2.2 Orthogonal Frequency Division Multiplexing

Figure 2.1-4. Reference subcarrier smoothing in the frequency domain (36.104 [2] Figure E.6-1) At the channel edges the width of the moving average gradually decreases until at the outermost reference subcarriers there is no averaging. The effect this has on the equalizer performance is that in the middle of the signal where it is expected to be flat there is the least amount of correction whereas at the channel edge where filter rolloff is expected, the equalizer can do the most correction. The only downside of shortening the moving average window is that the equalization at the outermost subcarriers is more susceptible to noise. There is an EVM window length requirement for the downlink similar to that described in Section 2.1.5.1 for the uplink. 2.2 Orthogonal Frequency Division Multiplexing Orthogonal Frequency Division Multiplexing (OFDM) is the modulation scheme chosen for the LTE downlink. It is a digital multi-carrier scheme that uses a large number of closely-spaced subcarriers to carry data and control information. Each individual subcarrier is modulated at a low symbol rate with a conventional modulation format such as Quadrature Amplitude Modulation (QAM). The combination of the many low-rate subcarriers provides overall data rates similar to conventional single-carrier modulation schemes using the same bandwidth. Today, OFDM is widely used in applications from digital television and audio broadcasting to wireless networking and wired broadband internet access. 29

2.2.1 History of OFDM OFDM was proposed as a mathematical possibility as far back as 1957 with Kineplex, a multi-carrier High Frequency (HF) modem designed by Mosier and Clabaugh, although the first patented application was not until 1966 when Chang of Bell Labs filed US patent 3488445. The first practical implementation of an OFDM system came in 1985 when Telebit introduced the Trailblazer range of modems that reached speeds of 9600 bps. This highlighted one of the key advantages of OFDM: its ability to perform well through a low quality channel in this case telephone lines thereby outperforming existing solutions. From this early beginning, OFDM has become the technology that now delivers up to 10 Mbps over Digital Subscriber Lines (DSL). It is also used in systems that communicate over domestic power lines. The 1980s and early 1990s saw a number of experimental broadcast systems, with companies including Thomson- CSF and TDF in France and BBC Research in the UK. The first international standard to specify OFDM was Digital Audio Broadcast (DAB) in 1995, the outcome of the European Eureka147 project, and this was followed two years later by the Digital Video Broadcast-Terrestrial (DVB-T) standard. Both DAB and DVB-T are now in widespread use. In addition to the use of OFDM in unidirectional broadcast technologies, parallel work throughout the 1990s led in 1999 to the first OFDM-based Wireless LAN (WLAN) standard, IEEE 802.11a. This was followed in succession by 802.11g, 802.11n (adding MIMO) and 802.16d (fixed WiMAX ), although the most widely deployed WLAN standard is still 802.11b, which uses direct sequence spread spectrum. The use of OFDM for cellular systems was first briefly considered back in the late 1980s as a candidate technology for GSM, but was quickly dropped due to lack of cost-effective computing power. A decade later, OFDM was seriously considered as one of the candidates for 3GPP s UMTS but was ruled out in favor of Wideband Code Division Multiple Access (W-CDMA). Again the decision was influenced by the cost of computing power and the associated power consumption in the terminals. However, with today s availability of small, low-cost, low-power chipsets, OFDM has become the technology of choice for the next generation of cellular wireless. The first cellular system to adopt OFDM was 802.16e (Mobile WiMAX ). It was followed soon after by 802.20, the basis for 3GPP2 s Ultra-Mobile Broadband (UMB), and most recently by 3GPP for the long-term evolution of UMTS. It now seems apparent that the evolution of these newest so-called 3.9G systems towards 4G will not result in any change to the underlying air interface, so OFDM will likely be the technology of choice for cellular wireless systems well into the future. The new OFDM cellular systems all focus on delivering high-speed data services and have similar goals in terms of improving spectral efficiency, with the widest bandwidth systems providing the highest single-user data rates. 2.2.1 OFDM Basic Signal Construction 30 The basic OFDM signal comprises a large number of closely spaced Continuous Wave (CW) tones in the frequency domain. The most basic form of modulation applied to the subcarriers is square wave phase modulation, which produces a frequency spectrum represented by a sinc or subcarrier frequency. A truncated sinc function is shown in Figure 2.2-1. ( ) function that has been convolved around the

