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The Single Carrier Orthogonal Frequency Division Multiple Access is used for LTE uplink. OFDMA suffered from the high peak to average power ration of the transmitted signal, makes it not suitable for the LTE uplink that's why there was a need for adopting a new LTE air interface scheme for the uplink and the choice was SC-FDMA , since it has the advantage of OFDMA frequency allocation flexibility as well as low Peak to Average power Ratio (PAPR) techniques . Another reason of adopting SC-FDMA for uplink is that the OFDMA has a disadvantage when it comes to frequency offset, because if there is a small frequency offset when multiple transmissions from different mobile stations occurring at the same time that can corrupt the orthogonality of OFDMA subcarriers .
By transmitting symbols sequentially, SC-FDMA can reduce the Peak to Average Power Ration (PAPR) by spreading a symbol power over the subcarriers. It also provides scheduling where adjacent subcarriers are assigned to a user. This enable the mobile station to be more resistant to frequency offset .
3.2.2 SC-FDMA vs. OFDMA
The diagram below is illustrating the main differences of operation between SC-FDMA and OFDMA. In the diagram SC-FDMA and OFDMA are transmitting a series of QPSK data symbols.
SC-FDMA is transmitting four QPSK data symbols in series with each symbol occupying 15 KHz for 4 subcarriers bandwidth, it can be seen that each data is shown by one wide signal so it is single carrier, while OFDMA is transmitting four QPSK data symbols in parallel one per subcarrier. So it is multi carrier with one data symbol per subcarrier .
The parallel transmission of multiple symbols in OFDMA and the QPSK narrowband waveform cause the undesirable high peak to average power ration (PAPR). In SC-FDMA although the occupied bandwidth is same as OFDMA, but the (PAPR) resembles the one used for the original data symbols . So we do not get that high (PAPR) which can add to the complexity of ADC and DAC as well as decrease the efficiency of radio frequency power amplifier.
SC-FDMA Signal Generation
SC-OFDMA is used for the LTE uplink. The block diagram in Fig. 3.8 is illustrating the process of signal generation and the process transmission and reception of data between User Equipment (UE)/ mobile equipment and eNB (Evolved Node B / base station). According to [Agilent, 2009] the process is explained as follow:
In the modulation symbol mapping the SC-OFDMA transmitter converts the input signal to a sequence of modulated sub-carriers. The generation of the SC-FDMA signal starts with a unique pre-coding process to produce a waveform of the QPSK data sub-symbols in time domain as illustrated in Figure. 3.7 Below.
Then these symbols are converted to be represented in the frequency domain by applying the DFT (Discrete Fourier Transform).
Then the DFT output of the data symbols are passed through the subcarriers mapping process where these data symbols are mapped to subcarriers. Subcarriers mapping assigns these data symbols values to the amplitudes of selected subcarriers.
Then applying IDFT to converts the subcarrier amplitudes back to the time domain.
Cyclic prefix (CP) is inserted to provide a guard interval to eliminate inter-symbol interference (ISI). Then the data stream is digitized, filtered and applied on the radio frequency to be transmitted
MIMO is an abbreviation that stands for Multiple Input Multiple Output. It is a multiple antenna technology that introduced in LTE to realise a higher data rate and enhance channel capacity. MIMO enhance the spectral capacity by transmitting two or more data streams in the same frequency and at the same time (simultaneously). Transmitted signals are prone to many reflections, for example, these signals can bounce off buildings, cars, trees, etc. the reflected signals proceed to the receiver in different direction and arrive to the receiver at different times. MIMO uses multiple antennas at the transmitter and the receiver with the aid of certain algorithm and signal processing it combines these signals and create one signal that has all the transmitted data. So that taking advantage of the different paths the signal takes, hence improving the performance. Multiple coherent radios for uplink and downlink, and antenna are used to transmit the multiple data streams .
3.2.5 MIMO Mechanism
The key technology features that MIMO uses to provide improved system efficiency and high data rate are explained below:
Diversity Gain: Diversity gain reduces the error probability due to multiple-paths occurred between the transmitter and receiver . So it increases the power of the received signal and reduces the fading by using multiple antennas at both ends (transmitter & receiver). So that results in an enhancement in channel SNR (signal-to-noise ratio) providing high throughput and reliability.
Array Gain: array gain is the average increase in the received signal-to-noise ratio (SNR). The signal strength is improved by coherently combining the received signals . the increase in SNR is linear with the number of antennas and that results in increase in the capacity based on Shannon's formula :
Spatial Multiplexing Gain: this can increase the channel throughput by utilising the independent paths of the multiple transmitters and receivers to transmit separate data streams. So it sends separate data from different antennas .
