2018 Comparative study of selected subcarrier index modulation OFDM

rawaajaafr@yahoo.com Abstract Orthogonal frequency division multiplexing with subcarrier index modulation (SIM-OFDM) is recently proposed to enhance the performance of traditional OFDM. By incorporating the index modulation in OFDM, the data can be sent on the indices of subcarriers as well as the subcarriers themselves reducing the system complexity. In addition, the Peak to Average Power Ratio (PAPR) and Inter Carrier Interference (ICI) can be reduced by switching on /off some OFDM subcarriers in OOK fashion. In this paper, a comparative study of OFDM with SIM_OFDM and Enhanced SIM_OFDM methods in terms of complexity, spectral efficiency and bit error rate over AWGN channel using two power policies is presented. The simulation results showed that at bit error rate of 10-3, SIM_OFDM and ESIM_OFDM achieved gains in Eb/No of 1.1 dB and 2 dB over 4-QAM OFDM respectively under power reallocation policy. However, the results also showed that traditional OFDM has better spectral efficiency compared to both SIM_OFDM and ESIM_OFDM especially at high M-ary


Introduction
Orthogonal Frequency Division Multiplexing (OFDM) is one of the most important enabling technology in broadband communications in last decades and crucial part in many wireless standards to meet the increasing requirements for high rate communication systems operating on multipath channels [1][2][3][4][5][6]. To serve many users and to get a high reliability. In multicarrier system the data is carried on low data rate subcarriers instead of single high data rate as in single carrier system. OFDM used in 4G wireless communication standards and a candidate for 5G due to its tremendous capacity in terms of number of subcarriers [5][6][7].
Many methods are proposed in the literature to improve the performance of OFDM system. Subcarrier Index Modulation OFDM (SIM_OFDM) is proposed in [8] and [9] to enhance the performance of OFDM where the data are sent on the indices of subcarriers. BER performance of the SIM scheme in coded and uncoded scenarios are evaluated. The main problem of SIM_OFDM is the high error rate due to the propagation of error in Additive White Gaussian Noise (AWGN) channel condition. This problem is solved by an enhanced scheme called ESIM_OFDM, where the indexing is based on the use of subcarrier pairs. A further benefit of their enhanced structure, the Peak-to-average power ratio (PAPR) can be reduced [10]. In [1], a low complexity detector for OFDM with index modulation (OFDM_IM) is proposed. In [7], a method that combines precoding and partial transmit sequence PTS to reduce the PAPR in SIM_OFDM is presented. In [8] BER performance of the SIM scheme in coded and uncoded scenarios are evaluated. In [7] improved the SIM structured proposed in [8] and analyzed the PAPR of SIM systems. In [11], two systems are proposed to improve PAPAR and BER of SIM-OFDM. They are named: Half-Symbol BPSK modulated SIM_OFDM (HS/BPSK/SIM-ODM) and double ASK-SIM. Finally, the authors in [12] studied the effect of Doppler spread in SIM-OFDM compared it with conventional OFDM.
In this paper, detailed descriptions of SIM_OFDM and ESIM-OFDM methods will be presented. Deep analysis enhanced by numerical examples will be given to understand how these methods act to improve OFDM performance. MATLAB Simulation will be used to evaluate the performances of the two methods under different operating conditions as compared to traditional OFDM system.

The Structure of OFDM and Subcarrier Indexed OFDM Systems
In this section, the models of SIM_OFDM and ESIM_OFDM systems are presented, to better understand these systems and highlight the differences between them and the traditional OFDM system, a description to OFDM system is given first in Figure1. Figure 1. Structure of OFDM [11] At the transmitter, the input bits are mapped by some modulation such as M-QAM to form QAM symbols which is fed to IFFT block. Then, the samples with guard interval insertion by D/A are converted from digital to analog signal and transmitted over the multipath channel. At the receiver side, the received signal is converted to samples by A/D and guard interval is removed. The samples get back to the original symbols After FFT block [4], [11].

