OFDM Principles and Modulation | Radio Interface Basics

Most recent communication systems like WiFi, WiMAX, and digital audio and video broadcasts make use of OFDM, as in the LTE DL transmission scheme and a slightly modified version in the LTE UL transmission scheme.

OFDM systems have some advantages for mobile wireless transmission as signals are robust against frequency-selective fading. Systems which make use of OFDM have been known since the 1950s and 1960s in military applications. Their realization was expensive as all components and filters were implemented as analog circuits. Nowadays, a wide range of applications profit from the benefits of OFDM systems since digital signal processing has become inexpensive and available in consumer products.

Information is modulated on very small adjacent carriers within the allocated bandwidth (baseband). The intrinsic design of an OFDM system prevents interference among the carriers (also called subcarriers or tones). This is the reason why the subcarriers are orthogonal to each other. Figure 1 shows the basic components needed for OFDM signal generation. The realization of an OFDM signal generator and analyzer is simple to achieve as the main computational functions are transformations between time and frequency spectra which are easy to implement in modern digital signal processing integrated circuits by using the Fast Fourier Transform (FFT) algorithm.

 
Figure 1: Block diagram of OFDM signal generation

The first step in the transmit chain is the serial-to-parallel conversion of the data to be transmitted. This is usually done within the transmit buffer. This binary data is now quadrature amplitude modulated by mapping bits to complex data symbols. The characteristic of complex data symbols is that each symbol describes a two-dimensional vector with a phase and amplitude. A complex data symbol is described with an in-phase and a quadrature component. These symbols are called IQ samples, as the modulated symbols are digitally sampled. It is possible to map a higher number of bits to symbols by using a higher modulation order like 16 or 64QAM resulting in a higher spectral efficiency, which means transmitting more bits per hertz of the utilized bandwidth. A higher spectral efficiency allows greater user and cell data throughput. The number of bits which are carried by the different modulation schemes can be seen in Table 1. Those numbers are OFDM independent and are equal to other transmission schemes.

Table 1: Bits to be carried by the modulation schemes used with LTE 

Modulation scheme	Number of bits which can be carried by one complex symbol
BPSK	1
QPSK	2
16QAM	4
64QAM	6

Mobile cell phone standards which do not use OFDM, like GSM, CDMA2000, or UMTS, modulate the data to complex symbols in the time domain. This means that the resulting sinusoid over time after modulation is the time domain signal of the baseband to be transmitted on the RF carrier frequency. OFDM systems interpret the modulated symbols as modulated frequency tones, which are to be transformed to a signal over time in order to be transmitted. Thus, the modulated symbols are mapped to orthogonal subcarriers (tones) of the baseband spectrum. The transformation to the time domain is done with an n-point inverse Fast Fourier Transform (iFFT). The Fourier transformation adds the orthogonal spectrum of each subcarrier to the resulting baseband spectrum. The spectrum of each subtone is a si(x) function (sin(x)/x), thus the resulting spectrum is an addition of si(x) functions as depicted in Figure 2. The inherent behavior of the Fourier transformation lets each si(x) maximum match zero transitions of all other si(x)functions, resulting in non-interfering subtones since the data was modulated to individual subcarriers (peaks of the si(x) functions). This characteristic is known as orthogonal behavior, which means data is perfectly demodulatable and no guard band between subcarriers is needed, in contrast to FDM, where intercarrier interference needs to be taken care of, for example, with guard bands.

 
Figure 2: OFDM signal of orthogonal Si functions (subcarriers); subcarriers do not interfere because at each subcarrier the signals from other subcarriers are zero

The designated system bandwidth (baseband bandwidth) is divided into m subcarriers which are sampled with an n-point Fourier transformation, where n > m, indicating oversampling. System bandwidth is defined by a number of resource blocks from 6 to 110, each resource block grouping 12 subcarriers. For approximately 20 MHz system bandwidth (100 resource blocks), 1200 subcarriers are defined and a common FFT size is 2048 samples. LTE defines the sampling frequency as f_s = 1/T_s = 30.72 MHz, which leads to a LTE OFDM symbol length of 66.67μs for normal CP (Cyclic Prefix). The CP is 5.2 μs or 160 samples in the first symbol and 4.7 μs or 144 samples in the other symbols for normal CP. The CP lasts 16.7 μs or 512 samples for extended CP. 

OFDM systems show robust characteristics against frequency-selective fading caused by the wireless channel, because fading holes are bigger compared to the subcarrier bandwidth, leading to a flat fading of individual subcarriers which is equalized by interpolating between defined reference symbols (reference subcarriers).

LTE defines a set of reference symbols in order to distinguish between various entities: cell-specific, UE-specific, antenna-port-specific, and MBMS-specific (Multimedia Broadcast/Multicast Service) reference symbols. MBMS data and reference symbols are always transmitted on antenna port 4 if MBMS data transmission is enabled.

In other words, the time domain is just the "transmit domain" for OFDM systems. The resulting time domain signal after transforming the modulated frequency signal representing the data is, so to say, "just noise" and cannot be interpreted without transformation back to the frequency domain. All channel estimation, equalization, and interpretation of the data are done in the frequency domain within OFDM systems.

A timely guard interval or GP between OFDM symbols is needed to prevent intersymbol interference due to channel delay spread (arrival of all reflections). This is realized by copying the end of each OFDM symbol in front of the OFDM samples to be transmitted. This GP, also known as the CP (Cyclic Prefix), decreases alias effects caused by a windowing effect of the Fourier spectrum as the Fourier transformation expects an infinite repeated spectrum, but the OFDM symbol has a time-limited duration. LTE defines two CP lengths, a normal CP and an extended CP, for cells with a larger channel delay spread. Additionally, the CP is used for frame synchronization using an auto/cross-correlation function.

OFDM systems have the drawback of a high dynamic range after transforming the frequency signal to a time domain signal which is amplified and transmitted. This high Peak-to-Average Power Ratio (PAPR) (squared peak signal amplitude to average signal power level) leads to cost-intense RF amplifiers and shorter battery life. This is especially a disadvantage for mobile handset devices; thus, another transmission scheme needs to be found for the UL.

LTE uses Single Carrier Frequency Division Multiple Access (SC-FDMA) or Discrete Fourier Transform (DFT) spread OFDM as the UL transmission scheme to overcome some drawbacks of pure OFDM systems. 

Figure 3 presents an overview of the functional steps needed for physical channel processing.

 
Figure 3: Overview of physical channel processing. Reproduced with permission from © 3GPP™