**Abstract:**

The rapid increasing demand on high data rates in wireless communications systems has arisen in order to support broadband services. The 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) aims at very high peak data rates such as 1 Gbps in local areas and 100 Mbps in wide areas. LTE has adopted Orthogonal Frequency Division Multiple Access (OFDMA) as downlink and Single Carrier Frequency Division Multiple Access (SC-FDMA) as uplink for multiple access schemes. SC-FDMA is a modified form of OFDMA, and also a promising technique for higher data rate communication in future mobile scenario. The SC-FDMA is chosen for uplink in LTE due to its low Peak to Average Power Ratio (PAPR) compared to OFDMA. The high PAPR ratio causes reduction in power efficiency which causes significant burden on portable devices due to fast dry out of batteries. The SC-FDMA is almost similar to that of OFDMA systems in its complexity and it provides same throughput as that of OFDMA. In this project give an overview of SC-FDMA. Also we analyse the effect of two subcarrier mappings used in SC-FDMA i.e. Localised FDMA (LFDMA) and Interleaved FDMA (IFDMA) on PAPR of SC-FDMA and makes a comparison of the two subcarrier mapping techniques.

**Introduction:**

Wireless mobile communications are undergoing rapid progression towards fourth generation (4G). One common design approach in 4G systems is OFDMA. OFDMA is a multicarrier communication technique on the air interface. It is broadly accepted due of its high resistance to frequency selective fading channels. The immunity to multipath fading is basically from the fact that the OFDMA signal in the frequency domain consists of several orthogonal sub-carriers. Even though OFDMA system has many advantages, it has a major drawback: the high value of PAPR of the transmit signal. PAPR is defined as the ratio of the peak power of a transmit signal to the average power of the transmit signal. The lower PAPR is greatly beneficial in the uplink communications where the mobile terminal is the transmitter. Signals with a high PAPR requires highly linear power amplifiers to avoid excessive intermodulation distortion. To achieve this linearity, the amplifiers have to operate with a large backoff from their peak power. The result is low power efficiency (measured by the ratio of transmitted power to dc power dissipated). For fixed applications where the device is connected to the mains this is not a problem, but for small mobile devices running on their own batteries it creates more challenges. Another problem with OFDMA in cellular uplink transmissions derives from the inevitable offset in frequency references among the different terminals that transmit simultaneously. Frequency offset destroys the orthogonality of the transmissions, thus introducing multiple access interference.

To overcome these disadvantages, 3GPP is introduced a modified form of OFDMA for uplink transmissions in the LTE of cellular systems. This modified version of OFDMA, referred as SC-FDMA, is the subject of this paper. SC-FDMA is an extension of single carrier modulation with Frequency Domain Equalization (SC/FDE) to accommodate multiple-user access. As that OFDMA, the SC-FDMA system also uses different orthogonal frequencies or subcarriers to transmit information symbols. But in SC-FDMA the information is transmitted serially not parallel as that of OFDMA. This arrangement reduces considerably the envelope fluctuations in the transmitted waveform. Due to this SC-FDMA signals have low PAPR than OFDMA signals.

**System Configuration of Single Carrier FDMA:**

An SC-FDMA transmitter sending one block of data to a receiver. The input of the transmitter and the output of the receiver are complex modulation symbols. Practical systems dynamically adapt the modulation technique to the channel quality. Generally Binary Phase Shift Keying (BPSK) is used in weak channels and up to 64-level Quadrature Amplitude Modulation (64-QAM) in strong channels. The data block consists of M complex modulation symbols generated at a rate Rsource symbols/second. Figure 2 provides details of the three important elements of transmitter in Figure 1.

The serial to parallel converter convert modulated input bits to parallel. The M-point discrete Fourier transform (DFT) produces M frequency domain symbols that modulate M out of N orthogonal subcarriers spread over a bandwidth W=N.f0 ,where f0 Hz is the subcarrier spacing. The Q denotes bandwidth spreading factor and is given by Q=N/M. The SC-FDMA system can handle Q orthogonal source signals with each occupy a different set of M orthogonal subcarriers. In the notation of Figure 2, xm (m = 0, 1, . . . ,M − 1) represents modulated source symbols and Xk (k = 0, 1, . . . , M − 1) represents M samples of the DFT of modulated source symbols, xm. Yl (l = 0, 1, . . . , N − 1) denotes the frequency domain samples after subcarrier mapping and yn (n = 0, 1, . . . , N − 1) represents the transmitted time domain channel symbols obtained from taking the Inverse DFT (IDFT) of Yl.

Generation of SC-FDMA transmit symbols; there are N subcarriers among which M (< N) subcarriers are occupied by the input data.

The subcarrier mapping block assigns frequency domain modulation symbols to subcarriers. The mapping is sometimes called as scheduling. After subcarrier mapping the N point IDFT creates a time domain representation, yn, of the N subcarrier symbols. The parallel-to-serial converter places y0, y1, . . . , yN − 1 in a time sequence suitable for modulating a radio frequency carrier and then transmitted.

