Generalized frequency division multiplexing method with multiple-input multiple-output and flexible index modulation

Abstract

A generalized frequency division multiplexing method with multiple-input multiple-output and flexible index modulation, which enables to have the energy efficiency provided by space and frequency index modulation systems with generalized frequency division multiplexing (GFDM) without complicating the transmitter and receiver structure and provide for the efficient use of frequency resources, increase in spectral efficiency, minimum complexity and increase in energy efficiency.

Claims

1. A generalized frequency division multiplexing method with multiple-input multiple-output and flexible index modulation, the method comprising the steps of: taking a generalized frequency division multiplexing (MIMO-GFDM) system with multiple-input multiple-output composed of T number of transmitters and R numbers of receiver antennas; then separating P number data bits to p-bit L groups each by a primary bit splitter, mapping p-bit in each group with a u-element subcarrier group; taking the p.sub.T=EN.sub.SM(1+EN.sub.QM)log.sub.2(T) bit part of p bits of data in the Tx Antenna selector block, wherein EN.sub.SM is a control signal used to control a spatial modulation (SM) mode in an on-off fashion, EN.sub.QM is a control signal used to control a quadrature spatial modulation (QM) mode in the on-off fashion, and EN.sub.SM and EN.sub.QM are equal to 0 or 1; defining the p bits as a binary number; determining a transmission antenna for the u-element subcarrier group at a transmitter antenna numbered by a decimal number corresponding to the binary number; the subcarrier index selector block taking p.sub.IM bits and choosing the p.sub.IM bits as subcarrier indexes indicated by I.sub.l.sup.A={i.sub.l,1.sup.A, i.sub.l,2.sup.A, . . . , i.sub.l,v.sup.A} in a primary subcarrier group according to a selection rule, wherein the p.sub.IM bits are index modulation (IM) bits, and A refers to a primary IM subgroup; then choosing remaining bits of p-bit data and QAM symbols to be assigned to the subcarriers; generating a generalized frequency division multiplexing (GFDM) symbol by bringing u-element L number of groups together; then, making a N.sub.CP-length cyclic prefix addition in order to convert a linear convolutional effect of the channel to a cyclic convolution; performing a cyclic prefix removal at the receiver; operating a near optimum decision rule with a maximum likelihood-successive interference cancellation (ML-SIC) technique in order to determine data transmitted at the receiver with maximum precision; then, obtaining a p-bit array for each space-frequency index modulation block at a secondary bit combiner; finally, obtaining the P bit input information bits by combining the p bit arrays with a primary bit combiner.

2. The method according to claim 1, wherein, a single antenna is configured to broadcast at a same time at one frequency channel.

3. The method according to claim 1, further comprising: realizing, a transition between different space-frequency index modulations by means of mode control signals.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The elements which take place in the multiple-input multiple-output generalized frequency division multiplexing method with flexible index modulation realized in order to achieve the purposes of this invention have been shown in the attached figures.

(2) These figures are;

(3) FIG. 1 shows a diagrammatic view of the transmitter structure used in the method of the subject invention.

(4) FIG. 2 shows a diagrammatic view of the receiver structure used in the method of the subject invention.

(5) FIG. 3 shows a view of the block diagram of ML-SIC MIMO Detection, GFDM and Space-Frequency Index Demodulation used in the method of the subject invention.

(6) FIG. 4a shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and methods for 2×2, SM, using 4-QAM.

(7) FIG. 4b shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and methods for 4×4 SM, using 4-QAM.

(8) FIG. 5a shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for 2×2, QSM, using 4-QAM.

(9) FIG. 5b shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for 4×4 QSM, using 4-QAM.

(10) FIG. 6a shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for 2×2, SFIM, using 4-QAM.

(11) FIG. 6b shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for, 4×4 SFIM, using 4-QAM.

(12) FIG. 7a shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for 2×2, QSFIM, using 4-QAM.

(13) FIG. 7b shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for, 4×4 QSFIM, using 4-QAM.

(14) FIG. 8a shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for 2×2, SFDMIM, using 4-QAM.

(15) FIG. 8b shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for 4×4 SFDMIM, using 4-QAM.

(16) FIG. 9a shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for 2×2, QSFDMIM, using 4-QAM.

