ORTHOGONAL frequency division multiplexing (OFDM) has become the most popular multicarrier

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1 IEEE SIGNAL PROCESSING LETTERS 1 MultipleInput MultipleOutput OFDM with Index Modulation Ertuğrul Başar, Meber, IEEE Abstract arxiv: v1 [cs.it] 1 Oct 015 Orthogonal frequency division ultiplexing with index odulation (OFDMIM) is a novel ulticarrier transission technique which has been proposed as an alternative to classical OFDM. The ain idea of OFDMIM is the use of the indices of the active subcarriers in an OFDM syste as an additional source of inforation. In this work, we propose ultipleinput ultipleoutput OFDMIM (MIMOOFDMIM) schee by cobining OFDMIM and MIMO transission techniques. The low coplexity transceiver structure of the MIMOOFDMIM schee is developed and it is shown via coputer siulations that the proposed MIMOOFDMIM schee achieves significantly better error perforance than classical MIMOOFDM for several different syste configurations. Index Ters OFDM, index odulation, MIMO systes, MMSE detection, VBLAST, 5G wireless networks. I. INTRODUCTION ORTHOGONAL frequency division ultiplexing (OFDM) has becoe the ost popular ulticarrier signaling forat for highspeed wireless counications and has been included in any standards such as Long Ter Evolution (LTE), IEEE wireless local area network (WLAN) and digital video broadcasting (DVB). Due to its efficient ipleentation and robustness to the frequency selectivity, OFDM and its cobination with ultipleinput ultipleoutput (MIMO) systes unsurprisingly appears as a strong alternative for 5G networks [1]. OFDM with index odulation (OFDMIM) is a recently proposed novel schee which transits inforation not only by Mary constellation sybols, but also by the indices of the active subcarriers which are activated according to the incoing inforation []. Subcarrier index odulation techniques for OFDM [] [4] have attracted considerable attention fro researchers and have been investigated in soe recent studies due to interesting tradeoffs they offer in error perforance and spectral efficiency copared to classical OFDM systes [5] [11]. The bit error probability of OFDMIM is analytically derived in [5]. The spectral efficiency of OFDMIM is iproved by selecting the active subcarriers in a ore flexible way in [6], where index odulation is applied for both inphase and quadrature coponents of the subcarriers. In [7] and [8], the authors deal with the proble of selecting the optial nuber of active subcarriers in OFDMIM. More recently, OFDMIM is cobined with coordinate interleaving to achieve additional diversity gains in [9]. However, the cobination of OFDMIM and MIMO transission techniques reains an open and interesting research proble. In this study, we propose MIMOOFDM with index odulation (MIMOOFDMIM) as an efficient alternative ulticarrier transission schee for 5G networks by cobining MIMO and OFDMIM transission techniques. In the proposed schee, each transit antenna transits its own OFDMIM frae as in Vertical Bell Labs layered spacetie (VBLAST) schee [1], and at the receiver side, these OFDMIM fraes are separated and deodulated using a novel and low coplexity iniu ean square error (MMSE) detection and loglikelihood ratio (LLR) calculation based detector. It is shown via E. Başar is with Istanbul Technical University, Faculty of Electrical and Electronics Engineering, 34469, Istanbul, Turkey. eail: basarer@itu.edu.tr. This work was supported by the Scientific Research Projects Foundation, Istanbul Technical University. c 015 IEEE. Personal use of this aterial is peritted. Perission fro IEEE ust be obtained for all other uses, in any current or future edia, including reprinting/republishing this aterial for advertising or prootional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted coponent of this work in other works. Digital Object Identifier /LSP

