expensive equalization systems [12].
2.2
FDMA
In FDMA (Frequency Division Multiple Access) the total available band is di-vided into separated portions, called subbands: a user, who wants to transmit, is allocated in one of the free sub-band, that have not been occupied yet from the others users. The receiver selects the proper subband using a selective filtering on the received radio frequency (RF) signal [1].
If the total available band is W and the number of users is M , the subband assigned in a far way to the generic user is:
2.2 FDMA
B = W
M (2.3)
The Fig. 2.3 represents the FDMA technique on a time-frequency diagram. All the M users are overlapped in the time domain and they are orthogonally divided in the frequency domain. The total available bandwidth is W and the subband assigned to each user is B.
Fig. 2.3: The FDMA time-frequency diagram.
The signals transmitted from users must be orthogonal in order to avoid in-terference. So, in the same way of TDMA, with the application of the Parseval’s Theorem, it is easy to demonstrate that si(t) and sj(t) are not correlated also
when the spectrums Si(f ) and Sj(f ) occupy disjointed frequency intervals:
Z +∞ −∞ si(t)sj(t)dt = Z +∞ −∞ Si(f )Sj∗(f )df. (2.4)
Guard bands are considered to minimize the inevitable interference between signals from the arriving subbands due to the not perfect limitation of the signals band and to the possible frequency oscillations in communication systems [2].
The first generation cellular technology 1G, born in the early 80s, was based on FDMA. The most important are: the U.S. analog cellular system AMPS (Ad-vanced Mobile Phone System), the TACS (Total Access Communication System), which was born in Great Britain and used in all the Europe and in Japan, the
NMT (Nordic Mobile Telephone System), which was born in the North of Europe [1].
The FDMA was also the first multiple access technique used for satellite com-munications and it is indicated for both analog and digital signals. A typical application is the transmission of telephonic and television analog signals on fre-quency modulated FM carriers [11], [12].
The other important example of the use of FDMA technique is GSM, which uses a mixed TDMA/FDMA technique. In the GSM the FDMA is used to assign different subbands to different groups of users.
GSM is a second-generation system based on digital technology. Originally the GSM used two frequency bands of 25MHz; the band which goes from 890 to 915MHz is used for uplink transmissions, while the band which goes from 935 to 960MHz is used for forward or downlink transmissions. Those bands have then be extended giving rise firstly to EGSM (Extended GSM) and secondly to DCS1800 (Digital Cellular System). Thus, the GSM uses Frequency division duplex (FDD) for the duplexing [1].
As mentioned in the previous paragraph, GSM uses a mixed TDMA/FDMA for the channel access scheme: M users are divided into N groups, every group has a frequency band of WN, where W is the total available band (FDMA). Every user of a specific group transmits on a different slot (TDMA) [1]. The related time-frequency diagram is represented in the Fig. 2.4.
2.3 OFDMA
The two uplink and downlink bands are therefore divided into sub-bands of 200kHz each; in this way, the number of carriers frequency is 125 in 25MHz, but only 124 are used because two guard bands of 100kHz are used at the beginning and at the end of the spectrum. Each sub-band is used with the TDMA technique with 8 slots for each frame [1].
The most important advantage of FDMA technique is that, instead of TDMA, the synchronization procedure required to synchronize the local oscillators (LO), which are often imperfect, is easier. Moreover, in the FDMA, the signal is trans-mitted M times lower than the signal in TDMA (in TDMA, time axis is divided into M time-slots). So, by considering equal available resources in TDMA and FDMA the symbol duration time, is large compared to the average delay spread, so the equalization system becomes easier.
On the other hand, in FDMA all users share the same channel simultaneously, but each user transmits at a single frequency. As a consequence, setting priority between users in FDMA is more complex because two or more frequency bands would have to be reserved. In addition, FDMA requires high-performing filters in the radio hardware to minimize the adjacent channel interference caused by high out of band emissions and high side lobe level [1].
2.3
OFDMA
With the growth of wireless multimedia applications, a higher data rate leads to the utilization of a wider transmission bandwidth. However, with a wider transmission bandwidth, the frequency-selective channel and the inter-symbol interference (ISI) become more serious problems, because the condition for a frequency-flat channel are not respected and the length of the time domain filter to perform equalization becomes too large since it linearly increases with the channel response length [13].
Orthogonal frequency-division multiple access (OFDMA) technique contrasts the selective fading and ISI by using the multicarrier orthogonal frequency-division multiplexing (OFDM) system which subdivides the entire available spec-trum into or sub-carriers. In the frequency domain, each subcarrier experienced a flat channel because its occupied bandwidth is smaller than the coherence
band-width. In the time domain, the high-rate data stream, R, is split into lower-rate data streams, Rs, that are transmitted in parallel [2]. Subsets of sub-carriers are
assigned to an individual user allowing simultaneous low-data-rate transmission from several users [2].
If 1/T is the symbol rate of the wideband signal and N is the number of the subcarriers, the symbol rate of the narrow-band signal of each sub-carrier is:
1 Ts
= 1/T
N , (2.5)
which corresponds to an OFDM symbol duration time over each subcarrier Ts =
N T . The narrowband signal bandwidth of each subcarrier is N times lower than the wideband single-carrier signal bandwidth [2].
The spacing between the subcarriers is
fsc =
1 Ts
= 1
N T, (2.6)
to avoid the interference due to the other subcarriers. This can be demonstrated, as in [1] and [2], by considering the OFDM modulated signal:
x(t) = +∞ X m=−∞ N −1 X k=0 cmkp(t − mTs)ej2πkfsct, (2.7)
where p(t) is a unitary rectangular impulse defined in 0 ≤ t ≤ Ts, cmk represents
the source symbol, k is the subcarrier index included between {0, ..., N − 1} and m is the temporal index of the general multicarrier symbol.
The optimum demodulator scheme requires the base-band conversion, the matched filter with sampling and the threshold decoding, [2]. Thus, the decision variable on the symbol of the subcarrier k is:
zk(0) = 1 Ts
Z Ts
0
r(t)e−j2πkfsctdt, (2.8)
where r(t) is the received signal.
The interference due to the subcarrier i on the decision variable of the sub-carrier k, with i 6= k, is:
2.3 OFDMA Ii,k0 = Z Ts 0 c(0)i ej2πifsct· e−j2πkfsctdt = c(0) i ej2π(i−k)fscTs − 1 j2π(i − k)fsc , (2.9)
where the effect of noise is not considered. The interference in the eq. 2.9 becomes zero when fscTs = q, q ∈ Z, therefore when the subcarriers are orthogonal.
Naturally, it is more convenient choosing the minimum value of q to keep the subcarriers as close as possible, in order to limit the modulated signal band achieving the eq. 2.6.