(17) FIG. 9b shows a view of the uncoded bit error rate performance of the ZF-SDD, MMSE-JDD, ML-SIC and ML methods for 4×4 QSFDMIM, using 4-QAM.

(18) FIG. 10 shows a view of the uncoded bit error rate performance of the ML-SIC method in 4×4 MIMO configurations of the SM, IM and QAM modulation parts of the SFIM-GFDM receiver, using 4-QAM.

(19) FIG. 11 shows a view of the uncoded bit error rate performance of the ML-SIC method in 4×4 MIMO configuration of the MIMO-GFDM-FIM system using 4-QAM, for convolutional channel coded different spectral efficiencies.

(20) FIG. 12 shows a view of the uncoded bit error rate performance of the ML-SIC method in MIMO configuration of the MIMO-GFDM-FIM system using 4-QAM, for convolutional channel coded 3.81 bit/s/Hz spectral efficiency.

(21) The elements in the figures have been numbered one by one and their references are given below.

(22) 1. Primary bit splitter

(23) 2. Secondary bit splitter

(24) 3. Tx Antenna selector

(25) 4. Index selector

(26) 5. Mapper A

(27) 6. Mapper B

(28) 7. FIM block generator

(29) 8. GFDM block generator

(30) 9. Block inter leaver

(31) 10. GFDM modulator

(32) 11. Cyclic prefix addition

(33) 12. Cyclic prefix removal

(34) 13. MIMO detection GFDM and space-frequency demodulation

(35) 14. Tx Antenna demapper

(36) 15. Index demapper

(37) 16. Q-ary Demapper A

(38) 17. Q-ary Demapper B

(39) 18. Secondary bit combiner

(40) 19. Primary bit combiner

(41) 20. QR decomposer

(42) 21. UFIM block ML detector

(43) 22. UFIM block re-creater

(44) 23. UFIM block dispatcher

DETAILED DESCRIPTION OF THE EMBODIMENTS

(45) The invention brings the space and frequency index modulation techniques together in an efficient way and combines these techniques with generalized frequency division multiplexing (GFDM) in the most eligible way.

(46) The subject method comprises the steps of; Taking a generalized frequency division multiplexing (MIMO-GFDM) system with multiple-input multiple-output composed of T number of transmitter antennas and R numbers of receiver antennas, Then separating the P number of data bits to L groups of p-bit each with the primary bit splitter (1), Mapping p-bit in each group to a subcarrier group with u elements, Taking the p.sub.T=EN.sub.SM(1+EN.sub.QM)log.sub.2(T) bit part of p-bit data in the Tx Antenna selector (3) block, Defining these bits as a number in the binary number order, Determining the transmission antenna for the subcarrier group with u-elements at the transmitter antenna numbered by a decimal number corresponding to this binary number, The subcarrier index selector (4) block taking p.sub.IM bits and choosing these bits as the subcarrier indexes indicated by I.sub.l.sup.A={i.sub.l,1.sup.A, i.sub.l,2.sup.A, . . . i.sub.l,v.sup.A} which will take place in the primary subcarrier group according to a selection rule. Then choosing the remaining bits of p-bit data and the QAM symbols to be assigned to the subcarriers, Generating the GFDM symbol by bringing L groups with u-elements together, Then, making the N.sub.CP-length cyclic prefix addition (11) in order to convert the linear convolution effect of the channel to cyclic convolution, Performing cyclic prefix removal (12) at the receiver, Operating the near optimum decision rule with the ML-SIC technique in order to determine the data transmitted at the receiver with maximum likelihood, Then, obtaining p-bit stream for each space-frequency index modulation block at the secondary bit combiner (18), Finally, obtaining the P bit input information bits by combining p-bit of streams with the primary bit combiner (19).

(47) As mentioned before, more than one timeslot is allowed at each subcarrier in GFDM. For this reason, in a GFDM symbol composed of K number of subcarriers, M number of timeslots are the number of timeslots allowed in each subcarrier and the total sample number in a GFDM symbol is N=KM. In other words, a GFDM symbol is composed of M number of sub-symbols. In the proposed method, a MIMO-GFDM system of T number of transmitter and R number of receiver antennas is addressed. The transmitter has four control signals named EN.sub.SM, EN.sub.QM, EN.sub.IM and EN.sub.DM. These control signals can take 0 and 1 value and they are used to control the SM, QSM, IM and double mode index modulation (DMIM) operating modes on-off respectively.

