| Sažetak (engleski) | Single carrier frequency division multiple access (SC-FDMA) is a modulation and a multiple access technique selected in the uplink for Long Term Evolution (LTE) standard, the dominant fourth generation mobile communications standard. Multiple antenna systems, known as multiple-input multiple-output (MIMO), are common in modern communication systems. In this paper, the issues related to the implementation of MIMO techniques in SC-FDMA is studied. Specifically, two MIMO techniques, spatial modulation and transmit diversity, applied to SC-FDMA are analyzed in detail. The main reason why SC-FDMA has been favored instead of orthogonal frequency division multiplex (OFDM), which has been selected with orthogonal frequency division multiple access (OFDMA) in LTE downlink, is its low peak-to-average power ratio (PAPR). PAPR is a measure of fluctuations in output power of the signal. If a signal has high PAPR the output amplifier has to operate well below the saturation point to avoid the work out of linear range and the linear range of the amplifier has to be wide. All of this increases the price of the transmitter. OFDM is known for high PAPR value, hence it can be used in downlink where the base station is transmitter. On the other hand, in uplink, it presents the problem as the transmitter is a mobile device. SC-FDMA uses precoding with discrete Fourier transform (DFT) prior to OFDM, reducing the PAPR level significantly while maintaining the well-known benefits of OFDM, such as low complexity, frequency domain equalization, the good performances in different channel models etc. The OFDM modulator is usually implemented using the inverse DFT (IDFT), therefore DFT precoding cancels the effect of IDFT and the output signal presents the oversampled signal of the input signal to OFDM modulator. In general, this signal is obtained after the conventional QAM/PSK modulation, therefore the output SC-FDMA signal is the oversampled QAM/PSK signal, known for significantly lower PAPR. As it is based on OFDM, the multiple access in SC-FDMA is analogous to OFDMA, used in downlink. The blocks of adjacent subcarriers are allocated to the users in the defined time periods, thus avoiding interuser interference while allowing flexible resource allocation to the users. MIMO systems utilize the existence of multiple antennas at the transmitter and/or receiver side. The multiple antennas can be used for the improvement of the performance, known as spatial diversity, or for increase of the data rate, usually regarded as spatial multiplexing. MIMO technique is limited with the multiplexing-diversity trade-off which implies that possible diversity of the MIMO technique is inversely proportional to the achieved data rate increase. The basic idea of MIMO systems is the fact that if there are multiple antennas in the system and if the correlation between them is low, then the spatial component of the channel can be utilized. Initially, LTE defined MIMO techniques only for the downlink and, as OFDM is widely adopted modulation, it used well-known techniques suitable for OFDM. Later, MIMO in the uplink has been introduced in LTE Advanced. SC-FDMA, as a new modulation technique, required some changes in the existing MIMO techniques. Any change in the output signals, required for the implementation of a MIMO technique, can affect PAPR level and the main advantage of SC-FDMA over OFDM is lost. Therefore, in this paper, MIMO techniques in SC-FDMA are analyzed with the constraint of low PAPR level on all transmit antennas. Transmit diversity is one of the techniques studied in this paper. In order to achieve transmit diversity, the transmitter sends coded signals via two or more transmit antennas. Therefore, the coding should be performed in a way that the output signals maintain low PAPR levels. The conventional transmit diversity techniques, such as space-time block codes (STBC) or space-frequency block codes (SFBC), are not directly applicable as they have significant limitations. STBC maintains low PAPR on all transmit antennas, but require the coding to be performed on the even number of subsequent SC-FDMA symbols. In LTE, the number of symbols in LTE subframe can be odd, therefore at least one symbol remains uncoded. This is known as “orphan“ symbol problem and it is the main reason why STBC is not directly applicable in SC-FDMA. SFBC, on the other hand, is performed inside one SC-FDMA symbol, hence the “orphan” symbol problem is avoided, but it shows the PAPR increase. In this paper, two transmit antenna transmit diversity is observed and if Alamouti scheme is used, PAPR is increased on both transmit antennas. Because of these limitations, an alternative techniques have been proposed. The most popular is single carrier – space frequency block coding (SC-SFBC) which implements Alamouti-based SFBC on non-adjacent subcarriers. This approach preserves low PAPR level on both antennas, but at the expense of performance loss. One of the constraints of Alamouti scheme, the unchanged channel response on adjacent subcarriers, is not satisfied, therefore the scheme shows a performance loss in the cases of greater number of subcarriers assigned to the user or in the channels with high frequency selectivity. In this paper, a new transmit diversity technique, denoted as space-frequency block coding with clipping and filtering (SFBC CF), is proposed. Using the transposed coding matrix of Alamouti scheme, the PAPR increase is avoided on the first antenna and for the PAPR increase on the second antenna clipping and filtering (CF) operation is proposed. CF is well-known as a simple PAPR reduction technique, used in techniques such as OFDM. Clipping is performed in the time domain, after the IFFT operation and prior to the modulation to radio-frequency, and it presents reduction of the