SC-FDMA and LTE Uplink Physical Layer Design

Transcription

1 Seminar Ausgewählte Kapitel der Nachrichtentechnik, WS 29/21 LTE: Der Mobilfunk der Zukunft SC-FDMA and LTE Uplink Physical Layer Design Burcu Hanta 2. December 29 Abstract The Long Term Evolution (LTE) physical layer design is covered as the main topic in this report. The main focus is on the single-carrier frequency division multiple access (SC-FDMA) scheme which has been selected as the multiple-access scheme of the LTE uplink. SC-FDMA and orthogonal frequency division multiple access (OFDMA) are similar schemes except for a discrete Fourier transform which is added to the SC-FDMA transmission which changes the way how the data symbols are distributed over different subcarriers. The data symbols-subcarrier mapping is not one-to-one but instead each subcarrier carries a part from each data symbol transmitted at that time instant. The reason for the selection of SC- FDMA comes mainly from its advantage to provide low a peak-to-average power ratio (PAPR) for the transmit waveform. This results in less power consumption in the mobile station compared to an OFDMA transmission. The uplink physical channel of LTE, the structures of the transmitter and receiver of the LTE uplink together with the criteria for the design of the transmitter and receiver are given as the main focus of interest of this report.

2 2 Burcu Hanta 1 Introduction In recent years, the need for a radio system with high data and throughput has been increasing gradually. After the UMTS cellular system, the Long Term Evolution (LTE) system under the consideration of Third Generation Partnership Project (3GPP) is the next focus of attention. Orthogonal frequency division multiple-access (OFDMA) is used for the downlink, and SC- FDMA is used for the uplink as multiple-access schemes in the LTE system. SC-FDMA is a modified form of the OFDMA due to some additional requirements for the uplink of the LTE system. Some of these requirements are: Support for wide range of data rates. Sufficiently low PAPR of the transmitted waveform, to avoid high power consumption in the mobile terminal (transmitter for the uplink). Enhanced uplink system throughput. To support these requirements, SC-FDMA is selected as the multiple-access scheme for the uplink of LTE. In terms of the generation of the transmit signals, SC-FDMA and OFDMA are similar schemes except for the discrete Fourier transform (DFT) performed on the modulated data symbols in SC-FDMA. DFT changes the logic of the transmission to a large extent. This will be discussed in more detail in Chapter 2. SC-FDMA transmit data frame and the components of the physical transmission channel are shortly explained to support the understanding of the distribution of the data symbols onto the resource grid. The allocation of the subcarriers of different users to the entire frequency band along with the frequency diversity techniques such as channel dependent scheduling (CDS) is important in terms of supporting the frequency and multi-user diversity. By changing between the subcarrier allocation modes (with CDS), system throughput and PAPR reveal differences. These allocation modes and CDS operation are investigated in light of given performance criteria. Pulse shaping is another operation comes after the cyclic prefix addition. In this part of the report, the effects of this operation on the system performance is depicted as well. In Chapter 5, generally, the transmission chain of the SC-FDMA scheme is covered. SC- FDMA signal generation and decomposition in the transmitter and receiver respectively are investigated. 2 SC-FDMA vs. OFDMA In this part, the difference between the structures of SC-FDMA and OFDMA is depicted. Besides, the PAPR problem is studied in more detail.