SIM_OFDM
In SIM_OFDM method, the data bit-stream B are divided into two parts [8]: one part of the bit streams is transformed to M-QAM symbols as usual and another part used to select the indices of active subcarriers, Figure 2 shows the working principle of SIM_OFDM system which consist of two functions. Firstly, depending on the value of each bit, there are two subsets form (ones and zeroes). By count zeros and ones based on N/2 where N is the number of IDFT points, and select the one with the highest count as a majority bit. Secondly, the index of each subcarrier is related to the location of each bit. The number of bits of the majority bit-value can be formulated as:  2 . In addition, the indices bits can be represented by = . Where N is the total number of subcarriers. Therefore, the total bits per SIM-OFDM symbol are [8]:

Power Saving Policy PSP and Power Relocation Policy PRP
For OFDM system, its maximum PAPR value can be written as where N is the number of subcarriers. For SIM-OFDM, its maximum PAPR value is: here, N_SIM is the number of active subcarriers. Since, in general, N_SIM is less than N, the maximumPAPR value of SIM_OFDM is smaller than that of ordinary OFDM system. Therefore, SIM_OFDM can reduce PAPR value to improve the PAPR performance [12]. In PRP, the excess power obtained by switching off some subcarriers can be reallocated to the active subcarriers. Hence SNR increases and BER is improved significantly. PRP can be written as follows [8]: where is the total transmit power allocated to the OFDM symbol, E[ ] is the average number of majority bit-value, and n is the per-subcarrier average Additive White Gaussian noise (AWGN) power.On the other hand, in PSP the excess power is not reallocated. Hence this leads to lower power consumption. The average SNR of an active subcarrier under PSP can be written as follows [8]:

Enhanced of SIM-OFDM
In SIM_OFDM each bit dictates the state of single subcarrier (active or inactive) this leads to error propagation as illustrate in [10]. In ESIM_OFDM a single bit dictates the state of two adjacent subcarriers. The 1bit in the makes the first subcarrier active and the second subcarrier inactive while 0 bit makes the first subcarrier inactive and the second subcarrier active. In this scheme the require size bits is reduced to N/2 compared to the original SIM-OFDM scheme which requires N bits. The advantage of this modification is that for each two consecutive subcarriers only one is active and the other one is inactive this leads to the elimination of the threshold detection and this means that the wrong detection of one subcarrier will not lead to the incorrect detection of the subsequent subcarriers, thus error will be localized. In addition, majority-bit calculation will no longer be required. Figures 4 and 5 illustrate the principle of the new encoding scheme These B bits are split into g groups each one having p bits, i.e. B=pg, each group of 3-bits is mapped to an OFDM subblock of length n, where n=N/g and N is the number of OFDM subcarriers, i.e., the size of the fast Fourier transform (FFT) [1]. The only disadvantage of the modified scheme, compared to the former SIM_OFDM, is the slightly reduced spectral efficiency. Spectral efficiency of SIM_OFDM, measured in bits/carrier, is [10]: while the spectral efficiency of the enhanced SIM_OFDM is To mathematically prove that ESIM uses less bits as compared to SIM_OFDM, consider the following numeric example: using (2) for SIM_OFDM and assuming that N=8, and 4_QAM modulation (M = 4),

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ESIM_OFDM scheme, the receiver can operate correctly without control signaling from the transmitter. However, in this scheme in order to achieve the same spectral efficiency, a higher order modulation is required as that of conventional OFDM [1].