amplitude to the predefined clipping level in the case when the clipping level is exceeded. This operation creates out-of-band radiation that presents interuser interference and in-band distortion that affects the performances. Out-of-band radiation must be reduced therefore, after the clipping, the signal is filtered in the frequency domain and all frequency components out of the user bandwidth are set to zero. This slightly reduces the effect of the clipping operation and CF operation can be performed multiple times, if this is acceptable from the implementation point of view. One or more CF operations reduced the average power level and it has to be normalized prior to the transmission. Before PAPR and performances comparisons of the proposed technique with the existing techniques, the clipping level had to be selected. Observing the bit-error rate (BER) as a function of the clipping level for different signal-to-noise ratios (SNR), while 16-QAM is used as an underlying modulation, the power clipping level of 4 dB is selected. Lower clipping level has a greater impact on the performances, but better PAPR curves, hence the selected level presents a trade-off. After that, the PAPR curves are observed and it is shown that CF operation significantly reduced the PAPR level and SFBC CF shows even better PAPR curves than the conventional SC-FDMA for PAPR levels above the clipping level. If the CF operation can be repeated multiple times, the PAPR curves have greater slopes after the bending point located slightly above the power clipping level. Finally, the performances are analyzed in different channel models for different number of subcarriers assigned to the user. It is shown that in cases of channels with low frequency selectivity or in the cases where user occupies small number of subcarriers SC-SFBC and the proposed SFBC CF have performances very near STBC and SFBC. The observed performance loss in negligible. However, in the cases of channels with greater frequency selectivity or users with greater number of subcarriers, SC-SFBC shows significant performance loss, in comparison to STBC and SFBC, whereas SFBC CF performance loss is maintained very low. Furthermore, SFBC CF performance loss depends on the SNR and the clipping level, hence it is negligible for lower SNR values and noticeable for higher SNR values. However, it seems unlikely that transmit diversity is used in high SNR regime. In addition, it has been shown that repeated CF operation does not introduce additional performance loss, hence, considering significantly better PAPR curves, multiple CF operations is reasonable, if it is acceptable from the implementation point of view. Besides transmit diversity, spatial modulation (SM), a novel MIMO technique, is studied in this paper as well. SM has been recently introduced as a low complexity MIMO technique in conventional QAM/PSK systems for channels with flat fading. It is a MIMO technique that increases data rate using the index of active transmit antenna. In SM, every QAM/PSK symbol is transmitted via only one antenna and during that symbol interval all other transmit antennas are inactive. This implies that the transmitter is very simple as it has only one RF chain. Further, it has been shown that performances are better in comparison to V-BLAST (Vertical Bell-Laboratories Layered Space Time) or transmit diversity techniques, such as STBC or SFBC, in different channel models. As transition to OFDM is straightforward, because narrow subchannel present channels with frequency flat fading. It has been shown that SM in OFDM maintains good performances, in comparison to V-BLAST or transmit diversity techniques for same data rate, but the advantage of single RF chain is lost and the transmitter must have as many RF chains as there are transmit antennas. However, the main advantage in this case is performance gain. Regarding the implementation of SM in SC-FDMA, there has been papers covering space-time shift keying (STSK), an SM alternative, and showing good performance, but the PAPR has not been analyzed. In this paper, it is shown that the conventional SM or any SM alternative that does not include low PAPR constraints shows significant PAPR increase. As SC-FDMA is based on OFDM, SM in SC-FDMA must have multiple RF chains, hence it is not necessary that only one antennas is active and all others inactive. Therefore, in this paper, a new SM alternative, denoted as low PAPR spatial modulation (LPSM), is proposed. The criteria for the selection of optimal phase shifts is the maximization of the minimal Euclid distance between any two possible transmission sets. With this implementation of SM, all transmit antennas are active and have same amplitude levels, but the spatial information is inserted in phase shifts. After detailed analysis for the case of two transmit antennas, the extension for four transmit antenna is provided. Further, the PAPR comparison is given and it is shown that LPSM for two and four transmit antennas has the same or even slightly better PAPR curves than the conventional SC-FDMA and conventional SM shows high PAPR increase, particularly for four transmit antennas. After the new LPSM scheme is proposed, the possible receivers are discussed. The optimal maximum likelihood receiver (MLD) in SC-FDMA systems suffers from inherited high receiver complexity, because the decision has to be made jointly for whole SC-FDMA symbols, consisting QAM/PSK symbols and the bits of spatial modulation. On the other side, linear receivers, such as minimum mean-square error (MMSE) or zero-forcing (ZF) receivers are known for low complexity, but with significant performance loss. Therefore, in this paper, two novel receivers are proposed as a trade-off between optimal performance and low complexity. The first one is regarded as near-MLD receiver as it achieves