3 SC-FDMA and LTE Uplink Physical Layer Design OFDMA Figure 1 illustrates the structure of the OFDMA signal generation. { } x n N N Figure 1: Transmitter and receiver structure of OFDMA [1]. OFDMA is a multiple-access scheme which provides multiple channels for different users. The data symbols of each user are spread over the entire frequency band. Each subcarrier is orthogonal to the others and carries the data symbol of one user. Since the time domain transmit symbols of each user are not transmitted in serial as for time domain multiple access (TDMA) but in parallel, each user has not the entire frequency band but some portion and the symbol duration is longer. Therefore, an OFDMA system is robust to time delays caused by multipath fading i.e. frequency selectivity of the radio channel. However, the subcarrier orthogonality should be ensured to avoid inter-symbol-interference (ISI). While OFDMA has important advantages compared to the multiple-access schemes of previous mobile communication systems and is used in the LTE downlink, it does not meet the challenges of the LTE uplink channel. Since the transmitter is the mobile station in this case, the transmit power should be below some certain threshold. This requirement follows from the need of efficiency and safety of users. To avoid high power consumption or high signal distortion, the PAPR should be limited to some extent. Although it would have been attractive to use OFDMA both for the uplink and downlink for full uplink-downlink commonality, SC-FDMA is more advantageous when PAPR and system throughput is considered. The PAPR is defined as: PAPR = P peak P avg, (1) where P peak is the power of the transmit symbol with the peak amplitude value, and P avg is the average power of the transmit symbols. This ratio is high for the OFDMA system since the independent identically distributed (i.i.d.) complex symbols are directly assigned to each subcarrier and a linear inverse DFT (IDFT) operation is performed over these subcarriers. This

4 4 Burcu Hanta overall process is a linear transform over a large number of i.i.d. QAM-modulated complex symbols. This causes that the amplitudes of the transmit symbols directly depend on the constellation points of the modulation scheme. Considering the central limit theorem, the time domain OFDMA signal can be approximated as a Gaussian waveform. This waveform holds the property of having large variations in the amplitudes of each transmit symbol, which leads to a high PAPR. In case of high variations in the amplitudes of the transmit symbols, the output power amplifiers of the transmitter no longer operate in their linear region. As a result, either a significant distortion occurs in the transmit signal due to non-linear clipping or the transmitter dissipates much more power in order to operate in linear region and prevent distortions. When the focus of consideration is the uplink (the transmitter is the mobile terminal), power efficiency becomes of crucial importance. Therefore SC-FDMA is the multiple-access scheme for the LTE uplink. 2.2 SC-FDMA Similar to OFDMA, SC-FDMA divides the transmission bandwidth into multiple parallel subcarriers maintaining the orthogonality of the subcarriers by the addition of the cyclic prefix (CP) as a guard interval. However, in SC-FDMA the data symbols are not directly assigned to each subcarrier independently like in OFDMA. Instead, the signal which is assigned to each subcarrier is a linear combination of all modulated data symbols transmitted at the same time instant. The difference of SC-FDMA transmission from the OFDMA transmission which is an additional DFT block before the subcarrier mapping can be seen in Figure 2. Following from this fact, this system is not a multi-carrier but a single-carrier system. { } x n M { } X k { X l } N { } x m M N { } Figure 2: Transmitter and receiver structure of SC-FDMA [1].

5 SC-FDMA and LTE Uplink Physical Layer Design 5 3 Uplink Time and Frequency Structure As depicted in Figure 3, one SC-FDMA frame constitutes 2 slots, each being.5 miliseconds long. Two slots are called a subframe or transmission time interval. Figure 3: Type 1 Frame structure [2]. The structure of one slot can be more clearly understood by looking at the resource grid structure in Figure 4. N symb = N N symb RB sc N N RB RB sc RB N sc = 12 Figure 4: Uplink resource grid for one slot [3]. The transmit signal in each slot is described by a resource grid with N RB Nsc RB subcarriers and N symb SC-FDMA symbols. The number of subcarriers for each resource block, Nsc RB, is

