Dual-Mode Index Modulation Aided OFDM

Index modulation has become a promising technique in the context of orthogonal frequency division multiplexing (OFDM), whereby the specific activation of the frequency domain subcarriers is used for implicitly conveying extra information, hence improving the achievable throughput at a given bit error ratio (BER) performance. In this paper, a dual-mode OFDM technique (DM-OFDM) is proposed, which is combined with index modulation and enhances the attainable throughput of conventional index-modulation-based OFDM. In particular, the subcarriers are divided into several subblocks, and in each subblock, all the subcarriers are partitioned into two groups, modulated by a pair of distinguishable modem-mode constellations, respectively. Hence, the information bits are conveyed not only by the classic constellation symbols, but also implicitly by the specific activated subcarrier indices, representing the subcarriers’ constellation mode. At the receiver, a maximum likelihood (ML) detector and a reduced-complexity near optimal log-likelihood ratio-based detector are invoked for demodulation. The minimum distance between the different legitimate realizations of the OFDM subblocks is calculated for characterizing the performance of DM-OFDM. Then, the associated theoretical analysis based on the pairwise error probability is carried out for estimating the BER of DM-OFDM. Furthermore, the simulation results confirm that at a given throughput, DM-OFDM achieves a considerably better BER performance than other OFDM systems using index modulation, while imposing the same or lower computational complexity. The results also demonstrate that the performance of the proposed low-complexity detector is indistinguishable from that of the ML detector, provided that the system’s signal to noise ratio is sufficiently high.


I. INTRODUCTION
Orthogonal frequency division multiplexing (OFDM) has 22 become a ubiquitous digital communications technique as a 23 benefit of its numerous virtues, including its capability of 24 providing high-rate data transmission by splitting the serial 25 data into many low-rate parallel data streams [1]. It is also 26 capable of offering a low-complexity high-performance solu- 27 tion for mitigating the inter-symbol interference (ISI) caused 28 by a dispersive channel [2], [3]. Due to the above-mentioned 29 merits, OFDM has been adopted in many broadband wireless 30 standards, such as 802.11a/g Wi-Fi, 802. 16 WiMAX, and 31 Long-Term Evolution (LTE) [1]. 32 The concept of index modulation (IM) is related to the 33 principle of spatial modulation [4]-[6] originally conceived 34 for multiple-input-multiple-output (MIMO) systems, which 35 was then also invoked in the context of OFDM, leading to the 36 index-modulation-based OFDM philosophy. Explicitly, the 37 information is transmitted using both the classic amplitude 38 as well as phase modulation and implicitly also by the indices 39 of the activated subcarriers [7]- [9]. Index-modulation-based 40 OFDM is capable of enhancing the power efficiency of the 41 classic OFDM, since only a fraction of the subcarriers is 42 modulated, but additional information bits are transmitted 43 by mapping them to the subcarrier domain. Hence various 44 attractive IM-aided OFDM systems have been proposed in 45 the literature. In [10], the specific choice of the activated 46 subcarrier indices conveys extra information in an on-off 47 keying (OOK) fashion, whereby the indices of the activated 48 subcarriers are determined by the corresponding majority 49 bit-values of the OOK data streams. Whilst it is capable 50 of attaining a high power efficiency, this scheme imposes 51 a potential bit error propagation, hence leading to bursts of 52 errors. To address this problem, an enhanced subcarrier index 53 modulation OFDM (ESIM-OFDM) scheme was proposed 54 in [11], where each bit of the OOK data streams determines 55 the active subcarrier in a corresponding subcarrier pair, thus 56 only half of the subcarriers are modulated. Although this 57 scheme is capable of enhancing the attainable performance, 58 constellations of higher order are required for modulation 59 in order to achieve the same spectral efficiency as conven-60 tional OFDM. 61 Basar et al. [12] combined OFDM with index modula-62 tion (OFDM-IM) by arranging for the subcarriers to be par- 63 titioned into several subblocks, where the specific indices 64 of the active subcarriers in each subblock are used for data 65 transmission. This OFDM-IM scheme is capable