Figure 5. ESIM_OFDM modulation approach [10]
An approach is proposed in [10] to increase the spectral efficiency of ESIM_OFDM, using division blocks. Assume for example there are N=32 sub-carriers, if these subcarriers are divided into 4 blocks (groups) of 8 subcarriers and each block have 7 active subcarriers and one is inactive. To find the number of states for each block take the combination to find the number of states for each block, all possible combinations are computed as: 8!/7!(8-7)!=8 states, then 3 bits OOK are needed to control the state of subcarriers in each block. If 4QAM is used, then two bits will be carried on each active subcarrier, so: spectral efficiency=(2*7+3)/8=2.125 bits/subcarrier, or using (9). Comparing this value with the spectral efficiency of OFDM which equal to ( 2 4 = 2). So, whenever we use an active subcarrier that are near in number to the total available subcarriers the spectral efficiency of ESIM will exceed the spectral efficiency of traditional OFDM. Furthermore, an amount of power will also be saved due to partial active subcarriers. However, on the other hand there will be a threat of high BER compared to OFDM because if a block falls, it leads to loss all bits that carried on that subcarrier while in OFDM we lose 2 bits only.

Performance evaluation of SIM-OFDM and ESIM-OFDM
This section presents the simulation results obtained for SIM_OFDM, ESIM_OFDM systems as well as traditional OFDM system when tested over AWGN channel. The simulation parameters are shown in Table 1.  Figure 6 shows BER versus Eb/No for 4QAM_OFDM and SIM_OFDM with PSP. This figure shows that although SIM-OFDM with PSP, the power used is half the power required by OFDM but there is a degradation in BER performance. For instance, at BER=10 -3 , the loss in Eb/No is 1.9 dB with PRP being used, the BER of SIM_OFDM is improved and becomes comparable to OFDM when Eb/No exceeds 4 dB as illustrated in Figure 7. It can be noticed that at BER=10 -3, SIM_OFDM outperforms OFDM by around 1.1 dB. This improvement is due to two reasons: Firstly, the power of activated subcarrier is increased, improves the detection quality of the signal constellation symbols. Secondly, the inherent high error rate performance of the coherent OOK detector, used to estimate the subcarrier activity, enhances the overall BER performance [8].  Figure 8 shows BER versus Eb/No for 4QAM_OFDM and ESIM_OFDM with PRP. The depicts clearly that ESIM_OFDM effectively improves the Bit Error Rate performance. For instance, when BER is 10 -3 , ESIM_OFDM achieves 2 dB gain in Eb/No over QAM_OFDM. This is because the allocated transmit power per subcarrier increases when PRP is used, which yields in improved error rate performance compared to conventional OFDM. However, when PSP is used instead of PRP the performance of ESIM_OFDM lags about 0.9 dB behind traditional OFDM as shown in Figure 9. Finally, the spectral efficiency of QAM_OFDM is better than both SIM_OFDM and ESIM_OFDM especially at higher M values as illustrated in the performance curves shown in Figure 10 which are plotted using (7), (8) and (10). Figure 11 shows PAPR performance results of QAM_OFDM, SIM_OFDM and ESIM_OFDM. It can be seen in this figure that SIM-OFDM has relatively worse PAPR performance compared to QAM_OFDM. But from other hand ESIM_OFDM has comparable performance to QAM_OFDM.

Conclusions
SIM_OFDM uses OOK bits for activating and/or deactivating some of the available subcarriers so each active OOK bit indicates the location of the active subcarrier and QAM symbol will be carried on this active subcarrier. If an incorrect detection is made to OOK bit this leads to in correct demodulation not only to the QAM symbol it encodes but also to all consecutive QAM symbols. This is because they will have carried on incorrect sequence of the active subcarriers and in causes error propagation so for this reason ESIM was found to solve this problem by localizing errors, which supposed that each OOK bit control the state of two consecutive instead of one as in SIM_OFDM. When 4-QAM is used, each active sub carrier will carry two bits and if there is any occurrence of error the total loss of transmitted bits will be three only in this case (1 for OOK and the rest for QAM symbol bits that transmitted on that active subcarrier), in other word, it leads to incorrect demodulation for the QAM symbol it encodes. When using PRP the allocated power per subcarrier is increased, this yields in improved BER performance compared to classical OFDM.