The Fig. 2.5 represents the block diagram of an OFDM waveform. Zeros before the IFFT block represent the virtual subcarriers which are added in order to reduce the signal band. In this way, the bandwidth of the signal is taken under control so that it is suitable for the sampling rate of the hardware systems. Moreover, the out of band emissions are reduced because the sinc amplitude decreases by increasing the distance from the maximum [2].
Fig. 2.5: The block diagram of an OFDM system.
As virtual subcarriers have been added in the transmission phase, they have to be removed at the receiver after the FFT block.
The cyclic prefix (CP) is used in OFDM to contrast multipath by making channel estimation easy, but also to eliminate the intersymbol interference from the previous and the next symbol, [2]. The CP comes from a guard interval
with an important difference. A common guard interval has only the function of spacing out the multicarrier symbols and it does not transmit anything. On the contrary, in this intervals the CP transmits the last N symbols of a multicarrier symbols. In this way, if the maximum propagation delay due to the channel is less than the length of the CP, the signal becomes pseudo-periodic. If the delay is bigger, the multicarrier symbol must be truncated and we have to research the perfect temporal synchronization before using the FFT.
Fig. 2.6: The LTE frame structure. An LTE frame of 10 ms is divided into 10 sub-frame of 1 ms each. Each sub-frame, in turn, is divided into 2 time-slots of 0.5 ms.
The OFDMA technique is used in the 4G cellular system, called LTE (Long Term Evolution) in the downlink [1]. The technique provides a subset of subcar-riers, that is a portion of the available band, to each user for the time period that is necessary for the transmission in the downlink channel [1].
The LTE standard defines the minimum time-frequency resource, the PRB (Physical Resource Block), for the downlink. The PRBs are assigned to the users by the e-nodeB according to specific radio resource protocols [1].
The most important advantage of OFDMA is that its signal waveform provides robustness against multipath interference. Moreover, each subcarrier can be seen as a flat fading channel, so OFDM resolves also the selective fading channel problem, as already described at the beginning of the paragraph. Then, OFDMA enables the equalization of the signal in the frequency domain, which is easier than
2.3 OFDMA
in the time-domain. Finally, the use of CP makes the synchronization procedure easier and enables the use of FFT algorithms [1].
But even OFDMA technique has its disadvantages. It is very sensitive to fre-quency offset therefore it requires a synchronization procedure, to keep orthogo-nality between signals in time and in frequency, which is computationally heavy and not energy efficient, especially in case of non-static users, where this proce-dure is done a lot of times, increasing the latency of the system. Finally, OFDM is characterized by a high peak-to-average power ratio (PAPR). The PAPR is a performance measurement that is indicative of the power efficiency of the trans-mitter. In the use of an ideal linear power amplifier, the transmitter reaches the maximum power efficiency when the amplifier is operating at the saturation point. But, if the PAPR in dB is positive, we need a power backoff in order to operate in the linear region of the power amplifier. The OFDM is the result of the combination of many subcarriers which carry independent symbols. So, the PAPR is high, as a consequence, the needed power backoff is high too and the transmit power efficiency performance degrades [13].
2.3.1
SC-FDMA
Single carrier frequency division multiple access (SC-FDMA) is an extension of single carrier with frequency domain equalization (SC/FDE) and is another way to contrast the frequency-selective fading channel. This technique is similar to the OFDM with the difference in using the single carrier modulation at the trans-mitter [13].
An SC-FDMA system has the same overall structure as an OFDMA system, except for the fact that time domain data symbols are transformed to the fre-quency domain by DFT before going through OFDMA modulation. The Fig. 2.7 shows the block diagram of an SC-FDMA system; the red blocks highlight this difference from OFDMA [13].
The orthogonality of the users is guaranteed in the same way as in OFDMA.
As shown in the Fig. 2.7, the transmitter of an SC-FDMA system first groups the modulation symbols into blocks each containing N symbols. Secondly, it per-forms an N-point DFT to transform the input symbols in the frequency domain.
Fig. 2.7: The block diagram of an SC-FDMA system.
Then, it maps each of the N-DFT outputs to one of the M orthogonal subcarriers, M ≥ N . If N = M/Q, where Q is the bandwidth expansion factor of the symbol sequence, and all terminals transmit N symbols per block, the system can cope with Q simultaneous transmissions without co-channel interference.
Even the SC-FDMA receiver is similar to the OFDMA receiver. The receiver chain is the same except for the addition of the final IDFT which transforms the signal out of the equalization back to the time domain. The detection and the decoding take place in the time domain [13].
Fig. 2.8: The difference in the time-frequency diagram of OFDMA on the left and SC-FDMA on the right.
2.3 OFDMA
The Fig. 2.8 shows the difference in the time-frequency diagram between OFDMA and SC-FDMA. In the OFDM the symbols are overlapped in the time domain and orthogonal in the frequency domain, while in the SC-FDMA the sym-bols are overlapped in the frequency domain and orthogonal in the time domain. The SC-FDMA technique is used in the uplink of the 4G cellular system LTE (Long Term Evolution).
For a better understanding of this technique, consider a single user in uplink where the entire available bandwidth is allocated. In this case, M corresponds to the number of active subcarriers and the subcarrier mapping simply sets the M signals of the DFT outputs, on the extreme of N-points block, in order to keep the virtual subcarriers in the center. The IDFT block provides the sequence of initials symbols. Thus, the final signal has the same structure of a single-carrier signal. The cyclic prefix does not change this property because it is simply the reply of some final symbols added at the beginning of the sequence [1].
If the number of subcarriers allocated to the user is lower than the number of available subcarriers, the subcarrier mapping sets the symbols on a smaller portion of the available band.
The SF-FDMA technique has many advantages. First of all, it is characterized by a low PAPR due to the single carrier modulation. The DFT, with also the following operations, provides a correlation between the symbols which will be transmitted on the subcarriers, as a consequence the PAPR of the resultant signal is lower. It has been demonstrated that SC-FDMA is characterized by a PAPR of 2-3 dB lower than OFDMA. Moreover, by reducing the PAPR, the system presents a better energy efficiency due to the fact that the power amplifiers keep operating in the saturation point without the need of a power backoff. Thus, with a low PAPR we avoid the distortions caused by the power amplifiers which happen in case of an increase of the system dynamic. This is why the SC-FDMA technique is used in the uplink, where the transmitted power is limited [2]. Secondly, SC-FDMA is robust to the spectral nulls in the channel because it performs the data detection after the additional IDFT operation, while the OFDMA performs it on a per-subcarrier basis. The SC-FDMA is also characterized by a lower sensitivity to carrier frequency offsets than OFDMA [1], [13].
has to be considered because pilots have to be periodically transmitted on some subcarriers in order to keep the system equalized. So, during the subcarrier map-ping, some subcarriers have to be left empty. This changes the signal structure. Nevertheless, the subcarriers for the transmission of pilots are low compared to the total available subcarriers, so the PAPR does not change significantly.