(48) All the parameters in the method of the subject invention are shown in Table-1. The operation modes to be applied according to the condition of the control signals can be seen in Table-2. By means of these control signals, all the operation modes seen in Table-2 can be performed with a single transmitter.

(49) The block diagram of the transmitters in the method of the subject invention is seen in FIG. 1. The primary bit splitter (1) takes P number of data bits from the input together with the control signals given in Table-2 and splits this P number of data bits to L groups of p-bit each. p bits in each group will be mapped to a subcarrier group with u-elements by a three-stage process. In this mapping process, the antenna index, the subcarrier index and QAM symbols will be used together. In addition, QAM symbols will be separated into their in-phase and quadrature phase components. In order to provide this mapping, the secondary bit splitter (2) splits p number of bits into four groups as p.sub.T, p.sub.IM, p.sub.A and p.sub.B according to the condition of the control signals.

(50) TABLE-US-00001 TABLE 1 System Parameters Description Parameter Transmitter antenna number T Receiver antenna number R Subcarrier number in the GFDM sub-symbol K GFDM sub-symbol number M Total subcarrier number in the GFDM symbol N SM mode control signal EN.sub.SM QSM mode control signal EN.sub.QM IM mode control signal EN.sub.IM DMIM mode control signal EN.sub.DM Subcarrier number in the subcarrier index group u Subcarrier number in the subcarrier primary index group v Subcarrier number in the subcarrier secondary index group u − v Subcarrier index group number L Primary signal constellation S.sup.A Secondary signal constellation S.sup.B Element number in the primary signal constellation Q.sub.A Element number in the secondary signal constellation Q.sub.B

(51) TABLE-US-00002 TABLE 2 Flexible Index Modulation Control Table Mode EN.sub.SM EN.sub.QM EN.sub.IM EN.sub.DM GFDM 0 0 0 0 GFDM-IM 0 0 1 0 GFDM-DMIM 0 0 1 1 SM-GFDM 1 0 0 0 QSM-GFDM 1 1 0 0 SFIM-GFDM 1 0 1 0 QSFIM-GFDM 1 1 1 0 SFDMIM-GFDM 1 0 1 1 QSFDMIM-GFDM 1 1 1 1

(52) The first stage of the mapping procedure is determining the antenna index. In this stage, the transmitter antenna selector (3) block takes the
p.sub.T=EN.sub.SM(1+EN.sub.QM)log.sub.2(T)  (1)
bit part of the p-bit data, accepts these bits as a number in the binary number order and chooses the transmitter antenna (3) numbered by a decimal number corresponding to this binary number as the transmission antenna for the subcarrier group with u-elements. If both SM and QSM modes are active, which means EN.sub.SM=1, EN.sub.QM=1, the first log.sub.2(T) bit part of the p.sub.T-bit is used to determine t.sub.l.sup.R, which is the antenna which will transmit the in-phase part of the modulated signals and the second log.sub.2(T) bit part is used to determine t.sub.l.sup.I, which is the antenna which will transmit the quadrature phase part of the modulated signals. Here, t.sub.l.sup.R, t.sub.l.sup.I∈{1, . . . , T}. If the QSM mode is not going to be used, which means if EN.sub.QM=0, only t.sub.l.sup.R is determined and this antenna is used for the transmission of both in-phase and quadrature phase parts of the modulated signals. When the SM mode is not used, which means EN.sub.SM=0, the transmitter antenna selector block is disabled and transmission is constantly realized through a pre-determined antenna.

