# OFDM in LTE

|**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).

**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.

**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.

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.

*N*subcarriers,

*N*set of parallel data streams are created. Each set contains a subset of parallel data streams, depending on the type of modulation.

**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:

*, in the same way of the complete modulated signal. As all the carriers are cyclic in*

**T**_{symb}*T*, 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.

_{symb}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

*T*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.

_{symb}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 *T _{symb}* 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:

# 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:

**COFDM**modulator (recall that letter “C” means that channel codification was applied, before the IFFT).

**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.

*, the expression for an OFDM symbol is:*

**N**_{CP }**transmitted signal**is:

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

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