of enhanc- 66 ing the bit error ratio (BER) performance of classical OFDM 67 at the cost of a reduced throughput, since many subcarri-68 ers remain unmodulated in order to implicitly convey infor-69 mation. In [13] Basar proposed an enhanced version of 70 OFDM-IM by combining space-time block codes with coor-71 dinate interleaving and OFDM-IM, which led to an additional 72 diversity gain. OFDM-IM was also combined by Basar [14] 73 with the MIMO concept, which led to the MIMO-OFDM-IM 74 philosophy, exhibiting a considerable performance gain over 75 classical MIMO-OFDM [15]. Besides, in [16] and [17], the 76 OFDM-IM scheme is introduced to the underwater acous-77 tic communications as well as the vehicle-to-vehicle and 78 vehicle-to-infrastructure (V2X) applications, which achieves 79 significant performance gains. Furthermore, the performance 80 trade-offs of OFDM-IM techniques have been theoretically 81 analyzed in [18]- [21]. Specifically, in [18], a tight BER 82 upper-bound of OFDM-IM was formulated, and the optimal 83 number of active subcarriers was considered in [19] and [20]. 84 In [21], the achievable performance of OFDM-IM and the 85 beneficial region of the OFDM-IM scheme over conven-86 tional OFDM are investigated, which provides the guide-87 lines for system designing of the OFDM-IM scheme. 88 Additionally, several feasible improvements on the perfor-89 mance of OFDM-IM have been discussed in [22] and [23]. 90 Yang et al. [22] proposed a spectrum-efficient index modula- In our DM-OFDM scheme the subcarriers are partitioned 105 into OFDM subblocks, and for each subblock, information 106 bits are transmitted not only by the modulated subcarriers 107 but implicitly also by the indices of the activated subcar-108 riers. More specifically, the subcarriers are split into two 109 groups, corresponding to two index subsets. Both groups 110 of subcarriers are then modulated by two different constel-111 lation modes, and the information bits conveyed by index 112 modulation can be determined by one of the two index sub-113 sets. At the receiver, a maximum likelihood (ML) detector 114 and a reduced-complexity near optimal log-likelihood ratio 115 (LLR) detector are employed to demodulate the signals. The 116 minimum distance between the different realizations of the 117 OFDM subblocks is calculated in order to evaluate the BER 118 performance of DM-OFDM with the aid of the ML detector. 119 Explicitly, the theoretical analysis is based on the pairwise 120 error probability (PEP) of the proposed DM-OFDM. Our 121 simulation results will demonstrate that DM-OFDM achieves 122 a signal to noise ratio (SNR) gain of several dBs over OFDM-123 IM both in additive white Gaussian noise (AWGN) channels 124 and in frequency-selective Rayleigh fading channel at the 125 spectral efficiency of 4 bits/s/Hz, while imposing the same 126 or lower computational complexity. Our simulation results 127 will also confirm that the performance of the low-complexity 128 LLR based detector is indistinguishable from that of the 129 ML detector, provided that the system's SNR is sufficiently 130 high. 131 The rest of this paper is organized as follows. Section II 132 describes the system model of DM-OFDM, while Section III 133 presents our theoretical analysis of the proposed DM-OFDM. 134 Section IV calculates the minimum distance between differ-135 ent OFDM subblocks, performs the PEP analysis, and carries 136 out Monte Carlo simulations for quantifying the performance 137 of the proposed DM-OFDM, using the existing OFDM-IM as 138 a benchmark. Finally, our conclusions are drawn in Section V. 139 The DM-OFDM transmitter is illustrated in Fig. 1. First, 142 m incoming bits are partitioned by a bit splitter into p groups, 143 each consisting of g bits, i.e., p = m/g. Each group of g 144 information bits is fed into an index selector and two different 145 constellation mappers for generating an OFDM subblock 146 of length l = N /p, where N is the size of fast Fourier 147 transform (FFT). In contrast to the existing index-148 modulation-based OFDM [12], whereby only part of the sub-149 carriers are actively modulated, in our DM-OFDM scheme all 150 the subcarriers are modulated in each subblock, which leads 151 to an enhanced spectral efficiency. The first g 1 bits of the 152 incoming g bits, referred as index bits, are utilized by the 153 index selector to divide the indices of each subblock into two 154 index subsets, denoted as I A and I B . The remaining g 2    are modulated by the mappers A and B, respectively.