2.4
CDMA
Fig. 2.9: The CDMA code-time-frequency diagram.
The Code Division Multiple Access (CDMA) allows overlapping among the signals from different devices in the time and frequency domain and is able to decode them by exploiting the code domain [1], [2].
This technique is one of the most important technique applied for the spread spectrum communications, which have been developed by the military in order to create a communication system which is robust to intentional interference (jamming). This robustness is explained below [1], [2].
If a signal is transmitted using square-root-raised-cosine (SRRC) impulses with roll-off α (0 ≤ α ≤ 1) and using a BPSK modulation, the radio-frequency signal bandwidth is:
B = 1 + α
2.4 CDMA
where Tb = 1/Rb and Rb is the bitrate. A spread spectrum system transmits Rb
information bits per seconds using a band M times wider than the band defined in the eq. 2.10,
Bw = M · B, (2.11)
where M is the spreading factor.
The spread spectrum technique is used in the same way as multiple access technique allowing signals from different users to share the same bandwidth in the same period of time. Each user in a CDMA system uses a different code to modulate their signal. The diagram in the Fig. 2.9 shows how the common resources are divided in the CDMA technique.
The main spread spectrum modulation is the Direct Sequence Spread Spec-trum (DS-SS) which is used to the multiple access system DS-CDMA [2].
Fig. 2.10: The block diagram of a DS-CDMA system.
The Fig. 2.10 shows the block diagram of a DS-CDMA system. bi is the
i-th information bit, wii-th a bit duration time of Tb; cl is the l-th code, with a
chip duration time of Tc, used for the spreading; al is the coded bit which is
transmitted on the channel, after the spreading, with a symbol duration time of Tc. The spreading means the operation of the information signal with narrow
bandwidth and bit duration time of Tb, multiply to the spreading code with wide
The oversampling block has the function to repeat the input symbol bi at
intervals of Tc.
So, al after the spreading is:
al = bbl/M cclM, (2.12)
where bl/M c is the floor operation of the argument l/M and lM is l in module
M . M is the spreading factor: Tc= Tb/M .
As a consequence, the transmitted signal is:
s(t) =X
l
alg(t − lTc), (2.13)
where g(t) is a transmission filter whose the Fourier transform is typically square-root-raised-cosine.
The spreading operation is shown in the Fig. 2.11.
Fig. 2.11: The spreading operation.
In the reception, g∗(t) is the matched filter. The signal, after the sampling at the rate 1/Tc, is despreaded using by the despreading sequence of the of the
proper user. The signal bandwidth turns back into B. On the other hand, the jamming spectrum suffers the opposite operation: its power spectral density is spread over a wider bandwidth and, as a consequence, the jamming power on the signal bandwidth is remarkably reduced (see the Fig. 2.12). After the de-spreading, the signal-to-interference ratio on the signal bandwidth is M times higher, with M = BW/B.
2.4 CDMA
Fig. 2.12: The de-spreading operation.
Then, the signal is filtered using the moving average technique in order to increase the signal-to-noise ratio. Finally, the decimator takes a sample every M samples and sends it to the decoder.
In general, CDMA can be synchronous and asynchronous. In the synchronous CDMA, signals from different users are received perfectly synchronized in time and frequency. In this case, CDMA performs orthogonal codes for the spreading: each user uses a code orthogonal respect to the other codes. The Walsh-Hadamard codes are the typical codes that are used to encode signals to separate different users. In the asynchronous CDMA, signals are not precisely coordinated, typically due to the difference in their distance from the base station. In this case, pseudo-random sequences are used to encode and decode signals in the asynchronous CDMA. Pseudo-random sequences are statistically uncorrelated and the sum of a large number of them is approximated by a Gaussian noise process. So, signals from the other users appear as noise to the signal of interest [2].
The CDMA technique is used in the 3G European cellular system UMTS (Universal Mobile Telecommunication System) and in CDMA2000, used in the USA and in the other countries, as a multiple access technique. The system uses subcarriers of about 2GHz, with QPSK modulation, the channel spacing of 5MHz and an SRRC transmitted impulse with roll-off α = 0.22. The spreading factor for the UMTS is 3.84Mchip/s (with a chip duration time Tc= 0.26µs) [1].
In the UMTS system, the chip-rate is the result of the application of two codes on the information bits: the channeling code cc, which gives the spreading
operation and the scrambling code cs, which is used to identify and distinguish
Fig. 2.13: Channeling and scrambling codes applied to the information bits oversampled at the chip duration time, Tc.
The CDMA technique is used also in the satellite communications to enable earth stations to transmit at the same time and frequency to the transponder [11], [12].
The most important advantage of this technique is the robustness against jamming. Moreover, it is robust also to the selective fading channel: if there is a notch, a spread signal can be recovered, while a normal signal cannot. Finally, it has a higher spectral efficiency than TDMA and FDMA technique because each user utilizes all the available bandwidth for as long as necessary [1].
On the other hand, the CDMA requires a greater complexity of the receiver circuits and of the decoding algorithms and is not able to manage a large num-ber of users because the overall quality of service decreases [1]. Moreover, its coding and decoding procedures increase the end-to-end latency of the system. Finally, in the asynchronous CDMA, users interfere with each other increasing the noise and leading to a degradation of the performance of the system, while in the synchronous CDMA, the procedure to keep signal perfectly synchronized is computationally heavy and not energy efficient [1].
2.5 NOMA
2.5
NOMA
All the conventional orthogonal multiple access techniques are characterized by an important disadvantage. They serve a single user in each orthogonal resource block causing spectral inefficiency: if we consider one user with very poor chan-nel conditions, the use of OMA means that it is inevitable that one of the scarce bandwidth resources is occupied only by this user, despite its poor channel con-ditions. This has a negative impact on the spectrum efficiency and throughput of the overall system [28]. This may lead to a non-orthogonal approach.
The Non-Orthogonal Multiple Access (NOMA) technique allows overlapping among the signals from different devices in the time and frequency domain. Sig-nals are transmitted with a different level of power and Successive Interference Cancellation (SIC) is performed at the receiver in order to remove the undesired interference [3]. The diagram in the Fig. 2.14 shows how the common resources are divided in the time, frequency and power domain [5]. In this case, the time, the frequency and the power domain are discrete domain, divided into slots. The various colors characterize the transmission of different users. The signals from different users are overlapped in the time and in the frequency domain. Different levels of power are used to decode the signals.