2 IEEE SIGNAL PROCESSING LETTERS T OFDM IM 1 OFDM IM IFFT IFFT CP 1 CP 1 CP CP FFT FFT Suc. MMSE Det. LLR 1 LLR OFDM IM T IFFT CP T R CP FFT LLR T Fig. 1. Transceiver Structure of the MIMOOFDMIM Schee for a T R MIMO Syste coputer siulations that the MIMOOFDMIM schee achieves significantly better bit error rate (BER) perforance than classical VBLAST type MIMOOFDM for several MIMO configurations. The rest of the letter is organized as follows. In Section II, the syste odel of MIMOOFDMIM is presented. In Section III, receiver structure of the MIMOOFDMIM schee is given. Siulation results are provided in Section IV. Finally, Section V concludes the letter. II. SYSTEM MODEL OF MIMOOFDMIM The block diagra of the MIMOOFDMIM transceiver is shown in Fig. 1. We consider a MIMO syste eploying T transit and R receive antennas. As seen fro Fig. 1, for the transission of each frae, a total of T inforation enter the MIMOOFDMIM transitter. These T are first split into T groups and the corresponding are processed in each branch of the transitter by the OFDM index odulators. The incoing inforation are used to for the 1 OFDMIM block x t = [ x t (1) x t () x t ( ) ] T, t = 1,,..., T in each branch of the transitter, where NF is the size of the fast Fourier transfor (FFT) and x t (n f ) {0, S}, n f = 1,,...,. According to the OFDMIM principle [], these are split into G groups each containing p = p 1 + p, which are used to for OFDMIM subblocks x g t = [ x g t (1) x g t () x g t (N) ] T, g = 1,,..., G of length N = NF /G, where x g t (n) {0, S}, n = 1,,..., N. According to the corresponding p 1 = log (C (N, K)), only K out of N available subcarriers are selected as active by the index selector at each subblock g, while the reaining N K subcarriers are inactive and set to zero. On the other hand, the reaining p = K log (M) are apped onto the considered Mary signal constellation. Therefore, unlike classical MIMOOFDM, x t, t = 1,,..., T contains soe zero ters whose positions carry inforation for MIMOOFDMIM. In this study, active subcarrier index selection is perfored by the reference lookup tables at OFDM index odulators of the transitter. The considered reference lookup tables for N = 4, K = and N = 4, K = 3 are given in Tables I and II, respectively, where s k S for k = 1,,... K. As seen fro Table I, for N = 4 and K =, the incoing p 1 = can be used to select the indices of the two active subcarriers out of four available subcarriers according to the reference lookup table of size C = p 1 = 4. Notation: Bold, lowercase and capital letters are used for colun vectors and atrices, respectively. (A) t and (A) t,t denote the tth colun and the tth ain diagonal eleent of A, respectively. ( ) T and ( ) H denote transposition and Heritian transposition, respectively. I N is the identity atrix with diensions N N and diag ( ) denotes a diagonal atrix. stands for the Euclidean nor. The probability of an event is denoted by P ( ) and E { } stands for expectation. X CN ( 0, σx) represents the distribution of a circularly syetric coplex Gaussian r.v. X with variance σx. C (N, K) stands for the binoial coefficient and is the floor function. S denotes Mary signal constellation. C denotes the ring of coplex nubers.