performance near the optimal MLD receiver. This receiver uses the fact that QAM/PSK symbols and SM bits can be separated. After MMSE or ZF equalization is performed, the receiver assumes that only few of detected SM bits have errors and creates new SM bits sequence that have few different SM bits in comparison to the detected sequence. After that, additional linear equalizations (MMSE or ZF) are performed using all generated sequences and additional QAM/PSK sequences are obtained. Finally, the receiver uses MLD approach on this reduced set of decisions in order to find the decision with minimum Euclid distance from the received signal. This receiver shows performance very near to the optimal receiver with significantly lower complexity. However, as many additional linear equalizations have to be performed, this receiver has significantly high complexity if greater number of subcarriers is assigned to the user. Therefore, a new receiver, regarded as improved MMSE receiver (iMMSE) is proposed as well. This receiver is very similar to the near-MLD and uses new SM bits sequences, but in this receiver additional linear equalizations are avoided. Hence, additional QAM/PSK decisions are obtained from the equalized signal that is obtained after initial linear equalization. With this approach, the complexity is further reduced and this receiver presents a trade-off between near-MLD and simple linear receivers from performance and complexity point of view. After this, the complexity analysis is performed and it is shown that near-MLD receiver has much lower complexity than MLD receiver and iMMSE is a trade-off between near-MLD and linear receivers. Finally, the performance comparisons are given in different channel models, antenna configurations and the number of subcarriers assigned to the user. In order to have a comparison with another MIMO technique of similar transmitter complexity, comparisons included Alamouti SFBC or STBC transmit diversity techniques with the same data rate. Overall conclusion is that LPSM with MLD, near-MLD and iMMSE receivers has better performance than Alamouti scheme, whereas linear receivers have performances very near to Alamouti. In addition, the comparison is given against conventional SM, despite the PAPR increase, and it is shown that LSPM is even slightly better than SM for the same type of receivers. Overall conclusion is that LPSM is shown as an acceptable MIMO technique that achieves data rate increase and different receivers are discussed. Essentially, the main contributions of this paper are two new MIMO techniques adapted to SC-FDMA system: - transmit diversity based on space-frequency block coding with clipping and filtering - low PAPR spatial modulation, as a MIMO multiplexing technique, and different suboptimal receivers. The paper is organized in 8 chapters as follows: - Chapter 1: Radio channel – this chapter provides a short description of the radio channel and the effect within. As the paper is related to LTE, a description of the channel models defined in LTE standard is provided. - Chapter 2: OFDM and OFDMA – as SC-FDMA is created as OFDM/OFDMA with DFT precoding, this chapter provides necessary information about OFDM and OFDMA. In addition, this chapter provides the definition of PAPR and the reasons for high PAPR level in OFDM. - Chapter 3: Single-carrier modulation – for better understanding of SC-FDMA, single-carrier with frequency domain equalization (SC-FDE) is described first. This technique presents a low PAPR OFDM alternative. Besides low PAPR and low transmitter complexity, SC-FDE is not suitable for the implementation of multiple access, hence SC-FDMA is derived. SC-FDMA combines the advantages of SC-FDE, such as low PAPR level, and OFDM/OFDMA, good performances and simple and flexible multiple access. Finally, SC-FDMA system is described in comparison to OFDM/OFDMA and it is shown that SC-FDMA has much lower PAPR level. - Chapter 4: SC-FDMA and OFDM with OFDMA in LTE system – as SC-FDMA is practically implemented in LTE system, this chapter gives a description of SC-FDMA using the specification given in LTE standard. Finally, a comparison of SC-FDMA and OFDM systems in frequency selective channels and the analysis of the performances of SC-FDMA system with different channel estimation techniques and equalizations is provided. - Chapter 5: Diversity in MIMO systems – as diversity presents the first practical implementation of MIMO systems, this chapter describes the diversity concept with accent on the transmit diversity techniques. After Alamouti scheme, an overview of STBC and SFBC codes is given. - Chapter 6: MIMO system – this chapter gives an overall discussion about MIMO systems. After the multiplexing-diversity trade-off is provided, MIMO technique that achieve data rate increase, the multiplexing MIMO techniques, are observed and spatial modulation, a relatively novel MIMO technique is described in detail. - Chapter 7: Transmit diversity in SC-FDMA – first of all, the limitations of conventional STBC and SFBC codes are explained and SC-SFBC, a transmit diversity technique suitable for SC-FDMA, is described. After the disadvantages of SC-SFBC are described, a new technique, SFBC CF, is proposed and it is compared to STBC, SFBC and SC-SFBC from PAPR and performance point of view. - Chapter 8: Spatial modulation in SC-FDMA – this chapter provides a detailed discussion about SM in SC-FDMA and it is shown that SM increases PAPR level on all antennas. Therefore, an SM alternative, regarded as LPSM, is proposed and the receivers for the new technique are discussed. The two novel receivers are proposed and it shown that LPSM shows good performance and low PAPR. In conclusion, LPSM is presented as an acceptable MIMO technique for SC-FDMA The main novelties of the paper are presented in the last two chapters. |