6 6 Burcu Hanta standardized as 12 for the LTE uplink. N RB depends on the uplink transmission bandwidth determined for that cell but should always be between 6 and 11. These numbers correspond to the smallest and largest uplink bandwidth [2]. When the time domain is considered, the number of the SC-FDMA symbols for each slot is 7 for the normal cyclic prefix. However, when the long cyclic prefix is used, this number decreases to 6. Each resource element in the grid has two indices which stand for the time and frequency axes, respectively. The resource element corresponds to a complex value which is the linear combination of all the data symbols transmitted at that time. 4 Uplink Physical Channel The components of the physical uplink shared channel are depicted in Figure 5. Scrambling Modulation mapper Transform precoder Resource element mapper SC-FDMA signal gen. Figure 5: Uplink physical channel [2]. The elements of the uplink physical channel and their influence are: Scrambler: Scrambles the coded bits in order to randomize the interference and thus ensure that the processing gain provided by the channel code can be fully used. Modulation mapper: Performs the 4QAM or 16QAM modulation on data blocks. Transform precoder: Supports multi-layer transmission in MIMO systems. Resource element mapper: Assignment of the data blocks to the suitable physical resource blocks. SC-FDMA signal generation: Is investigated in the subsequent part of the report. 5 SC-FDMA Transmission 5.1 Subcarrier Allocation Methods The allocation of the subcarriers to each user is an important issue which has an influence on the system performance of the LTE uplink data transmission. In Figure 6 the two most common techniques can be seen embedded into a transmitter scheme. These techniques are localized

7 SC-FDMA and LTE Uplink Physical Layer Design 7 Incoming Bit Stream Serial to Parallel Converter m bits m bits Bit to Constellation Mapping x(,n) Bit to x(1,n) Constellation Mapping M-point DFT Spreading f f1 Subcarrier Mapping N-point IFFT Add cyclic prefix Parallel to Serial converter Transmission circuitry m bits Bit to x(m - 1,n) Constellation Mapping fm- 1 Frequency f f1 1 f 2 f 3 Localized Subcarrier Mapping f M- 4 f M- 3 fm- 1 2 f M-1 Localized f M- 4 f M- 3 fm- 2 f M- 1 f f1 1 f 2 f 3 Distributed Subcarrier Mapping Distributed Frequency Figure 6: SC-FDMA transmitter for localized and distributed subcarrier mappings [5]. carrier assignment mode (localized mode) and distributed carrier assignment mode (distributed mode). In the localized mode, each terminal uses a set of adjacent subcarriers to transmit its symbols. In the distributed mode, the subcarriers used by a single terminal are distributed over the whole frequency band. Figure 7 shows a representation of the different modes in the frequency domain. Figure 7: Subcarrier allocation methods for multiple users (3 users, 12 subcarriers, and 4 subcarriers per user) [1].

8 8 Burcu Hanta Although distributed mode provides high frequency diversity as the subcarriers are spread over the different parts of the frequency band and the subcarrier data transmitted over different channels are subject to different fading, with channel dependent scheduling (CDS), localized mode offers higher system throughput. 5.2 Comparison Criteria for Different Carrier Modes The criteria for the comparison of these carrier allocation schemes are: System throughput which can be measured by the channel capacity formula of Shannon: C = BW log (1 + SNR), where BW is the channel bandwidth and SNR is the signal-tonoise ratio. PAPR. PAPR is a major issue in the mobile terminals, but system throughput is even a stronger indicator of the system performance. Regarding the transmission errors, distributed mode is robust against frequency selective fading because the data symbols for each user are spread over the entire transmission band. Therefore it offers high frequency diversity. On the other hand, in case of high channel gain for each user, localized mode can achieve multi-user diversity. In the localized mode channel dependent scheduling (CDS) of the subcarriers is also required. When the system is monitored and the channel quality is obtained as a function of the frequency for each user, with CDS, the system adapts subcarrier assignments according to the channel quality data. The problem occurs due to the tradeoff between the PAPR and system throughput. Because when PAPR is decreased, system throughput decreases as well. Thus, the required allocation method should be determined separate for different systems. But due to its higher performance in total, the localized mode is standardized for the LTE uplink Effect of CDS on the System Performance As already mentioned, with CDS, the system monitors the frequency band and determines which portion of the frequency band belongs to which terminal for that time interval. Therefore the optimization problem to be solved by CDS can be stated as: How to allocate time and frequency resources among users to reach the maximum user utility in each transmission time interval while achieving multi-user diversity and frequency diversity? With CDS, the system throughput is increased significantly for the localized mode, but since the distributed mode already has frequency diversity, coming from its nature, CDS does not have a big influence on the system throughput for the distributed mode. When the distributed and localized mode are compared in terms of the capacity of the number of terminals, the localized mode with CDS has considerably higher performance [4].