3 IEEE SIGNAL PROCESSING LETTERS 3 TABLE I REFERENCE LOOKUP TABLE FOR N = 4, K = AND p 1 = Bits Indices OFDMIM subblocks (x g t ) T [ [0 0] {1, 3} s1 0 s 0 ] [ ] [0 1] {, 4} 0 s1 0 s [ ] [1 0] {1, 4} s1 0 0 s [ [1 1] {, 3} 0 s1 s 0 ] TABLE II REFERENCE LOOKUP TABLE FOR N = 4, K = 3 AND p 1 = Bits Indices OFDMIM subblocks (x g t ) T [ [0 0] {1,, 3} s1 s s 3 0 ] [ ] [0 1] {1,, 4} s1 s 0 s [ 3 ] [1 0] {1, 3, 4} s1 0 s s [ 3 ] [1 1] {, 3, 4} 0 s1 s s 3 The OFDM index odulators in each branch of the transitter obtain the OFDMIM subblocks first and then concatenate these G subblocks to for the ain OFDM blocks x t, t = 1,,..., T. In order to transit the eleents of the subblocks fro uncorrelated channels, G N block interleavers (Π) are eployed at the transitter. The block interleaved OFDMIM fraes x t, t = 1,,..., T are processed by the inverse FFT (IFFT) operators to obtain q t, t = 1,,..., T. We assue that the tiedoain OFDM sybols are noralized to have unit energy, i.e., E { q } H t q t = NF for all t. After the addition of cyclic prefix of C p saples, paralleltoserial and digitaltoanalog conversions, the resulting signals sent siultaneously fro T transit antennas over a frequency selective Rayleigh fading MIMO channel, where g r,t C L 1 represents the Ltap wireless channel between the transit antenna t and the receive antenna r, whose eleents are independent and identically distributed with CN (0, 1 ). Assuing the wireless channels L reain constant during the transission of a MIMOOFDMIM frae and C p > L, after reoval of the cyclic prefix and perforing FFT operations in each branch of the receiver, the inputoutput relationship of the MIMOOFDMIM schee in the frequency doain is obtained as ỹ r = T t=1 diag ( x t) h r,t + w r (1) for r = 1,,..., R, where ỹ r = [ ỹ r (1) ỹ r () ỹ r ( ) ] T is the vector of the received signals for receive antenna r, h r,t C 1 represents the frequency response of the wireless channel between the transit antenna t and receive antenna r, and w r C 1 is the vector of noise saples. The eleents of h r,t and w r follow CN (0, 1) and CN (0, N 0,F ) distributions, respectively, where N 0,F denotes the variance of the noise saples in the frequency doain, which is related to the variance of the noise saples in the tie doain as N 0,T = ( /(KG))N 0,F. We define the signaltonoise ratio (SNR) as SNR = E b /N 0,T where E b = ( + C p )/ [joules/bit] is the average transitted energy per bit. The spectral efficiency of the MIMOOFDMIM schee is T/( + C p ) [/s/hz], which is equal to T ties that of the OFDMIM schee. III. DETECTION OF MIMOOFDMIM SCHEME After block deinterleaving in each branch of the receiver, the received signals are obtained for receive antenna r as y r = T t=1 diag (x t) h r,t + w r () where h r,t and w r are deinterleaved versions of h r,t and w r, respectively. The detection of the MIMO OFDMIM schee can be perfored by the separation of the received signals in () for each subblock

4 IEEE SIGNAL PROCESSING LETTERS 4 g = 1,,..., G as y r = [ (yr) 1 T (yr G ) ] T T, xt = [ (x 1 t ) T (x G t ) ] T T, hr,t = [ ( h 1 r,t) T ( h G r,t) ] T T, w r = [ ( w r) 1 T ( w r G ) ] T T for which we obtain y g r = T t=1 diag (xg t ) h g r,t + w g r (3) for r = 1,,..., R, where yr g = [ yr(1) g yr() g yr(n) ] g T is the vector of the received signals at receive antenna r for subbblock g, x g t = [ x g t (1) x g t () x g t (N) ] T is the OFDMIM subblock g for transit antenna t, h g r,t = [ hg r,t(1) h g r,t() h g r,t(n) ] T and w g r = [ w r(1) g w r() g w r(n) ] g T. The use of the block interleaving ensures that E { hg r,t( h g r,t) H} = I N, i.e., the subcarriers in a subblock are affected fro uncorrelated wireless fading channels for practical values of. A straightforward but costly solution to the detection proble of (3) is the use of axiu likelihood (ML) detector which can be realized for each subblock g as R (ˆx g 1,..., ˆx g T ) = arg in T yg r diag (x g t ) h g r,t. (4) (x g 1,...,xg T) r=1 As seen fro (4), the ML detector has to ake a joint search over all transit antennas due