OFDM in LTE

On January 2014, more than 200 million of users demanded mobile communications services based on the 4G technology LTE (Long Term Evolution). This standard improves the performance of predecessor wireless systems by optimizing spectral efficiency and managing the challenges of hostile wireless channels. The principal requirements for this high demand are a faster network and robustness.
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These requirements are covered by using OFDM (Orthogonal Frequency Division Multiplexing), MIMO (Multiple-Input, Multiple-Output) and multi-level modulation schemes. OFDM is suitable for the enhancement of data-rates and capacity which compiles the increasing demand of mobile services around the world. In addition, it is well known that OFDM offers a high performance in multipath environments that characterize the mobile wireless systems. In fact, OFDM was the key technology of other standards like DBV-T; this system transmits audio, video and information data through a MPEG-2 stream by using COFDM (Coded OFDM).
LTE or 4G provides a series of improvements over UMTS (Universal Mobile Telecommunications System) and it is introduced from 3GPP (3rd Generation Partnership Project). Final users will find data-rates up to 150 Mbps in downlink and 50 Mbps in uplink and lower latencies (about 10-20 ms) which improves notably the user experience for all kind of services. In addition, LTE is based on open and global standards which promote compatibility and low costs; final users and operators will take advantage from this fact. Finally, there are huge advances in energetic efficiency for the user equipment batteries last longer.
LTE allows operators offering services through an extreme-to-extreme IP network in an efficient manner, low cost and easy convergence between mobile and fixed phones. More advantages of LTE are the reduced number of nodes in the network and a more automatic and easier operation and maintenance.
As it was mentioned earlier, LTE uses OFDMA (Orthogonal Frequency Division Multiple Access) in the radio interface, which works with a large number of orthogonal sub-carriers very close between them. LTE performs in the frequency ranges from 1,4 MHz to 20 MHz and supports MIMO  antennas which allow to increase the data-rate and coverage. In this way, it can obtain bigger bandwidths and more spectral efficiency and flexibility over different frequency bands than predecessor technologies.
OFDM by itself it is not a modulation technique, though often is referred as such. Actually, it is a multicarrier transmission technique which allows the transmission of data on multiple adjacent subcarriers, each subcarrier being modulated in a traditional manner with a linear modulation scheme such as QAM or QPSK. In the LTE system, it is employed after modulation and channel codification, and this is the reason why it is called COFDM.
In an OFDM system, data for transmission is converted into several parallel streams and each stream is used to modulate a separate subcarrier. Thus, only a small amount of the total data is sent via each subcarrier, in a subchannel (a fraction of the bandwidth of the total channel). It is a limited data rate per subcarrier that gives OFDM its superior performance in a NLOS multipath environment in comparison with the single carrier transmission.
With OFDM, subcarriers are cleverly allocated close to each other. This results in overlapping the spectrum and it eliminates the spectral utilization drawback of standard FDM without introducing inter-channel interference. OFDM achieves this compacting property, without introducing interference, by making subcarriers orthogonal to each other.
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Orthogonality is accomplished by placing each subcarrier frequency into an integer multiple of the symbol rate of the modulating symbols, and each subcarrier is separated from nearest neighbour(s) by the symbol rate.
To avoid the construction of a large number of subchannel modulators and demodulators, OFDM systems utilize Digital Signal Processing (DSP) devices. Directly as a result of the orthogonality of the OFDM signal structure, modulation can be implemented by using the inverse discrete Fourier transform (IDFT). Similarly, demodulation can be performed by using the discrete Fourier transform (DFT). The Fourier transform allows events in the time domain to be related to events in the frequency domain, and vice versa for the Inverse Fourier transform and Conventional Fourier transform, both two based on continuous signals. However, DFT/IDFT is based on signal samples.
In fact, a rapid computational version of DFT/IDFT, namely the fast Fourier transform (FFT) and its inverse (IFFT) is normally used on OFDM implementations.
In an IFFT processor, a signal defined in the frequency domain as a complex number representation, is converted to time domain samples. Inversely, in an FFT processor, a signal defined in the time domain as samples is converted into a signal in the frequency domain.
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Incoming serial data are first converted from serial to parallel. If there are subcarriers, set of parallel data streams are created. Each set contains a subset of parallel data streams, depending on the type of modulation.
OFDM is the basis of the multi-access technique called orthogonal frequency division multiple access (OFDMA). With OFDMA, subcarriers are always divided into subchannels and that implies subcarriers in each subchannel are spread over the full channel spectrum to minimize multipath fading effects. OFDMA can be used as a DL access scheme, with the MAC layer assigning subchannels to the DL data destined to the various UEs. Recall that LTE uses OFDMA in the DL. OFDMA can also be used as an uplink access scheme, where specific subchannels are assigned to specific UEs via MAC messages sent on DLs. With UL OFDMA, several UE transmitters can transmit simultaneously since each transmits different subchannels and hence subcarriers. However, in order to reduce the UEs power, and to save battery, LTE specifies to use SC-FDMA in the UL.
Carriers are modulated by signals represented as complex numbers which change between symbols. The integration period in the receiver extends to the duration of two symbols, because, as in the case of delayed signals, there will be not only ISI (inter-symbol interference) over the subcarrier correspondent to the symbol which is supposed to integrate, but also there will be ICI (inter-carrier interference) and, therefore, the information will be disturbed. To avoid these effects, a guard interval is added as it is shown in the next figure:

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The duration of the symbol increases until exceeding the integration period at the receiver, Tsymb, in the same way of the complete modulated signal. As all the carriers are cyclic in Tsymb, the complete modulated signal is cyclic too. Therefore, the added segment at the starting symbol to form a guard interval has the same length than the segment added at the end of the symbol. As the delay in the signal due to any path, in comparison to the minimum path, will be smaller than the guard interval, all the components of the signal during an integration period belong to the same symbol, and in this way, it is satisfied the orthogonally condition. The inter-symbol or inter-carrier interference will occur only when the delay exceeds the duration of the guard interval.
As it can be inferred, the guard interval extends the duration of the transmitted symbol and, hence, it reduces the effective data-rate slightly. However, the greater guard interval, the smaller interference due to multipath effects.
Guard interval is selected according to the expected delay in a particular channel. For example, in environments similar to great building’s indoors, the fading could be up to some dozens of nanoseconds while in outdoor environments, in which the distances are greater, it could be about 50 µs or more. As the insertion of the guard interval reduces the effective binary rate, it doesn’t have to consume an important fraction of the symbol duration Tsymb in order to maintain an adequate bit-rate and spectral efficiency. During the guard interval period, the receiver ignores (by removing it) the received signal.

Orthogonality is achieved in the receiver by integrating the demodulated signal over the useful period of symbol. For echoes which duration is smaller to the guard interval, the receiver can find an interval of duration Tsymb in which there won’t be transitions in the symbol.
In addition to the multipath effects which are difficult to control, there are other facts that cause loosing of orthogonality and inter-carrier interference. The main causes are the frequency or phase deviations in the receiver local oscillator, noise-phase on it, and variations in the sample frequency. These effects can be controlled by a suitable design like the one we have analysed in the transmitter and receiver blocks for LTE.

Channel synchronization

As mentioned above, for a correct demodulation, the receiver has to take samples during the useful period of OFDM symbol, but not during the guard interval. Therefore, the time window has to be placed in the instant in which each symbol appears. This is equivalent, in the analogic case, to the coherent demodulation in the receiver in which is absolutely necessary that the locally generated carrier has the same frequency and phase of the generated carrier by the transmitter. In LTE, this problem is solved by using pilot subcarriers which are regularly distributed in the symbols and they act as a synchronism performer:

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As the information in the pilot subcarriers is known, it is possible to make an estimation of the frequency response at the receiver. The estimation for a given subcarrier can be interpolated for completing the gaps which separate different pilots, and it can be used for equalization in the entire constellation which transports data.

OFDM Modulator and Demodulator

In an OFDM modulator, the input signal is a binary continuous stream. This stream is segmented in symbols according to the constellation used, and a map of symbols is obtained which is represented by complex numbers which correspond to the signal in the frequency domain. Let be N subcarriers to modulate at the same time, then the first operation is to convert the series input stream into a parallel stream of complex coefficients. The next step is applying the inverse Fourier transform over those N coefficients to obtain a signal in the time domain and, as the input signal in the channel has to be a series stream, converting again the signal, in this case, into a series stream. This is the transmitted signal and this process is shown in the next block diagram:

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In the previous image, as the input signal comes from the channel coder, the whole scheme represents a COFDM modulator (recall that letter “C” means that channel codification was applied, before the IFFT).
Note that, at the output of the parallel to series converter, the guard interval is inserted, also known as the cyclic prefix in which the symbols are copied from the end of the stream and pasted at the beginning. That makes delayed signals due to multipath effects be inside the guard interval and the receiver ignore them.

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Therefore, if the length of the cyclic prefix is NCP , the expression for an OFDM symbol is:

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The entire transmitted signal is:

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The demodulator performs the inverse function of the modulator and the simplified block diagram is:

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We hope this was useful. If you would like to know more about OFDM, comment or contact us and we will do our best to post more info!
 
Also, have a look to this post to get a LTE Simulink model and play with it! 😀

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