Fig. 2.14: The NOMA power-time-frequency diagram.
In the following paragraphs, we focus on a single-carrier NOMA both in the downlink and in the uplink. The multi-carrier system is an extension of the single-carrier system and channel gains can be considered over every subcarrier.
2.5.1
NOMA downlink
This section describes the basic principle of the downlink NOMA. For simplicity, we consider a scenario where a single-antenna base station (BS) serves simul-taneously two single-antenna users (UE) in the downlink channel at the same frequency [7]. The BS is able to build the NOMA multi-user signal by perfectly overlapping every single-user signal. The transmitted signal will carry the signals completely aligned, despite the channel distortion.
Fig. 2.15: A downlink NOMA system where a antenna base station serves simultaneously two single-antenna users at the same frequency.
The base station transmits a signal for UE-i, si, with the transmission power
pi. The transmitted signal is:
x = U X i=1 √ pi· si, (2.14)
where U = 2, therefore the eq. (2.1) simply becomes
x =√p1· s1+
√
p2· s2. (2.15)
The received signal at UE-i is represented as:
yi = hi⊗ x + wi, i = 1, 2 (2.16)
where hi is the channel impulse response, whose length depends on the specific
propagation channel models, and wi denotes the Gaussian noise including
2.5 NOMA
Fig. 2.16: A Downlink NOMA system with one BS and two users.
In the downlink, the channel impulse response for the two transmitted signals, s1 and s2, is the same because BS transmits the overlapped signal, x, to every
UE. The downlink channel quality between UE-1 and the BS is supposed to be better than that between UE-2 and the BS because UE-2 is farther than UE-1 and so the power allocated to UE-2 is higher than that allocated to UE-1, as shown in the Fig. 2.15. Before the transmission, a power allocation scheme is used to adjust the power for the signal to each UE, as it is described in [29].
In the downlink NOMA, the SIC process is implemented at the UE receiver [7]: the Fig. 2.16 shows how the SIC receiver works. The optimal order for decoding in downlink NOMA starts from the closest to the BS (normally it has the greater Channel-to-Noise Ratio) [7],
|Hi| 2
/σ2wi, (2.17)
where i denotes the fact that |Hi| 2
is calculated for the UE-i and
|Hi|2 = N −1 X k=0 hi[k] e −j2πk N 2 (2.18)
is the channel gain defined by the square of the channel frequency response. In a single-carrier 2-UE case, where UE-2 is farther than UE-1, |H1|2/σw21 >
|H2| 2
/σw22, UE-2 does not perform interference cancellation since it comes first in the decoding order so it directly decodes s2 by treating message from
removes its component from received signal y1 before decoding its own message. Secondly, assuming the error-free detection, UE-1 can correctly decode s1without
interference from s2 [7].
2.5.2
NOMA uplink
As in the previous section, we consider the same scenario where two single-antenna users transmit to a single-single-antenna base station at the same frequency. At the beginning, the signals from different users are transmitted in different time-slots. But, by exploiting the transmission control mechanisms, they come to the BS perfectly overlapped.
Fig. 2.17: An Uplink NOMA system where two antenna users transmit simultaneously to a single-antenna base station at the same frequency.
As it is shown in the Fig. 2.18, UE-2 is supposed to transmit a signal with much power than UE-1, because it is farther than UE-1. However, it doesn’t mean that the two signal comes at the BS with the same power, otherwise, SIC doesn’t work correctly. SIC receiver always needs a difference in power between the two signal to decode received signal [7], [3]. Therefore, also in uplink, a power allocation scheme is used to adjust the power for the signal of each UE before the transmission [29]: the signal from UE-2 must reach the BS with much power than the signal from UE-1.
In the general case, UE transmits signal si with the transmission power pi to
the BS. So, the transmitted signal of the UE-i is zi =
√ pisi.
For a 2-UE uplink NOMA system the received signal at the base station can be represented:
2.5 NOMA
y =√p1· h1⊗ s1+
√
p2· h2⊗ s2+ w, (2.19)
where hi is the channel impulse response and w denotes the receiver Gaussian
noise, w ∈ CN (0, σ2 w).
In the uplink, the channel impulse response for the two signals transmitted by the users is not the same because even if UE-1 and UE-2 are not so far, the multipath channel will be completely different.
Fig. 2.18: An Uplink NOMA system with two users and one BS.
In the NOMA uplink, the SIC process is implemented at the base station receiver, as the Fig. 2.18, in the order of the decreasing power: the strongest signal, coming from UE-2, is decoded first, then it is removed from the received signal, so the new strongest signal is decoded and then removed, and so on [7].
In a 2-UE case, if p2 > p1, in the first stage, the BS decodes s2 treating s1 as
noise. Once s2 is correctly decoded, it can subtract the s2 component from the
received signal y and then decode correctly s1.
2.5.3
Advantages and disadvantages of NOMA
Many advantages have been demonstrated in the use of NOMA. This technologies provide more efficiency than TDMA and FDMA because they serve more than one user in each orthogonal resource block [5].
Furthermore, if we compare NOMA to CDMA, in CDMA users are separated by exploiting the differences between their spreading codes; whereas the concept
of NOMA can be seen like multiple users employ exactly the same code. As a consequence, CDMA requires a chip rate much higher than the supported infor-mation data rate, i.e. few hundred Gbps to support a data rate of 10 Gbps, which is difficult to realize in practice [28]. Instead, NOMA does not show this problem. Moreover, NOMA can be integrated into existing and future wireless systems because of its compatibility with other communication technologies. For example [28] demonstrates that NOMA is compatible with OFDMA.
On the other hand, NOMA presents also some disadvantages. The SIC proce-dure increases the end-to-end latency between the transmitter and the receiver. In addition, in the uplink the transmitted power of the users is limited so the power difference between he signals from different users can’t be too high.
2.6
Channel capacity of Multiple Access
Tech-niques
It is useful to compare TDMA, FDMA, CDMA and NOMA in terms of some performance metric, such as the channel capacity achievable in the AWGN chan-nel. We consider 2 users which have the average power Pi = P . According to
the Shannon theorem, the capacity of a single user who transmitts a signal with power P in a band-limited AWGN channel of bandwidth W is:
C = W log2 1 + P W N0 , (2.20)
where N0 is the power spectral density of the additive noise [2].