9 SC-FDMA and LTE Uplink Physical Layer Design Effect of Pulse Shaping on the System Performance Pulse shaping is another signal processing operation performed after the cyclic prefix addition. One of the commonly used pulse shaping filter is the raised-cosine filter. The frequency and time domain graphical representation of this filter is given in Figure 8. The general aim of pulse shaping is to mitigate the out-of-band signal energy, thus to conserve more power and cause less interference. On the other hand, pulse shaping causes distortion in the signal which causes an increase in PAPR. The level of this distortion depends upon the rolloff factor of the pulse that is convolved with the transmit signal. The decrease in PAPR does not mean that the PAPR of the SC-FDMA signal is higher than the OFDMA signal because even in the worst case, the PAPR of the SC-FDMA signal is lower than that of an OFDMA signal. 1 P(f) p(t).8.6 α = α =.5 α = α = 1.2 Frequency -.2 α = Time α =.5 Figure 8: Depending on the rolloff factor α, the frequency domain and time domain appearance of the pulse-shaping filter [1]. sin / cos / ( ) ( ) / 1 4 / Figure 9 shows the relationship between the complementary cumulative distribution function (CCDF) and the rolloff factor. As the rolloff factor of the pulse increases, CCDF decreases as well. Although PAPR of the localized FDMA is higher than the distributed FDMA, the selection of different schemes is based on system throughput.

10 1 Burcu Hanta 1 CCDF of PAPR: QPSK, N fft = 256, N occupied = 64 IFDMA LFDMA 1 CCDF of PAPR: 16-QAM, N fft = 256, N occupied = 64 IFDMA LFDMA Pr(PAPR>PAPR ) α=1 α=.8 α=.6 α=.4 α=.2 α= Solid lines: without pulse shaping Dotted lines: with pulse shaping PAPR [db] Pr(PAPR>PAPR ) α=1 α=.8 α=.6 α=.4 Solid lines: without pulse shaping Dotted lines: with pulse shaping α=.2 α= PAPR [db] Figure 9: Comparison of complementary cumulative distribution function (CCDF) of PAPR for distributed FDMA and localized FDMA with 256 system subcarriers, 64 subcarriers per user and rolloff factor of α {,.2,.4,.6,.8, 1} [1]. All of these results explain why localized FDMA is preferred for the LTE uplink. 5.3 Transmitter Structure a 1 [k] M DFT W A 1 [µ] Subcarrier Mapping K B 1 [ν] N IDFT V H b 1 [κ] CP b c1 [κ] extension P in a 2 [k] M DFT W A 2 [µ] Subcarrier Mapping K B 2 [ν] N IDFT V H b 2 [κ] CP b c2 [κ] extension P in Figure 1: Transmitter structure of LTE uplink [6]. The properties for the transmitter structure depicted in Figure 1 are listed: Single user MIMO transmission with 2 transmit antennas. Data streams are divided into blocks of length M. a i [k]: 4QAM or 16QAM coded complex data symbols.