the interference between the subblocks of different transit antennas. Since x g t has CM K different realizations, the total decoding coplexity of the ML detector in (4), in ters of coplex ultiplications (CMs), is O ( M ) KT per subblock, which becoes ipractical for higher order odulations and MIMO systes. Instead of the exponentially increasing decoding coplexity of the ML detector, we propose a novel MMSE detection and LLR calculation based detector, which has a linear decoding coplexity as that of classical MIMO OFDM with MMSE detection. For the detection of the corresponding OFDMIM subblocks of different transit antennas, the following MIMO signal odel is obtained fro (3) for subcarrier n of subblock g: y g 1(n) h g 1,1(n) h g 1,(n) hg y(n) g 1,T (n) h g,1(n) h x g 1(n) w g 1(n) g,(n) hg,t (n) x g (n) w (n) g. y g R (n) t=1 = h g R,1 (n) h g R, (n) h g R,T (n) x g T (n). w g R (n) ȳ g n = H g n x g n + w g n (5) for n = 1,,..., N and g = 1,,..., G, where ȳn g is the received signal vector, H g n is the corresponding channel atrix which contains the channel coefficients between transit and receive antennas and assued to be perfectly known at the receiver, x g n is the data vector which contains the siultaneously transitted sybols fro all transit antennas and can have zero ters due to index selection in each branch of the transitter and w n g is the noise vector. For classical MIMOOFDM, the data sybols can be siply recovered after processing the received signal vector in (5) with the MMSE detector. On the other hand, due to the index inforation carried by the subblocks of the proposed schee, it is not possible to detect the transitted sybols by only processing ȳn g for a given subcarrier n in the MIMOOFDMIM schee. Therefore, N successive MMSE detections are perfored for the proposed schee using the MMSE filtering atrix [13] ( Wn g = (H g n) H H g n + I ) 1 T (H g ρ n) H (6) for n = 1,,..., N, where ρ = σ x/n 0,F, σ x = K/N and E { x g n ( x g n) H } = σ xi T due to zero ters in x g n coe fro the index selection. By the left ultiplication of ȳ g n given in (5) with W g n, MMSE detection is perfored as z g n = W g nȳ g n = W g nh g n x g n + W g n w g n, (7)

5 IEEE SIGNAL PROCESSING LETTERS 5 where z g n = [ zn(1) g zn() g zn(t g ) ] T is the MMSE estiate of x g n. The MMSE estiate of MIMO OFDMIM subblocks ˆx g t = [ˆx g t (1) ˆx g t () ˆx g t (N) ] T can be obtained by rearranging the eleents of z g n, n = 1,,..., N as ˆx g t = [ z1(t) g z(t) g z g N (t)] T for t = 1,,..., T and g = 1,,..., G. As entioned earlier, unlike classical MIMOOFDM, ˆx g t contains soe zero ters, whose positions carry inforation; therefore, independent detection of the data sybols in ˆx g t (with linear decoding coplexity) is not a straightforward proble for the proposed schee. As an exaple, rounding off individually the eleents of ˆx g t to the closest constellation points (the eleents of {0, S} for the proposed schee) as in classical MIMOOFDM ay result a catastrophic active index cobination that is not included in the reference lookup table, which akes the recovery of index selecting p 1 ipossible. In order to deterine the active subcarriers in ˆx g t, the LLR detector of the proposed schee calculates the following ratio which provides inforation on the active status of the corresponding subcarrier index n of transit antenna t: M λ g =1 t (n) = ln P (xg t (n) = s ˆx g t (n)) P (x g t (n) = 0 ˆx g (8) t (n)) for n = 1,,..., N, where s S. Using Bayes forula and dropping the constant ters in (8), we obtain M λ g =1 t (n) = ln P (ˆxg t (n) x g t (n) = s ) P (ˆx g t (n) x g (9) t (n) = 0) which requires the conditional statistics of ˆx g t (n) (zn(t)). g However, due to successive MMSE