In a TDMA system of two users, each user transmits for the half of the time through the channel of bandwidth W , but with the total available power 2 · P [2]. Therefore, the capacity per user is:
Cu = W 2 log2 1 + 2 · P W N0 . (2.21)
In a FDMA system of two users, each user makes use of a bandwidth W/2 and transmits with power P [2]. So, the capacity of each user is:
Cu = W 2 log2 1 + P W 2 N0 ! = W 2 log2 1 + 2 · P W N0 , (2.22)
2.6 CHANNEL CAPACITY OF MULTIPLE ACCESS TECHNIQUES
which is equal to the capacity of a TDMA system. If we consider a system with K users, the eq. 2.21 and 2.22 become:
CK = W Klog2 1 + K · P W N0 . (2.23)
It is interesting to note that for a fixed bandwidth FDMA system, as K increases, each user is allocated a smaller bandwidth (W/K) and consequently, the capacity per user decreases. Instead, in a TDMA system, it may not be possible for the transmitters to sustain a power of KP if K is very large. These are the limits of TDMA and FDMA systems in the capacity.
In a CDMA system, each user transmits a pseudo-random signal of a band-width W and average power P . The capacity of the system depends on the fact that the CDMA is synchronous or asynchronous.
In the asynchronous CDMA, the other users are seen as Gaussian interference at the receiver of each user. Thus, each user signal is corrupted by the Gaussian interference of power (K − 1)P and an additive Gaussian noise power W N0 [2].
The capacity per user is:
CK = W log2 1 + P W N0+ (K − 1)P . (2.24)
In the two UE case the eq. 2.24 becomes:
Cu = W log2 1 + P W N0+ P . (2.25)
On the other hand in the synchronous CDMA, it is demonstrated by [2] that the capacity of CDMA has a form similar to that of TDMA and FDMA.
In a NOMA system of two users, the channel capacity of UE-1 is different from UE-2. We consider 2 users which have the average power Pi.
Where UE-1 performs the SIC process, (see the Fig. 2.16 in the previous paragraph), the capacity of the generic user i can be represented as:
C1 = W log2 1 + P1 W N0 C2 = W log2 1 + P2 P1+ W N0 , (2.26)
It is demonstrated in [7] that the capacity region of NOMA with SIC is much wider than that for OMA in the asymmetric channel case, where, for example, P1 = 0dB and P2 = 20dB as shown in the Fig. 2.19 from [7].
Fig. 2.19: Capacity region for the two users in the downlink NOMA and OMA in the asymmetric channel.
Chapter 3
System Model: UFMC
The actual LTE technology does not satisfy the most important 5G requirements. The advent of Internet of Things (IoT) and Machine to Machine (M2M) commu-nications will increase the number of users [14]. So, they will have low out-of-band emissions in order to minimize the inter-user interference. In addition, since the most of these users will be sensors or autonomous entities, they have to increase the battery lifetime up to 10 years [14].
LTE is based on OFDM architecture which does not have a well-localized spec-trum due to its out of band emissions. This results in an increasing of inter-user interference especially when there are a lot of contiguous users [15]. Moreover, the OFDM requires a procedure in order to obtain a strict synchronization for preserving the orthogonality between signals, which is computationally heavy and is not energy efficient.
Thus, the future generation technologies arises the need of new waveform that have to coexist with the actual modulation.
Different types of waveform have been proposed as an alternative to OFDM in order to overcome these problems. The Filter Bank Multicarrier (FBMC) is based on an architecture, quite similar to OFDM, but it applies a filtering to each of the subcarriers. In this way, FBMC provides a well-localized per-subcarrier spectrum because the sidelobes are much weaker and the intercarrier interference becomes smaller [31]. Despite these advantages, FBMC is difficult to realize in practice: the FBMC signal is very frequency-selective and so signals have to be very long in their duration time. This is in contrast with the IoT communications [31].
The other waveform proposed is the Generalized Frequency Division Multi-plexing (GFDM), which digitally implements the filter band approach. GFDM combines both the advantage of flexibility, due to the fact that each single sub-carrier can be modulated individually, and low PAPR, which reduce the power consumption. Nevertheless, it required appropriate filter designs to control the orthogonality of the subcarriers, which increase the complexity of the entire sys-tem. The multi-carrier system is well described in [30].
UFMC is another waveform proposed as new physical layer in the standard-ization process of 5G. It is quite similar to OFDM and we will describe in deep in the next paragraphs. Furthermore, we apply the NOMA technique as a multiple access technique for the multi-user UFMC system.
3.1
UFMC single-user
3.1 UFMC SINGLE-USER
The UFMC system is an extension of the OFDM system, but with important characteristics that make it more advantageous than the OFDM system: in the UFMC system the same input mapped signal is divided into B sub-bands of D subcarriers and after the IDFT, each subband is individually filtered in order to improve the signal spectral efficiency and its robustness [14], [15], [16], [17], [19]. The Fig. 3.1 shows the block diagramm of a single-user UFMC system.
The matrix format explains better the analytic processing of the signal. The input signal b ∈ BNbit×NsymbM C is mapped into S ∈ CNsymb×NsymbM C, where
Nbit is the number of bit per multi-carrier symbols and NsymbM C is the number
of multi-carrier symbols. S is then divided into B sub-bands, Si ∈ CD×NsymbM C.
The number of mapped symbols that are transmitted from the user is
Nsymb = B · D (3.1)
and the number of the input bits is
Nbit = log2(M ) · Nsymb, (3.2)
where M is the modulation index.
For each subband, after the zero-padding operation, the Si pass through the
IDFT block. So, the IDFT matrix is:
V = V0 0 . . . 0 0 V1 . . . 0 .. . ... . .. ... 0 . . . VB−1 , (3.3)
where ViNF F T×D is the IDFT matrix of each subband, with i = 0, ..., B − 1, and
the generic element of the Vi matrix is:
Vm,n = 1 √ NF F T e( j2πmn NF F T), (3.4) where m = 0, ..., NF F T − 1 and n = 0, ..., B · D − 1.
The filter matrix is F(NF F T+Lf ilter−1)×(NF F T·B) which is composed by:
where
Fi = toepl(fi) (3.6)
is the Toeplitz matrix needed for the convolution between the symbols si out of
the IDFT block and the Dolph-Chebyshev filter in which
fi,k = fk· e
j2π(∆f2 +i∆f ) k
NF F T (3.7)
is the filter impulse response centered in the proper subband, where ∆f = D, k = 0, ..., Lf ilter− 1, i = 0, ..., B − 1 and fk = chebwin(Lf ilter, α), where Lf ilter =
73, and α = 60. α is the side lobe level (SLL) of the filter and Lf ilter is the
filter length, respectively. The filter parameters are chosen in order to compare the UFMC system with the uplink LTE@10MHz based on the OFDM. In order to have a fair comparison between the two waveforms, the output length of each transmittere must be the same. Given that, the cyclic prefix of the OFDM system is composed by Lcp= 72 samples, therefore the filter length Lf ilter must be :
NF F T + Lcp = NF F T + Lf ilter− 1 =⇒ Lf ilter = Lcp+ 1 (3.8)
The Fig. 3.2 shows the impulse response and the frequency response of the Dolph-Chebyshev filter.