11 SC-FDMA and LTE Uplink Physical Layer Design 11 The channel matrices that are in the incoming operations are assumed to have MIMO ISI channel characteristics. Block by block explanation of the transmitter: In the first block M-point DFT is applied to the data sequences which can be represented as follows: A i = Wa i where, a i are the time domain modulated data symbols matrices represented as: a i = [a i [] a i [1]... a i [M 1]] T, A i are the matrices consisting of the frequency domain data symbols, and represented as: A i = [A i [] A i [1]... A i [M 1]] T, W is unitary M-point DFT matrix with entries w mn = 1 M exp ( j2πmn ), m,n {, 1, 2,...,M 1}. The subcarrier mapping operation is performed in the second block. M X X X X X 1 X 1 X 2 XN 1 XN 1 XM 1 XM 1 Figure 11: Subcarrier Mapping in Distributed and Localized Mode [1]. Figure 11 is a more mathematical representation of the different subcarrier mapping methods mentioned before. Subcarrier mapping is performed as the second operation following the discrete Fourier transform. At the output of this block, the frequency domain mapped symbols are obtained. From a resource allocation point of view, static and channel-dependent scheduling (CDS) methods are the possible selections. CDS assigns subcarriers to users according to the

12 12 Burcu Hanta channel frequency response of each user. Since the transmitted signal is spread over the entire bandwidth, distributed subcarrier mapping provides frequency diversity. That is the reason for the difference of the effect of CDS on different subcarrier allocation methods. The vector B i in frequency domain is then: B i = [ } {{... } A i [] A i [1]... A i [M 1] } {{... } ] T = KA i with frequency shift ν, ν N M ν the assignment matrix K is: K = ν M I M (N M ν ) M, where I M is M M size identity matrix and a b represents a matrix with a rows, b columns and all zero entries. Third block is an inverse DFT block. N-point inverse DFT is applied to the frequency domain data symbols that are mapped to different subcarriers. In the output of this block, there are the time-domain transmit sequences, b i = V H B i where V is a unitary N-point DFT matrix. The function of the fourth block is cyclic prefix extension of length L c q h, where q h is the channel order. The transmission blocks are: b ci = [b i [N L c ]... b i [N 1] b i [] b i [1]... b i [N 1]] T. Cyclic prefix (CP) is a copy of the last L c symbols of the block of interest which is pasted in front of the block. This operation is illustrated in Figure 12. There are mainly two reasons for CP extension. First, CP works as a guard interval between subsequent blocks, avoiding the ISI due to multipath fading. Therefore, if the length of the CP is longer than the maximum delay spread of the channel, in other words, longer than the channel impulse response, ISI is prevented. In addition the fact that the CP is a copy of the last L c symbols of the block, converts a discrete time linear convolution to a discrete time circular convolution. Thus, the received data can be presented as a result of the circular convolution between the channel impulse response and the transmit data block along with additive white Gaussian Noise (AWGN). In fact, this operation brings us to a one-to-one multiplication of frequency domain data symbols and channel frequency response in the frequency domain. This yields a simple frequency equalization scheme to remove the channel distortion, which is the division of the DFT of the received data by the DFT of the channel impulse response. Therefore frequency domain equalization is possible to be employed here which is simpler to implement.

13 SC-FDMA and LTE Uplink Physical Layer Design 13 copy CP b i b ci Figure 12: Addition of cyclic prefix [6]. 5.4 Receiver Structure In the receiver for the LTE uplink, the received symbols are processed in the reverse manner as in the transmitter. With the effect of the circular convolution between channel impulse response and transmit data symbols, low complexity frequency domain equalization schemes (zero-forcing (ZF) linear equalization or linear minimum-mean-squared error (MMSE) equalization) could be employed after subcarrier demapping. On the other hand, it is possible to employ a time domain equalization scheme (e.g. succesive interference cancellation (SIC)) after the IDFT operation. r c1 [κ]... CP deletion P out r 1 [κ] N DFT V R 1 [ν] Subcarrier Demapping K H Y 1 [µ] y M IDFT 1 [k] W H... r cnr [κ] CP deletion P out r NR [κ] N DFT V R NR [ν] Subcarrier Y NR [µ] Demapping K H M IDFT W H y NR [k] Figure 13: System model of the LTE Base Station [6]. When the system given in Figure 13 is considered, the properties could be listed as follows: N R -fold receive antenna diversity. Received signal at lth antenna is: r cl [κ] = 2 i=1 L 1 λ= h l,i[λ]b ci [κ λ] + n l [κ].