Figure 2.2-1. Spectrum of a single modulated OFDM subcarrier (truncated) The rate of change of the phase modulation will determine the position of the zero crossings in frequency. The trick that makes OFDM a practical transmission system is to link the subcarrier modulation rate to the subcarrier spacing such that the nulls in the spectrum of one subcarrier line up with the peaks of the adjacent subcarriers. For standard LTE each modulating symbol lasts 66.7 µs. By setting the subcarrier spacing to be 15 khz, which is the reciprocal of the symbol rate, the peaks and nulls line up perfectly such that at any subcarrier frequency, the subcarriers are orthogonal; i.e., there is no interference between them. This can be seen in Figure 2.2-2. Figure 2.2-2. Spectrum of multiple OFDM subcarriers of constant amplitude In Figure 2.2-2 each subcarrier has the same magnitude, which is the case when any of the LTE-supported constant amplitude modulation formats are used: Zadoff-Chu sequences, Binary Phase-Shift Keying (BPSK) and Quadrature Phase-Shift Keying (QPSK). It is also possible for the subcarriers to vary in amplitude since LTE also supports 16 Quadrature Amplitude Modulation (16QAM) and 64 Quadrature Amplitude Modulation (64QAM). Compared to the 3.84 Msps of UMTS, the 15 ksps subcarrier symbol rate of LTE is very low, but in the same 5 MHz channel bandwidth, LTE can simultaneously transmit 300 subcarriers to provide an aggregate 4.5 Msps rate. Thus on first inspection, CDMA and OFDM have similar capacity for carrying data. 31

2.2.2 Guard Intervals and Immunity From Delay Spread In 1971 Weinstein and Ebert proposed the introduction of a guard interval between each symbol to reduce the Inter-Symbol Interference (ISI) caused by delay spread in the transmission channel. To illustrate the principle of ISI, consider the simple five-tap delay profile in Figure 2.2-3. This shows the amplitude and phase response of delayed copies of the transmitted signal, which arrive at the receiver having taken different paths through the transmission channel. By definition, the first detected path is assigned a relative amplitude of 1 and phase of 0 degrees. The X-axis is given in units of symbol length, so for this example the difference between the earliest and latest components known as the delay spread is 15% of the symbol length. Figure 2.2-3. Amplitude and phase response for a five-tap channel delay profile Figure 2.2-4 shows the effect of passing one subcarrier of an OFDM signal through this channel and how the delay spread creates ISI at the symbol boundaries. The ideal received signal is shown in the top trace of Figure 2.2-4. This signal represents two adjacent BPSK symbols with a 180 degree phase shift between them. The number of baseband cycles per symbol is shown as five, indicating that this is the fifth subcarrier on either side of the channel center frequency. The next four traces show the amplitude, phase and timing of the delayed copies of the ideal signal at the receiver. The bottom trace represents the composite received signal, being the sum of the five components. In order to show the extent of the delay spread, the dotted line in the bottom trace is a copy of the ideal signal. From this it is very evident that during the period from 1.05 to 1.2, the received signal is severely distorted and of negative value to the demodulation process. The received signal is undistorted only after the last component has arrived and before the first component leaves. For this delay profile the undistorted symbol is reduced to 85% of its transmitted length. 32

CHAPTER 2 Air Interface Concepts Figure 2.2-4. Inter-symbol interference caused by delay spread In order to optimize demodulation performance and reject Inter-Carrier Interference (ICI), the symbol must be sampled for exactly its nominal length. At baseband, each successive subcarrier has one more cycle during the OFDM symbol period. When error energy from an adjacent subcarrier is added to the wanted subcarrier, the only time period for which the signals are orthogonal (multiply and integrate to zero) is at the reciprocal of the subcarrier spacing. 33