Fig. 3.2: The impulse response on the left and the fre-quency response on the right of the Dolph-Chebyshev filter used in the UFMC transmitter.
3.1 UFMC SINGLE-USER
The transmitted signal is
z = T · S, (3.9)
where T ∈ C(NF F T+Lf ilter−1)×Nsymb is the transmission matrix composed by:
T = F · V . (3.10)
The Fig. 3.3 shows the difference between the power spectrum of the UFMC and the OFDM transmitted signal. The OFDM spectrum has high side lobe levels due to the rectangular pulse in the time domain. This causes inter-carrier interference (ICI) and a degradation of the performance of the system when the orthogonality between subcarriers is not perfect and also inter-user interference when others OFDM signals are nearly [14]. Instead, the UFMC system has a frequency well-localized spectrum thanks to the shape of Dolph-Chebyshev filter applied on each sub-band in the time domain, which reduces the out-of-band leakage in the frequency domain. In addition, the UFMC system does not require the cyclic prefix as a consequence it has a higher spectral efficiency than the OFDM system.
Then, the signal passes through the channel and the noise is added. So, the received signal is:
r + w = H · z + w, (3.11)
where H is the frequency channel response, whose dimensions depend on the channel and w denotes the noise at the receiver, w ∈ CN (0, σ2
w).
The estimated signal is
ˆ
S = R · U1· (r + w), (3.12)
where R is the pseudo-inverse matrix defined below:
R = pinv(U1 · H · T ), (3.13)
where T is the transmission matrix defined in the eq. 3.10.
U(2Nsymb)×(NF F T+Lf ilter+Lchannel−2) is the DFT matrix, with size 2N
F F T, the
Fig. 3.3: The power spectrum of UFMC, in the blue, compared with the power spectrum of OFDM, in the red.
received symbols is larger than the transmitted symbols due to the channel and to the fact that no cyclic prefix is added to the transmitted symbols. So the con-volution is linear and not circular, like in the OFDM. In this way, the transmitted symbols will be received exactly in the subcarriers with even index [23]. In the R matrix, U(Nsymb)×(NF F T+Lf ilter+Lchannel−2)
1 is the undersampled matrix of U , which
is composed only by the subcarriers of even index. The single element of U is
Ul,n= 1 √ 2NF F T e( −j2πln 2NF F T), (3.14)
where l = 0, ..., NF F T + Lf ilter+ Lchannel− 2 and n = 0, ..., 2Nsymb− 1
3.2
UFMC multi-users
The UFMC system described in the previous paragraph is designed for supporting only one user. In this paragraph, we project the uplink UFMC system in a multi-user scenario. The NOMA technique is used as an access method in order to
3.2 UFMC MULTI-USERS
allow several users to share the same communication channel. The SIC process is exploited at the receiver to decode the signals coming from different users.
Fig. 3.4: The block diagram of a two-user UFMC system in the uplink.
The Fig. 3.4 shows the multi-users UFMC system in the uplink. We consider two users and one BS, all with a single antenna. In this preliminary analysis, we suppose perfect synchronization at the BS, so the signals are received perfectly overlapped.
The two users transmit two different signals with two different level of power:
x1 = √ p1 · T · S1, x2 = √ p2 · T · S2, (3.15)
where p1 and p2 represent the powers, T is the transmitted matrix defined in
the eq. 3.10, equal for both users, S1and S2are the mapped symbols transmitted
from UE-1 and UE-2 respectively.
The two signals pass through two different channels, and then they are received and noise is added.
The received signal at the BS is the sum of the two transmitted signals:
r + w = H1·
√
p1· T · S1+ H2·
√
p2· T · S2+ w, (3.16)
where H1 is the frequency response of the channel between the UE-1 and the BS
and H2 is the frequency response of the channel between the UE-2 and the BS,
w denotes the receiver gaussian noise, w ∈ CN (0, σ2 w).
3.2.1
SIC receiver in UFMC multi-users
Fig. 3.5: The SIC process UFMC multi-user receiver.
The SIC process at the receiver is described in the Fig. 3.5. The transmission power of UE-2 is supposed to be higher than the transmission power of UE-1: p2 > p1.
The classic notation of the received signal in the time domain is given by
zi = h1· √ p1⊗ f1⊗ F −1{S 1} + h2· √ p2⊗ f2⊗ F −1{S 2} + w, (3.17)
where hi, is the channel impulse response and fi is the filter impulse response,
of the i-th user. The received signal in the frequency domain can be written as:
Zk= rk+ wk =
√
p1· H1,k· F1,k · S1,k+
√
3.2 UFMC MULTI-USERS
where k=0, ..., BD-1 is the subcarrier index and B and D are the number of sub-bands and subcarriers, respectively, while Hi,k is the channel frequency response
and Fi,k is the filter frequency response, for the i-th user on k-th subcarrier.
Therefore, the SINR experiences on the air before the reception by user 2 on the k-th subcarrier can be expressed as:
SIN R2,k = p2· |H2,k|2· |F2,k|2· ES2 p1· |H1,k| 2 · |F1,k| 2 · ES1 + σw2 (3.19)
The eq. 3.19 represents the SINR for each subcarrier. The average SINR is represented below: SIN R2 = p2· H2 2 · F2 2 · ES2 p1· H1 2 · F1 2 · ES1 + σ 2 w . (3.20)
In both the eq. 3.19 and 3.20, the ES1 and ES2 represent the energy of the signal
from UE-1 and from UE-2 respectively, H2
2
is the mean square value of the frequency channel response and F2
2
is the mean square value of the frequency filter response.
So, the BS does not perform the SIC process to decode S2 since it comes
first in the decoding order. The signal S2 is directly estimated by treating S1 as
Gaussian Noise: ˆ S2 = 1 √ p2 · Q2· H2· T · √ p2· S2+ 1 √ p2 · Q2· w + Q2· H1· √ p1 √ p2 · T · S1 | {z } noise (3.21)
The eq. 3.16 and 3.21 represent the matrix notation of the received and the estimated signal ˆS2.