14 14 Burcu Hanta where, h l,i [λ] is the discrete time channel impulse response of length L (channel order q h = L 1) from ith transmit antenna to the lth receive antenna, and n l [κ] is the discrete time AWGN of lth receive antenna. Block by block explanation of the receiver: In the first block, the cyclic prefix is removed as seen in Figure 14. In other words, the first L c values in r cl [κ] are removed, which results in r l [κ] deletion CP r l r cl Figure 14: Deletion of cyclic prefix [6]. After this operation. the following matrix model is obtained: r l = H l,1 b 1 + H l,2 b 2 + n l with the circulant channel matrices: h l,i [] h l,i [q h ] h l,i [q h 1] h l,i [1] h l,i [1] h l,i [] h l,i [q h ] h l,i [2] H l,i = h l,i [q h ] h l,i [2] h l,i [1] h l,i [] Second block is the N-point DFT block. DFT is applied to r l, and the frequency domain representation of the data symbol sequence is obtained. The operation is: R l = V r l = 2 i=1 V H l,iv H B i + N l H l,i is already defined as a circulant matrix, this results in H l,i V H = V H Λ l,i, where Λ l,i = diag{h l,i [],H l,i [1],H l,i [N 1]}. Since the columns of V H are the eigenvectors of H l,i, (V H l,i V H = Λ l,i ), the following equation is obtained: R l = 2 i=1 Λ l,ib i + N l.

15 SC-FDMA and LTE Uplink Physical Layer Design 15 Third block performs the subcarrier demapping operation. At the output of this operation, there are frequency domain symbols which are linearly combined by a DFT operation at the transmitter. However these symbols are distorted due to the overall channel effect. To overcome this effect, as mentioned before, either a frequency domain equalization is applied or the IDFT operation is performed and equalization is applied afterwards in time domain. The operation is as shown with K H as the demapping matrix: Y l = K H R l. In the fourth block, M-point IDFT is applied on demapped symbols as follows: y l = W H Y l The effect of all blocks in SC-FDMA signal generation then can be presented as follows: y l = 2 W H K H V P out H l,i P in V H KWa i + W H K H V P out n l, (2) i=1 where P in and P out are the CP extension and deletion matrices, respectively. 6 Conclusion To sum up the context of this report, the main points of SC-FDMA scheme and LTE uplink physical layer are covered. Some of those main points are: Although the PAPR is higher than in case of distributed FDMA, localized FDMA with a scheduling algorithm (most often CDS) provides higher throughput. Therefore, localized subcarrier assignment has been chosen for the LTE uplink. On the other hand, SC-FDMA provides a lower PAPR and higher system throughput in any case compared to OFDMA. The pulse shaping operation that comes after the CP extension might cause performance degradation if not carefully designed. The design parameter which should be taken into account is the rolloff factor of the pulse shaping filter. High power consumption at the mobile station is avoided by applying equalization at the base station. In other words, with complicated signal processing tools in the receiver (base station), it is possible to produce transmit symbols with low PAPR which helps the transmitter (mobile station) to reduce the power dissipated on the power amplifiers.

16 16 Burcu Hanta References [1] H. G. Myung: Single Carrier Orthogonal Multiple Access Technique for Broadband Wireless Communications, Dissertation, Jan. 27. [2] 3GPP TS V8.3., 28. [3] H. G. Myung: Technical Overview of 3GPP LTE, Internet, May 28. [4] H. G. Myung, J. Lim, D. J. Goodman: Single Carrier FDMA for Uplink Wireless Transmission, IEEE Vehicular Technology Magazine, Sep. 26. [5] S. Sesia, I. Toufik, M. Baker: LTE-The UMTS Long Term Evolution: From Theory to Practice, John Wiley, 29. [6] M. Ruder: Multiuser MIMO Receiver for the Uplink of Long Term Evolution (LTE), Nov. 28.