II. DM-OFDM SYSTEM MODEL
A , · · · , I       229 where diag X (β) is the diagonal matrix with its diagonal 230 elements given by the elements of X (β) , while 231 233 235 Given each index pattern I (i) legitimate transmit signal vectors for X (β) , which is defined 239 by the set Thus, there are a total of n X = 243 legitimate transmit signal vectors for 244 X (β) . 245 It is indicated that the spectral efficiency of the proposed 246 DM-OFDM can be calculated as p(g 1 +g 2 ) N +L . According to (1) 247 and (2), the spectral efficiency can be further improved by 248 enlarging the subblock size l. Assuming N is fixed, then the 249 total number of transmitted bits conveyed by index modula-250 tion becomes n IM = N /l log 2 l k . To maximize n IM for 251 a fixed l, k is set as l/2 according to the innate property of the 252 combinatorial expression. It is indicated that n IM increases as 253 l becomes larger, leading to an improved spectral efficiency 254 for DM-OFDM. However, the computational complexity of 255 the brute-force ML detector is increased exponentially with 256 the size of the OFDM subblocks. Therefore, a trade-off has 257 to be struck between the spectral efficiency and the compu-258 tational complexity in order to optimize the overall perfor-259 mance of DM-OFDM, which is set aside for our future work. 260

261
At the receiver, a full ML detector may be invoked for detect-262 ing the information bits by processing the FD received signals 263 on a subblock by subblock manner. For the βth subblock, 264 the optimal index pattern and transmitted symbols can be 265 obtained by minimizing the ML metric After obtaining the ML estimate of both the index pattern 269 and of the symbol vector I information bits can be demodulated by employing the index-271 pattern look-up table and the two constellation sets, which 272 map the information bits to the corresponding index pattern 273 and to the constellation symbols. It can be seen from (14) that 274 the computational complexity of the ML detector in terms 275 of complex multiplications is on the order of 2 . Therefore, the 277 ML detector is impractical to implement for large g 1 , l, k 278 and modulation orders M A and M B , due to its exponentially 279 increasing complexity.

333
Remark: Under an extremely high noisy condition, it is 334 possible that aγ (β) obtained may not correspond to a legiti-335 mate index pattern. In such a situation, a solution is to reverse 336 the sign of the LLR having the smallest magnitude in the 337 subblock to see if a legitimate index pattern can be inferred. 338 If the resultant modifiedγ (β) is still illegitimate, the LLR with 339 the second smallest magnitude can be examined, and so on 340 until a legitimate index pattern is produced [26]. 341 This LLR based detector is clearly a near-ML solu-342 tion. However, its computational complexity is much lower 343 than that of the ML detector. Recently, a novel reduced-complexity receiver was pro-356 posed for the detection of index-modulated OFDM in [27]. 357 Since there is still slight performance gap between the pro-358 posed LLR detector and the ML detector at low SNRs, the 359 reduced-complexity detector in [27] will be also applied in 360 DM-OFDM in our future study, which may harvest on perfor-361 mance gain over the proposed low-complexity LLR detector.

363
According to (14), the performance of DM-OFDM relying 364 on the ML detector is determined by the minimum distance 365 between the different realizations of the OFDM subblock. 366 First, let us define the set of n X realizations for the OFDM 367 subblock by 369 and let us denote the l-dimensional realization vector by 370 T . The distance metric 371 between two different realization vectors X (i 1 ,j 1 ) and X (i 2 ,j 2 ) 372 is given by Then the corresponding unconditioned pairwise error proba-403 bility (UPEP) is formulated as  where I l denotes the l×l identity matrix. After the calculation 420 of the UPEP, the average bit error probability (ABEP) can be 421 derived as [12] 422 P ave = 1 gn X where ε X diag , X diag is the number of bit errors in the cor-425 responding pairwise error event. P ave is approximately equal 426 to the system's BER, and therefore it can be used to estimate 427 the performance of DM-OFDM. 428 Although the PEP analysis presented here is based on the 429 ML detection, the result of the approximate BER given above 430 can also be applied to the DM-OFDM relying on the LLR 431 based detector, especially under high-SNR conditions. This 432 is because the reduced-complexity LLR based detector offers 433 a near-ML solution, and its performance is