The CP adds redundancy through repetition of the signal rather than by adding any new information. When the CP is added, it guarantees that the symbol will be undistorted for at least its nominal symbol length in the presence of multipath up to the length of the CP. By correctly aligning with the signal timing, the receiver is then able to sample the signal for exactly one nominal symbol period. This allows the receiver to avoid the frequency domain ICI while at the same time avoiding all the time domain ISI due to multipath. For the example channel in Figure 2.2-3, the CP would have to be at least 15% of the symbol length. The choice of CP in cellular systems depends on the propagation conditions and cell size. Typical figures are in the region of 5 µs, which represents 1.5 km of path delay difference. Note that this delay spread is the difference in path length and not the absolute path length. For LTE, the standard CP is set to 4.69 µs creating an extended symbol of some 71.35 µs. An obvious consequence of adding redundancy to the symbol is a loss in capacity due to a lower symbol rate, in this case a reduction of about 7%. Thus there is a tradeoff between the amount of protection from delay spread and the consequent loss of capacity. It is interesting to contrast the way OFDM and CDMA deal with multipath distortion. The symbol length in CDMA systems is the reciprocal of the chip rate. All lower-rate data is spread (multiplied) up to this fixed system chip rate by use of spreading codes. For UMTS, which uses the 3.84 Mcps W-CDMA air interface, this spreading results in a symbol length of 260 ns and a 3 db bandwidth prior to filtering of 3.84 MHz. A 5 µs delay spread on this system would create serious ISI extending to around 20 CDMA symbols. Since the delay spread would be nearly 20 times the symbol length, it is impractical to consider extending the symbol with a CP in the way described for OFDM. This is why CDMA systems have to rely on rake receivers and frequency-domain equalizers to untangle the ISI. In CDMA systems, the wider the channel bandwidth, the higher the chip rate and the worse the ISI becomes. This is why it is impractical to design CDMA systems with channel bandwidths much wider than the 5 MHz of today s UMTS. This situation is in sharp contrast to OFDM, whose symbol length is set not by the reciprocal of the channel bandwidth but rather by the subcarrier spacing. This makes OFDM systems highly scalable in the frequency domain with no impact on the symbol length. The 15 khz subcarrier spacing in LTE provides a symbol length that is 256 times longer than is used for W-CDMA, and the sheer length of the OFDM symbol makes it feasible to extend the symbol by 4.69 µs with a loss of only 7% in system capacity. It is reasonable to ask why OFDM does not continue to make the symbols even longer by using ever-narrower subcarrier spacing. However, there are practical considerations which limit how close the subcarriers can become. The first factor is phase noise, which causes the energy of each subcarrier to leak into the adjacent subcarriers causing ICI. The second factor is the consequence of frequency errors between the transmitter and receiver, which can shift energy sideways in the frequency domain also causing ICI. Simple frequency errors due to Doppler shift or other single-sided errors can be corrected using normal closed loop frequency tracking methods. Even then, the closer the subcarrier spacing, the better these tracking loops have to perform. 34 There is, however, a double-sided frequency error that can occur if the UE simultaneously receives downlink signals from behind and in front as a result of reflections. If the UE is moving towards or away from the reflector, one signal could be reduced in frequency while the other is increased. This creates a symmetrical image in the

frequency domain that cannot be removed using a simple frequency tracking loop. This kind of ICI is possible to remove using digital techniques but the process can require huge amounts of computing power if the ICI becomes significant. This and the earlier reasons are why practical subcarrier spacing in OFDM systems do not get much lower than the 7.5 khz defined for LTE s optional Multimedia Broadcast over Single Frequency Network (MBSFN) service. 2.2.3 Example of OFDM Signal Generation Figure 2.2-5 illustrates the principles of OFDM signal generation using a simple four subcarrier example. Figure 2.2-5. Example of OFDM signal generation using four subcarriers Since four subcarriers are used in this example, it will be possible to transmit four data symbols in parallel. The four possible data symbols are represented by phases of the subcarrier, which in the IQ plane are represented as (1, 1), ( 1, 1), ( 1, 1) and (1, 1). One of these symbols will be mapped to each subcarrier for the duration of an OFDM symbol. The four possible subcarrier phases are shown. Each subcarrier is defined in the frequency domain by a vector, which represents the amplitude and phase of the data symbol that has been mapped to it. After symbol mapping, the subcarriers are each converted to time domain waveforms using an Inverse Fast Fourier Transform (IFFT). At this point the CP is inserted for each waveform and then the waveforms are vector summed to produce the composite waveform for transmission. The lower trace in Figure 2.2-5 shows the composite waveform (without the CP, for simplicity) resulting from the parallel transmission of the four symbols shown. Due to the summation of the four waveforms, the peak of the signal now reaches nearly four times the voltage of one subcarrier. With increasing numbers of subcarriers 35