The transmitter performs two more signal processing operations before signal is transmitted. First it inserts a set of symbols referred to as Cyclic Prefix (CP) in order to provide a guard time so as to prevent Inter-Block Interference (IBI) caused due to multipath propagation in cellular systems. The cyclic prefix is a copy of the information at the last part of the block which is inserted at the start of each block. The CP acts as a guard time between successive blocks. If the length of the CP is longer than the maximum delay spread of the channel, or roughly, the length of the channel impulse response, then, there is no IBI. Generally length of cyclic prefix is taken as twice or four times as that of delay spread. The transmitter also performs a linear filtering operation referred to as pulse shaping in order to reduce out-of-band signal energy.

Block diagram of SC-FDMA is similar to that of OFDMA but has an additional DFT at the input of the transmitter and a corresponding IDFT at the output of the receiver. Due to the fact that SC-FDMA transmitter expands the signal bandwidth to cover the bandwidth of the channel, SC-FDMA is generally called as DFT-spread OFDMA. Several approaches to mapping transmission symbols Xk to SC-FDMA subcarriers are currently under consideration.

**Subcarrier Mapping:**

Subcarrier mapping is the processing of mapping DFT of data symbols to a subset of subcarriers. The subcarrier mapping assigns DFT output complex values as the amplitudes of some of the selected subcarriers. Several approaches to map transmission symbols Xk to SC-FDMA subcarriers are currently under consideration. The subcarrier mapping is divided into two categories; distributed mapping and localized mapping.

**1. Distributed Mapping (DFDMA):**

In the distributed subcarrier mapping mode, DFT outputs of the input data are allocated over the entire bandwidth with zeros occupying the unused subcarriers resulting in a non-continuous comb-shaped spectrum. The case of N = Q×M for the distributed mode with equidistance between occupied subcarriers is called Interleaved FDMA (IFDMA). IFDMA is a special case of DFDMA and it is very efficient in that the transmitter can modulate the signal strictly in the time domain without the use of DFT and IDFT.

**2. Localized Mapping:**

The DFT outputs of the input data occupy consecutive subcarriers in the localized subcarrier mapping mode. We will refer to the localized subcarrier mapping mode of SC-FDMA as Localized FDMA (LFDMA).The data in the localized subcarrier mapping mode results in a continuous spectrum that occupies a fraction of the total available bandwidth.

**PAPR analysis of SC-FDMA:**

In this section, we analyze the PAPR of the SC-FDMA signal. We assume that the total number of subcarriers is N = Q * M, where M is the number of data blocks. The integer Q is the maximum number of terminals that can transmit simultaneously or simply called as bandwidth spreading factor. For distributed subcarrier mapping, we consider the case of IFDMA with subcarriers equally spaced over the system bandwidth.

The PAPR is defined as the ratio of peak power to average power of the transmitted signal in a given transmission block. PAPR is generally represented in dB.

After calculating PAPR for each block, we present the data as a CDF (Cumulative Distribution Function). The CDF is the probability that PAPR is higher than a certain PAPR value PAPR0 (Pr{PAPR > PAPR0}).

**Simulation Results:**

To evaluate the PAPR of SC-FDMA we take 256 (N) subcarriers and data block size of 64 (M). The modulation scheme used is 16 QAM which is one of the most commonly used modulation systems in SC-FDMA. The bandwidth spreading factor (Q) is taken as 4 bits since 16 QAM is used. We take the probability that PAPR exceeds a certain threshold value PAPR0. We observe the PAPR0 value that is exceeded with probability less than 0.1% (Pr{PAPR > PAPR0} = 10-3), or 99.9 percentile PAPR.

The figure 5 shows the CDF plots of LFDMA, IFDMA and OFDMA. From the graph it is clear that the PAPR of OFDMA is higher than that of the two SC-FDMA techniques. We observe that the PAPR of LFDMA is 2dB lower than the PAPR of OFDMA or in other words the PAPR of LFDMA is 30% lower than PAPR of OFDMA. The PAPR of IFDMA is 5dB lower than the PAPR of IFDMA or in percentage case we got a reduction of 67% in PAPR in case of IFDMA compared to IFDMA. The PAPR of IFDMA is 7dB lower than PAPR of OFDMA and it have the lowest PAPR value among the three methods.

**Conclusion:**

SC-FDMA is a promising technique for high data rate uplink communication in future cellular systems. There are many operational and design choices which affects the performance of SC-FDMA within a specific system configuration. In this paper, we mainly focused on the effects of subcarrier mapping on PAPR in SC-FDMA. Results show that in comparison with OFDMA the SC-FDMA has lower PAPR value for same system configurations. Among SC-FDMA techniques, IFDMA has the lowest PAPR compared to OFDMA, than LFDMA. The results indicate that SC-FDMA is more economic and useful in the LTE uplink schemes than OFDMA due to its low PAPR.

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