indistinguishable 434 from that of the ML detector at high SNRs. 435 Recently, several improvements based on the conventional 436 OFDM-IM have been proposed [7], [13], [ slight performance loss compared to the DM-OFDM relying 493 on the ML detector at low SNRs. When the SNR is suf-494 ficiently high, the performance of the LLR based detector 495 becomes indistinguishable from that of the ML detector, 496 despite the fact that it imposes a much lower computational 497 complexity than the ML detector, specifically O(32) in com-498 parison to O(1024) in this example. Furthermore, the BER 499 performance of DM-OFDM is compared to that of the exist-500 ing ESIM-OFDM arrangement at the spectral efficiency of 501 2.22 bits/s/Hz under the AWGN and the frequency-selective 502 Rayleigh fading channel conditions. It can be readily seen that 503 the proposed DM-OFDM regime achieves 1dB and 3dB per-504 formance gain over ESIM-OFDM for the AWGN channel and 505 the frequency-selective Rayleigh fading channel respectively, 506 because ESIM-OFDM only activates half of its subcarriers 507 for modulation, hence requiring higher order constellations to 508 reach the spectral efficiency of DM-OFDM, therefore leading 509 to a BER performance loss. 510 Additionally, the theoretical PEP analysis is compared with 511 the simulated BER performance in Fig. 4 for the DM-OFDM 512 under the frequency-selective Rayleigh fading channel 513 considered. At low SNRs, the theoretical analysis becomes 514 inaccurate, because there are several approximations in the 515 PEP calculation, which become inaccurate when the noise 516 is dominant. However, the simulation results agree with the 517 theoretical PEP analysis well when the E b /N 0 is above 30 dB, 518 indicating that the PEP analysis of DM-OFDM is more accu-519 rate at high SNRs.    Since the computational complexity of both DM-OFDM 551 associated with the ML detector and of OFDM-IM using the 552 ML detector is on the order of O(262144) per subblock in 553 terms of complex multiplications, the ML detection is diffi-554 cult to implement in practice. However, in order to demon-555 strate that the performance of the reduced-complexity LLR 556 detector is indistinguishable from that of the ML based detec-557 tor for sufficiently high SNRs, we implemented both the ML 558 based detector and the LLR based detector for DM-OFDM 559 in our Monte Carlo simulations. Note that the DM-OFDM 560 using the LLR based detector has a complexity on the order of 561 O(128) per subblock, while OFDM-IM using the LLR based 562 detector has a complexity on the order of O(512), which is 563 considerably higher than that of DM-OFDM employing the 564 LLR based detector. Fig. 7 portrays our BER performance 565 comparison of DM-OFDM and OFDM-IM, where it can be 566 seen that at the BER level of 10 −3 , the DM-OFDM scheme 567 relying on our LLR based detector achieves SNR gains of 568 6 dB and 5 dB over OFDM-IM using the LLR based detec-569 tor for the AWGN and frequency-selective Rayleigh fading 570 channels respectively, since two 16-QAM constellation sets 571 are invoked by the DM-OFDM, which is naturally more 572 robust both to noise and to interference than OFDM-IM 573 in conjunction with 256-QAM. These large gains are par-574 ticularly remarkable, considering the fact that in this high 575 spectral efficiency case, the DM-OFDM combined with the 576 LLR based detector actually has a lower complexity than 577 the OFDM-IM with the LLR based detector. The results 578 of Fig. 7 also confirm that the performance loss of the 579  Additionally, the theoretical performance based on the PEP 616 analysis of the DM-OFDM under AWGN channel conditions 617 is also compared with its simulated counterpart for Example 1 618 and Example 3, which is illustrated in Fig. 10. It can be seen 619 that, despite the slight performance gap at low SNRs, the 620 theoretical BER results are almost the same as the simulated 621 counterparts at the SNR of 6dB and 10dB at the spectral 622 efficiency of 1.33 bits/s/Hz and 2.22 bits/s/Hz respectively, 623 which are achievable for practical DM-OFDM systems. It is 624 indicated that the PEP analysis under the AWGN channel is 625 more accurate than that of the frequency-selective Rayleigh 626 fading channel condition. This is mainly because the FD 627 channel coefficients are all one under the AWGN channel, 628 and the UPEP can be directly calculated by (26), without 629 the need of taking the approximation of (29), hence reducing 630 the deviations compared with the PEP analysis under the 631 frequency-selective Rayleigh fading channel. 632 VOLUME 4, 2016