detection, the eleents of ˆx g t are still Gaussian distributed but have different ean and variance values. Let us consider the ean vector and covariance atrix of z g n conditioned on x g t (n) {0, S}, which are given as E {z g n} = W g nh g ne { x g n} = (W g nh g n) t x g t (n) cov(z g n) = W g nh g ncov ( x g n) (H g n) H (W g n) H +N 0,F W g n (W g n) H (10) where E { x g n} is an allzero vector except its tth eleent is x g t (n), and cov ( x g n) = E {( x gn E { x gn}) ( x gn E { x gn}) H} = diag ([ ]) σx... σx 0 σx... σx is a diagonal atrix whose tth diagonal eleent is zero. Fro (10), the conditional ean and variance of ˆx g t (n) are obtained as E {ˆx g t (n)} = (W g nh g n) t,t x g t (n) (11) var (ˆx g t (n)) = (cov(z g n)) t,t. (1) Cobining (9) and (1), the LLR for the nth subcarrier of tth transitter for subblock g can be calculated as λ g M ˆx g t (n) (WnH g g n) t,t s t (n)=ln exp (cov(z g + ˆxg t (n) n)) t,t (cov(z g (13) n)) t,t =1 for n = 1,,..., N, t = 1,,..., T and g = 1,,..., G. After the calculation of N LLR values for a given subblock g and transit antenna t, in order to deterine the indices of the active subcarriers, the LLR detector calculates the following LLR sus for c = 1,,..., C according to the lookup table: d g t (c) = K k=1 λg t (i c k ), where Ic = {i c 1, i c,..., i c K } denotes the possible active subcarrier index cobinations. As an exaple, for Table I, we have I 1 = {1, 3}, I = {, 4}, I 3 = {1, 4} and I 4 = {, 3}. The LLR detector deterines the active subcarriers for a given subblock g and transit antenna t as ĉ = arg ax c d g t (c) and

6 IEEE SIGNAL PROCESSING LETTERS 6 Î g t = { iĉ1, iĉ,..., iĉk}. The Mary sybols transitted by the active subcarriers are deterined with ML detection as ( ) ŝ g t (k) = arg in ˆx g t (iĉk) W g H g s s S iĉk iĉk (14) for k = 1,,..., K, where the etrics in (14) were calculated in (13) and do not increase the decoding coplexity. After this point, index selecting p 1 are recovered fro the lookup table and Mary sybols are deodulated to obtain the corresponding p inforation. The total nuber of CMs perfored in (6)(14) for the MIMOOFDMIM schee is T 3 + 5T R + T (R + M + 1) per subcarrier while this value is equal to T 3 + T R + T (R + M) for classical MIMOOFDM, where the decoding coplexity of both schees increases linearly with respect to M ( O(M)) due to MMSE detection. t,t IV. SIMULATION RESULTS In this section, we provide coputer siulation results for MIMOOFDMIM and classical VBLAST type MIMOOFDM schees eploying BPSK, QPSK and 16QAM (M =, 4 and 16) odulations and MMSE detection. We consider three different T R MIMO configurations:, 4 4 and 8 8. The following OFDM paraeters are assued in all Monte Carlo siulations: = 51, C p = 16, L = 10. In Fig., we copare the BER perforance of the proposed MIMOOFDMIM schee for N = 4, K = with classical MIMOOFDM for M = at sae spectral efficiency values. As seen fro Fig., the proposed schee provides significant BER perforance iproveent copared to classical MIMOOFDM, which increases with higher order MIMO systes. As an exaple, the MIMOOFDMIM schee achieves approxiately 10 db better BER perforance than classical MIMOOFDM at a BER value of 10 5 for the 8 8 MIMO syste. In Figs. and 3, we extend our siulations to higher spectral efficiency values and copare the BER perforance of the proposed MIMOOFDMIM schee (N = 4, K = 3) with classical MIMOOFDM for M = 4 and 16, respectively. As seen fro Figs. and 3, the proposed schee still aintains its advantage over classical MIMOOFDM in all considered configurations. It is interesting to note that the proposed schee has the potential to achieve close or better BER perforance than the reference schee, even using a lower order MIMO syste in ost