the I and Q waveforms that represent the composite signal become Gaussian, which creates a chi-square power distribution. This simple example illustrates one of the key disadvantages of OFDM, which is that the Peak to Average Power Ratio (PAPR) of the composite signal can have peaks exceeding 12 db above the average signal power, which presents significant challenges for transmission by an enb operating at high power. There are many steps that can be taken to reduce the signal peaks and to extend the useful operating range of the power amplifier. These are discussed further in Section 6.4.1.4. 2.2.4 Comparing CDMA and OFDM The attributes of CDMA technology upon which UMTS is based and the corresponding attributes of OFDM are summarized in Table 2.2-1. Table 2.2-1. Comparison of CDMA and OFDM Attribute CDMA OFDM Transmission bandwidth Full system bandwidth Variable up to full system bandwidth Frequency-selective scheduling Symbol period Equalization Resistance to multipath Suitability for MIMO Sensitivity to frequency domain distortion and interference Separation of users Not possible Very short inverse of the system bandwidth Difficult above 5 MHz Difficult above 5 MHz Requires significant computing power due to signal being defined in the time domain Averaged across the channel by the spreading process Scrambling and orthogonal spreading codes A key advantage of OFDM although it requires accurate real-time feedback of channel conditions from receiver to transmitter Very long defined by subcarrier spacing and independent of system bandwidth Easy for any bandwidth due to signal representation in the frequency domain Completely free of multipath distortion up to the CP length Ideal for MIMO due to signal representation in the frequency domain and possibility of narrowband allocation to follow real-time variations in the channel Vulnerable to narrow-band distortion and interference Frequency and time although scrambling and spreading can be added as well The commercial use of OFDM until now has been primarily for broadcast and wired applications in which interference has not been a major factor. OFDM is used in some of the WLAN protocols, which are typically found in hotspot deployments; however, to date there are no large-scale deployments of cellular systems based on OFDM. The first such systems are likely to be based on the 802.16e standard. Cellular systems are different from broadcast and hotspot systems in that they have to operate seamlessly across a wide area, including the area around the cell boundaries where signal levels are at their lowest and inter-cell interference is at its highest. 36

It is expected that OFDM will be more difficult to operate than CDMA at the cell edge. CDMA relies on scrambling codes to provide protection from inter-cell interference at the cell edge, whereas OFDM has no such intrinsic feature. In addition, the interference profile at the cell edge for CDMA is relatively stable across frequency and can be modeled and removed using interference cancelling receivers. The situation for OFDM is more complex because the presence or absence of interference is a function of narrow-band scheduling in the adjacent cell, and the resulting noise profile is likely to be far less stable and predictable. One solution to this is to use some form of frequency planning at the cell edge. Figure 2.2-6 gives one example of how this might be done. The white central area of the cell is where the entire channel bandwidth would get used and the colored areas show a frequency reuse pattern with a repetition factor of four. Figure 2.2-6. Example of cell-edge frequency planning to mitigate inter-cell interference This approach can significantly reduce cell-edge interference, although it remains a challenge to know the location of the UE for scheduling purposes. Moreover, such a re-use scheme has a direct impact on cell edge capacity, in this case reducing it by a factor of four. Operating OFDM efficiently at the cell edge is likely to require significant network optimization after initial deployment. 2.2.5 Orthogonal Frequency Division Multiple Access Until now the discussion has been about OFDM, but LTE uses a variant of OFDM for the downlink called Orthogonal Frequency Division Multiple Access (OFDMA). Figure 2.2-7 compares OFDM and OFDMA. 37

Figure 2.2-7. OFDM and OFDMA subcarrier allocation With standard OFDM the subcarrier allocations are fixed for each user and performance can suffer from narrowband fading and interference. OFDMA incorporates elements of Time Division Multiple Access (TDMA) so that the subcarriers can be allocated dynamically among the different users of the channel. The result is a more robust system with increased capacity. The capacity comes from the trunking efficiency gained by multiplexing low rate users onto a wider channel to provide dynamic capacity when needed, and the robustness comes from the ability to schedule users by frequency to avoid narrowband interference and multipath fading. 2.3 Single-Carrier Frequency Division Multiple Access The high Peak-to-Average Power Ratio (PAPR) associated with OFDM led 3GPP to look for a different modulation scheme for the LTE uplink. SC-FDMA was chosen since it combines the low PAPR techniques of single-carrier transmission systems, such as GSM and CDMA, with the multipath resistance and flexible frequency allocation of OFDMA. A mathematical description of an SC-FDMA symbol in the time domain is given in 36.211 [6] sub-clause 5.6. A brief description is as follows: data symbols in the time domain are converted to the frequency domain using a Discrete Fourier Transform (DFT); once in the frequency domain they are mapped to the desired location in the overall channel bandwidth before being converted back to the time domain using an Inverse FFT (IFFT). Finally, the CP is inserted. SC-FDMA is sometimes called Discrete Fourier Transform Spread OFDM (DFT-S-OFDM) because of this process, although this terminology is becoming less common. 38