On the contrary, as regards S1, the BS performs the SIC strategy to decode
S1: it first decodes S2 and then removes its components from the received signal,
before decoding its own message. Supposing perfect knowledge of the channel at the BS, the first step (cancellation of the signal coming from user 2) of the SIC process can be expressed as follows:
r0 + w = H1· √ p1· T · S1+ w + H2· √ p2 · T · S2− H2· √ p2· T · ˆS2
= H1·
√
p1 · T · S1+ w + H2·
√
p2· T · (S2− ˆS2) (3.22)
In this case, the evaluation of the SNR of S1 can be seen from two different
perspectives. If S2 is perfectly estimated, there is no interference caused by this
signal in the detection of S1. On the other hand, if the estimation of S2 is not
completely corrected, the SNR becomes a SINR. The two situations are described with the equations below:
SN R1 = p1· H1 2 · F1 2 · ES1 σ2 w , Sˆ2 = S2 (3.23) SIN R1 = p1· H1 2 · F1 2 · ES1 p2· H2 2 · F2 2 · E {2} + σ2 w , Sˆ2 = S2+ (3.24)
where is the estimation error and E {2} is the root mean square error.
3.3
UFMC in presence of a carrier frequency
offset
In order to reproduce a better real scenario, a carrier frequency offset (CFO) is introduced in the reception to simulate the imperfect synchronization of the system.
In a single-user UFMC system and supposing an ideal channel without the presence of noise, the signal after the IFFT conversion into the time domain, for a subband with the index i, is:
xi(l) = 1 NF F T X k∈Ei Si(k)e2jπkl/NF F T, (3.25)
with l = 0, ..., NF F T − 1, where NF F T = 1024 is the FFT size, i = 1, ..., B,
where B is the number of subbands. Ei is a set of D subcarriers of the subband
(i − 1) · D + 1, ..., i · D, and Si is the signal in the frequency domain after the
mapper.
The signal after the filtering operation is a discrete linear convolution between the Dolph-Chebyshev filter fi and the time domain signal si:
3.3 UFMC IN PRESENCE OF A CARRIER FREQUENCY OFFSET
yi = si⊗ fi. (3.26)
If a CFO is added, the receiver signal becomes
r = 2 ∗ NF F T B
X
i=1
ci(si⊗ fi), (3.27)
where ci is the time domain expression of frequency offset for the subband i:
ci(k) =
1 2NF F T
e2jπk/NF F T, (3.28)
with k = 0, ..., NF F T+ Lf ilter−2, where is the CFO normalized to the subcarrier
spacing, which is equal for every subcarrier.
The signal is then converted in the time domain by the 2NF F T-point FFT. So,
by supposing the same consideration done in [17] that without loss of generality, we can assume that the estimated symbol in the subcarrier k belongs to the subband i, all the estimated symbols are
Y (k) = 2NF F T−1 X j=0 Ck−jX˜i(j)Fi(j) + B X l=1,l6=i · 2NF F T−1 X j=0 Cl(k − j) ˜Xl(j)Fl(j), (3.29)
where Ci, ˜Xi and Fi are the 2Nfft-FFT of ci, xi and fi respectively.
Moreover, from the eq. 3.28, Ci is also
Ci(k) = sin(2Nπ F F T(2 − k)(NF F T + Lf ilter− 1)) 2NF F Tsin(2Nπ F F T(2 − k)) · ej2NF F Tπ (2−k)(NF F T+Lf ilter−2) . (3.30) The aim is to separate the signal part from the interference part in the eq. 3.30. Firstly, we have to derive ˜Xi from the eq. 3.25 as follows:
˜ Xi(k) = Si(k2), if k is even P n∈EiSi(n) sin(π 2(2n−k)) NF F Tsin(2NF F Tπ (2n−k))· e jπ2(2n−k)(1− 1 NF F T), if k is odd (3.31) where Xi is the signal of the subband i in the frequency domain and it can be
expressed as ˜ Xi(k) = 0, if k /∈ Ei Si(k), if k ∈ Ei (3.32)
As described in [17], in the eq. 3.31 all the odd subcarriers contain both a part of the signal energy and inter-carrier interference (ICI) from other subcarriers in the subband. The eq 3.31 can be rewritten for a considered subcarrier k in subband i as
˜
Xi,k(m) = ˜Xi,Sk(m) + ˜Xi,ICIk(m), (3.33)
where ˜Xi,Sk(m) represents the signal in the subcarrier m of the subcarrier k and
˜
Xi,ICIk(m) is the corresponding ICI.
Due to convolution, even if only subcarriers of index k = 0, 2, ..., 2NF F T−2 are
of interest, also subcarriers of index m = 0, 1, ..., 2NF F T − 1 must be considered
to get the estimated symbol in subcarriers k. This relation is described below:
˜ Xi,Sk(m) = Si(m2), if m = k Si(k2) sin(π 2(k−m)) NF F Tsin(2NF F Tπ (k−m))· e jπ2(k−m)(1− 1 NF F T), if m is odd 0, otherwise (3.34)
and in the same way
˜ Xi,ICIk(m) = 0, if m is even P l∈Ei,l6=k2 Si(l) sin(π2(2l−m)) NF F Tsin(2NF F Tπ (2l−m)) · e jπ2(2l−m)(1− 1 NF F T), if m is odd (3.35)
In conclusion, with the eq 3.33 and 3.35, the estimated symbols in the eq 3.30 can be divided in the signal part and in the interference part as
3.3 UFMC IN PRESENCE OF A CARRIER FREQUENCY OFFSET Y (k) =P2NF F T−1 j=0 Ci(k − j) ˜Xi,Sk(j)Fi(j) ...Signal +P2NF F T−1 j=0 Ci(k − j) ˜Xi,ICIk(j)Fi(j) ...ICI +PB l=1,l6=i P2NF F T−1 j=0 Cl(k − j) ˜Xl(j)Fl(j) ...IBI , (3.36)
where the last addition term is the Inter-Band Interference (IBI).
The eq 3.36 shows that under the presence of a CFO, the estimated sym-bol gets distortion both from subcarriers in subband (ICI) and from all other subbands (IBI).
3.3.1
UFMC in presence of a channel perturbation
The imperfect knowledge of the channel can be also considered by evaluating the BER performance of the system varying the Mean Squared Error (MSE) of the channel estimation.
So, the transmitted signal is
z =√p1· T · S1+
√
p2· T · S2 (3.37)
and the received signal is
r = H · z, (3.38)
where the noise is not considered in order to focus on the channel perturbation. The pseudo-inverse matrix is
Q1,2 = pinv(H · T ) + WQ, (3.39)
where WQ is the noise that perturbs the channel matrix. In this case, H is
supposed to be the same for the two users.
This description of the system better shows the BER performance behavior when the channel is not perfect estimated.
Simulation Results
In this chapter we evaluate the performance of the single-user and multi-user UFMC system considering the bit error rate (BER) as metric and varying the power allocation of them, in case of perfect and imperfect synchronization. The results of UFMC are compared with the results of the current OFDMA transmis-sion system.
4.1
UFMC single-user
In order to simulate a single-user UFMC system, we consider one single-antenna user and one single-antenna base station at the same frequency.