cases. V. CONCLUSIONS AND FUTURE WORK A novel schee called MIMOOFDM with index odulation has been proposed as an alternative ulticarrier transission technique for 5G networks. It has been shown via extensive coputer siulations that the proposed schee can provide significant BER perforance iproveents over classical MIMOOFDM for several different configurations. The following points reain unsolved in this study: i) perforance analysis, ii) the selection of optial N and K values, iii) diversity techniques for MIMOOFDMIM, and iv) ipleentation scenarios for high obility. REFERENCES [1] J. Andrews, S. Buzzi, W. Choi, S. Hanly, A. Lozano, A. Soong, and J. Zhang, What will 5G be? IEEE J. Sel. Areas Coun., vol. 3, no. 6, pp , Jun [] E. Başar, Ü. Aygölü, E. Panayırcı, and H. V. Poor, Orthogonal frequency division ultiplexing with index odulation, IEEE Trans. Signal Process., vol. 61, no., pp , Nov [3] R. Abualhiga and H. Haas, Subcarrierindex odulation OFDM, in Proc. IEEE Int. Sy. Personal, Indoor and Mobile Radio Coun., Tokyo, Japan, Sep. 009, pp [4] D. Tsonev, S. Sinanovic, and H. Haas, Enhanced subcarrier index odulation (SIM) OFDM, in Proc. IEEE GLOBECOM Workshops, Dec. 011, pp [5] Y. Ko, A tight upper bound on bit error rate of joint OFDM and ulticarrier index keying, IEEE Coun. Lett., vol. 18, no. 10, pp , Oct [6] R. Fan, Y. Yu, and Y. Guan, Generalization of orthogonal frequency division ultiplexing with index odulation, IEEE Trans. Wireless Coun., vol. PP, no. 99, pp. 1 10, May 015. [7] M. Wen, X. Cheng, and L. Yang, Optiizing the energy efficiency of OFDM with index odulation, in IEEE Int. Conf. Coun. Systes, Nov. 014, pp

7 IEEE SIGNAL PROCESSING LETTERS 7 [8] W. Li, H. Zhao, C. Zhang, L. Zhao, and R. Wang, Generalized selecting subcarrier odulation schee in OFDM syste, in IEEE Int. Conf. Coun. Workshops, Jun. 014, pp [9] E. Başar, OFDM with index odulation using coordinate interleaving, IEEE Wireless Coun. Lett., vol. PP, no. 99, pp. 1 4, Apr [10] Y. Xiao, S. Wang, L. Dan, X. Lei, P. Yang, and W. Xiang, OFDM with interleaved subcarrierindex odulation, IEEE Coun. Lett., vol. 18, no. 8, pp , Aug [11] X. Cheng, M. Wen, L. Yang, and Y. Li, Index odulated OFDM with interleaved grouping for VX counications, in IEEE Int. Conf. Intelligent Transportation Systes, Oct. 014, pp [1] W. Zhang, X.G. Xia, and K. Ben Letaief, Spacetie/frequency coding for MIMOOFDM in next generation broadband wireless systes, IEEE Wireless Coun., vol. 14, no. 3, pp. 3 43, Jun [13] Y. Jiang, M. Varanasi, and J. Li, Perforance analysis of ZF and MMSE equalizers for MIMO systes: An indepth study of the high SNR regie, IEEE Trans. Inf. Theory, vol. 57, no. 4, pp , Apr Classical MIMOOFDM,x,1.94 /s/hz,ml Classical MIMOOFDM,x,1.94 /s/hz,mmse 10 1 Classical MIMOOFDM,4x4,3.88 /s/hz,mmse Classical MIMOOFDM,8x8,7.76 /s/hz,mmse MIMOOFDMIM,x,1.94 /s/hz,ml 10 MIMOOFDMIM,x,1.94 /s/hz,mmse MIMOOFDMIM,4x4,3.88 /s/hz,mmse MIMOOFDMIM,8x8,7.76 /s/hz,mmse BER SNR(dB) Fig.. Perforance coparison of MIMOOFDM and MIMOOFDMIM (N = 4, K = ) for BPSK odulation (M = ), MMSE/ML detection

8 IEEE SIGNAL PROCESSING LETTERS Classical MIMOOFDM,x,3.88 /s/hz Classical MIMOOFDM,4x4,7.76 /s/hz 10 1 Classical MIMOOFDM,8x8,15.5 /s/hz MIMOOFDMIM,x,3.38 /s/hz MIMOOFDMIM,4x4,7.76 /s/hz 10 MIMOOFDMIM,8x8,15.5 /s/hz BER SNR(dB) Fig. 3. Perforance coparison of MIMOOFDM and MIMOOFDMIM (N = 4, K = 3) for QPSK odulation (M = 4), MMSE detection 10 0 Classical MIMOOFDM,x,7.76 /s/hz Classical MIMOOFDM,4x4,15.5 /s/hz 10 1 Classical MIMOOFDM,8x8,31.03 /s/hz MIMOOFDMIM,x,6.79 /s/hz MIMOOFDMIM,4x4,13.58 /s/hz 10 MIMOOFDMIM,8x8,7.15 /s/hz BER SNR(dB) Fig. 4. Perforance coparison of MIMOOFDM and MIMOOFDMIM (N = 4, K = 3) for 16QAM (M = 16), MMSE detection