Interference Reduction: the transmitted signal may suffer from interference known as co-channel interference, that is where multiple antennas are used to detect and remove the interference from the transmitted signal
3.3.1 MIMO Channel Model
MIMO system contains m transmit antennas at base station and n receive antennas at the mobile terminal as shown in Figure 3.11. At the Transmitter the data streams are encoded then the outputs are forwarded to the m transmit antennas. Then the signal is transmitted through the MIMO channel which has a long coherence time so a great number of bits can be transmitted within this time  to the receive antennas. The antenna receives both the assigned signals and other signals assigned for other antenna . The signal then gets decoded to reconstruct the original input signal. The direct connection is represented from antenna 1-to-1 with h11 and the indirect is represented as cross component h21 as shown in the transmission matrix H with nxm dimension
Fig.3.10 Matrix H 
The transmission formula  can be written as:
y= the received signal vector
x= the transmitted signal vector
n= the noise vector
The capacity of the MIMO channel is directly proportional to the number of streams M as shown in the formula below:
3.3.2 Receive Diversity
Receive diversity in MIMO is widely used in LTE uplink; the diagram in Figure 3.12 is illustrating the operation mechanism of receive diversity. Two copies of the signal is transmitted form the mobile equipment to the eNB (base station), eNB involves two antennas to receive the two copies of the signal. Normally the received signals are in different phase shifts. This issue can be tackled by antenna specific channel estimation, and then eNB combines the signals together in phase. However these two signals can be prone to channel fading since they are formed of small rays, but in MIMO the antennas are correctly spaced to avoid the signals to experience fading at the same time. This results in reducing the amount of fading in the two signals which also reduces the error rate .
3.3.3 Transmit Diversity
The function of transmit diversity is quite similar to the function of receive diversity, as they are both reduce the amount of channel fading by the applying multiple antennas. But the issue with transmit diversity is the signals might pile up at single receive antenna and that can cause high interference . However there are two ways to tackle this issue:
Closed Loop Transmit Diversity
Before transmitting two copies of the signal, the transmitter applies a phase shift to one or both signals to make sure both signals are received in phase and without interference. Pre-coding matrix indicator (PMI) is used to determine the phase shift, which can be computed by the receiver which is then can be fed back to the transmitter. This feedback loop can experience a delay so the PMI can be invalid when it is used for rapid moving mobiles because it needs to keep changing frequently, that is why closed loop is used for the relatively slow moving mobiles .
Open Loop Transmit Diversity
Open loop is used for rapid moving mobiles. It uses a technique called Alamouti's technique . It sends two symbols in two stages; the first stage sends s1 from the first antenna then sends s2 from second antenna. The second stage it does the opposite. Then the alamouti receiver can perform the measurements of the two symbols s1 and s2 to obtain these transmitted symbols .
3.3.4 Spatial Multiplexing
The spatial multiplexing is used to increase the data rate by dividing data into separate streams . So by using multiple antennas we can have multiple parallel streams transmitting data hence increase data rate. Spatial multiplexing system is illustrated in figure 3.15; two antennas are used at both ends (transmitter & receiver) the antenna mapping processes two symbols at a time and sends one to each antenna which then will be transmitted simultaneously, therefore increasing the transmitted data rate .
The beamforming technique is used in MIMO to incrase the coverage of the antenna. Figure 3.16 is illustating the princple of beamforming , mobile equipment 1 is located far away from eNB (base station) but on a line of sight which is at right angle to the antenna array. mobile equipment 1 receives the signals in phase with high power. Mobile equipment 2 is not at right angle with the antenna array but at slope angle, therefore it receives the signals with 180 phase shift with low power.as it can be seen the main beam is directed towards mobile equipment 1 so mobile 1 is getting more power and this increases the range of the eNB .
Multiple user MIMO is another technique used by MIMO to increase the cell capacity. it is commonly used in the LTE uplink due to the its low cost of implementation in mobiles,as only one transmit antenna and one power implifier are required. Figure 3.17 is illustating the principle of MU-MIMO operation. the transmit antennas are on two different mobile equipment and located apart from each other, so the data streams are originating from different mobile equipment , they are both transmitting on the same carrier frequecny and simeltanously. then the eNB receives the signals and separate them using mean square error detector .
3.3.7 LTE transmission modes (downlink)
3GGP have defined the LTE multiple antenna transmission modes for the downlink to realise better downlink performance under different radio condition :
open loop spatial multiplexing
closed loop spatial multiplexing
closed loop rank=1
3.3.8 LTE transmission modes (uplink)
3GGP defined the LTE uplink transmission modes for multiple antennas in 3 categories :
Single user- MIMO