Tab. 4.1: The parameters for the sim-ulation of a single user UFMC system.
4.1 UFMC SINGLE-USER
The parameters for the simulations are collected in the Tab. 4.1. We consid-ered 7 multicarrier symbols in order to compare UFMC with the current LTE system based of OFDM. As a matter of fact, the channel can be considered time-invariant in a period of 7 multicarrier symbols in an LTE system.
The number of sub-bands is 15, the number of subcarriers per sub-band is 12, in order to have a very close connection with the LTE PRBs, so a multicarrier symbol is composed of 15 · 12 = 180 symbols. The modulation used is the QPSK, as a consequence the number of transmitted bits per multicarrier symbol is 180log2(4) = 360.
Fig. 4.1: The Bit Error Rate of a QPSK UFMC system. Different types of channels are considered: AWGN, Rayleigh, EVA, EPA, ETU.
The Fig. 4.1 shows the bit error rate (BER) of the single user UFMC system considering different types of channels: AWGN, Extended Pedestrian A model (EPA), Rayleigh, Extended Vehicular A model (EVA) and Extended Typical Urban model (ETU) [32], [33]. The BER has been calculated by comparing the bit generated in the transmission with the bit estimated by the receiver.
BER of a QPSK modulation. In the other channel case, the UFMC performs approximately the theoretical Rayleigh BER of a QPSK modulation.
In next simulations, we focus on the BER performance of the system in the AWGN channel and in the EVA channel.
The Fig. 4.2 shows the bit error rate of a UFMC system in the blue and an OFDM system in the red, in the AWGN channel. The BER has been calculated in case of perfect synchronization of the system: no carrier frequency offset (CFO) between the transmitter and the receiver has been considered. The two systems have almost the same performance. As a result in the single-user case in the perfect synchronization of the system, the UFMC can be an alternative of the OFDM by keeping the same performance.
Fig. 4.2: BER of a QPSK UFMC and a QPSK OFDM system in the AWGN channel in perfect synchroniza-tion.
In order to better simulate a real scenario, we evaluate the bit error rate also in the EVA channel.
4.1 UFMC SINGLE-USER
delay profile represents a medium delay spread environment.
Tab. 4.2: EVA delay profile.
The Fig. 4.3 shows the bit error rate of a UFMC system in the EVA channel. In this case, the UFMC system provides little better results at high SNR because it is more robust to the interference caused by the channel.
Fig. 4.3: BER of a QPSK UFMC and a QPSK OFDM system in the EVA channel in perfect synchronization.
4.1.1
Simulation results under the presence of CFO
Under the presence of a carrier frequency offset (CFO), the UFMC and the OFDM system behave differently.
The time domain expression of the Carrier Frequency Offset (CFO) added to the system is
c(k) = 1 2NF F T
e2jπk/NF F T, (4.1)
with k = 0, ..., NF F T+ Lf ilter−2, where is the CFO normalized to the subcarrier
spacing.
The parameters for the simulation are the same collected in the Tab. 4.1. The Fig. 4.4 represents the BER performance of a UFMC system and of an OFDM system varying the of the CFO in the eq. 4.1 and considering the Eb/N0 = 15dB.
Fig. 4.4: BER of a QPSK UFMC and a QPSK OFDM system in an AWGN channel varying the CFO and considering a Eb/N0= 15dB.
4.1 UFMC SINGLE-USER
(a) CF On= 0.01 (b) CF On = 0.05
(c) CF On= 0.1 (d) CF On = 0.15
Fig. 4.5: UFMC single-user with different Carrier Fre-quency Offset (CFO) considering an AWGN channel.
of fact, the Dolph-Chebyshev filter in the UFMC system makes the UFMC wave-form well-localized in frequency by reducing the sidelobe levels and out-of-band emissions. Thus, the the inter-carrier interference (ICI) induced by the CFO in the UFMC is smaller than in the OFDM. This results in a greater robustness to CFOs of the UFMC system compared to the OFDM system, providing better performance in terms of BER.
The Fig. 4.5 shows the UFMC performance BER compared with the OFDM under the presence of four different CFO in the AWGN channel condition. With low CF On, 0.01 and 0.05, which correspond to a CFO of 0.55kHz and 2.75kHz
respectively, the difference between the UFMC and the OFDM is smaller, but it increases when the CF On is 0.1 and 0.15, which correspond to a CFO of 5.5kHz
The difference between UFMC and OFDM, under the presence of a CFO, becomes more evident in the EVA channel. The Fig. 4.6 shows the BER perfor-mance of UFMC and OFDM systems varying the CFO in an EVA channel by considering the same Eb/N0 of the previous AWGN case. All the two systems
provide worse performances compared with the AWGN channel condition, but the UFMC proves better robustness than the OFDM under different CFOs. In this case, the Eb/N0 = 15dB is not great enough to make the system works
cor-rectly, or better, to reach a performance BER of 10−4 or 10−5. That is why even for low CFOs the UFMC and the OFDM do not achieve a BER≈ 10−3 either.
Fig. 4.6: BER of a QPSK UFMC and a QPSK OFDM system in an EVA channel varying the CFO and con-sidering a Eb/N0= 15dB.
4.1 UFMC SINGLE-USER
(a) CF On= 0.01 (b) CF On = 0.05
(c) CF On= 0.1 (d) CF On = 0.15
Fig. 4.7: UFMC single-user with different Carrier Fre-quency Offset (CFO) considering an EVA channel.
The Fig. 4.7 shows the behavior of the UFMC compared to the OFDM under the presence of four different cases of CFOs in the EVA channel. In this case, the difference between UFMC and OFDM is greater than the AWGN case even for lower CFO.
Under the presence of CF On = 0.15, both in the AWGN, in the Fig. 4.5, and
in the EVA channel, in the Fig. 4.7, the BER performance of the system decades. As a matter of fact, a CF On = 0.15 means a CFO of 8.25kHz for the UFMC
system, which is very high value for a carrier frequency offset in the system.
The Fig. 4.8 highlights the gain of the UFMC compared to the OFDM varying the CFO by considering a bit error rate of 10−3 in both the AWGN and the EVA channel. In the AWGN case, the gain is lower because in the two systems the
inter-carrier interference (ICI) is due only to the CFO. On the contrary in the EVA case, the gain is higher because there is the channel effect in addition to the CFO effect which provides a much more interference in the OFDM system than in the UFMC system.
Fig. 4.8: The gain (dB) of UFMC compared to OFDM varying the CFOs in the AWGN and in the EVA chan-nel by considering a BER = 10−3.
In conclusion, under the presence of a CFO, the UFMC system provides better results in terms of BER performance than the OFDM system both considering the AWGN and the EVA channel.