(53) The second stage of the mapping is the subcarrier index selection stage. This stage operates when the IM mode is active, which means EN.sub.IM=1. In this stage, the subcarrier index selector (4) block takes p.sub.IM bits and uses these bits according to a selection rule in order to select the subcarrier indexes which will take place in the primary subcarrier sub-group shown by
I.sub.l.sup.A={i.sub.l,1.sup.A,i.sub.l,2.sup.A, . . . ,i.sub.l,v.sup.A}.  (2)

(54) Here, i.sub.l,γ.sup.A∈{1, . . . u}, γ=1, . . . v, and l∈{1, . . . L}. The subcarriers chosen by I.sub.l.sup.A determine v number of subcarriers. If the DMIM mode is used together with the IM mode, which means EN.sub.DM=1, the remaining u−v number of subcarriers form the secondary subcarrier sub-group shown by
I.sub.l.sup.B={i.sub.l,1.sup.B,i.sub.l,2.sup.B, . . . ,i.sub.l,u−v.sup.B}.  (3)

(55) Here, i.sub.l,γ.sup.B∈{1, . . . u}, γ=1, . . . u−v, and l∈{1, . . . L}. Since I.sub.l.sup.A can take c=2.sup.p.sup.IM possible values, only c number of the C (u, v) combinations can be used. Therefore p.sub.IM is determined as
p.sub.IM=EN.sub.IM└log.sub.2(C(u,v))┘.  (4)

(56) If the IM mode is not active, the subcarrier index selector (4) block cannot be active, in this case, u=1 and all the subcarriers are used without a selection.

(57) The third stage of mapping is QAM modulation stage. At this stage, in order to modulate the subcarriers chosen by I.sub.l.sup.A, mapper A (5) takes p.sub.A number of bits and uses S.sup.A signal constellation with the Q.sub.A-elements to modulate v number of subcarriers. Therefore p.sub.A is defined as
p.sub.A=v log.sub.2(Q.sub.A).  (5)

(58) If the DMIM mode is active together with the IM mode, which means EN.sub.DM=1, mapper B (6) takes p.sub.B number of bits in order to modulate the subcarriers chosen by I.sub.l.sup.B and uses the S.sup.B signal constellation with Q.sub.B-elements in order to modulate u−v number of subcarriers. Therefore p.sub.B is defined as
p.sub.B=EN.sub.IMEN.sub.DM(u−v)log.sub.2(Q.sub.B).  (6)

(59) At this point, in order to detect the subcarrier index sub-groups at the receiver healthily, the intersection of the signal constellations used by the mapper A (5) and mapper B (6) should be empty set, which means, S.sup.A∩S.sup.B should be Ø.

(60) As a result, the vector of the modulated symbols mapped by mapper A (5) for the index subgroup I.sub.l.sup.A, which carries p.sub.A bits, and the vector of the modulated symbols mapped by mapper B (6) for the index subgroup I.sub.l.sup.B, which carries p.sub.B bits, can be expressed by:
s.sub.l.sup.A=[s.sub.l.sup.A(1),s.sub.l.sup.A(2), . . . ,s.sub.l.sup.A(v)].sup.T,  (7)
s.sub.l.sup.B=[s.sub.l.sup.B(1),s.sub.l.sup.B(2), . . . ,s.sub.l.sup.B(u−v)].sup.T.  (8)

(61) Here, s.sub.l.sup.A(γ)∈S.sup.A, γ=1, . . . , v, s.sub.l.sup.B(γ)∈S.sup.B, γ=1, . . . , u−v. If paid close attention, when the IM mode is not active, which means EN.sub.IM=0, u=1, v=1 and s.sub.l.sup.A includes only one QAM signal, s.sub.l.sup.B is null vector. Then, FIM Block generator (7) combines s.sub.l.sup.A and s.sub.l.sup.B and obtains the signal vector for subcarrier group l as in the following:
s.sub.l=[s.sub.l(1),s.sub.l(2), . . . ,s.sub.l(u)].sup.T.  (9)

(62) Here, s.sub.l(γ)∈{S.sup.A, S.sup.B, 0} and γ=1, . . . , u. In Table 3, an exemplary subcarrier index sub-groups placement for u=4, v=2 is seen. When the DMIM mode is not active, in subcarrier index sub-groups, s.sub.l.sup.B(1) and s.sub.l.sup.B (2) elements will be 0.

(63) The next step of selecting transmitter antenna is performed according to the condition of the EN.sub.QM control signal. When the QSM mode is active, which means EN.sub.QM=1, the in-phase part of s.sub.l is assigned to the transmitter antenna determined by t.sub.l.sup.R, the quadrature phase part is assigned to the antenna determined by t.sub.l.sup.I:
s.sub.t.sub.l.sub.R.sub.,l=[s.sub.t.sub.l.sub.R.sub.,l(1),s.sub.t.sub.l.sub.R.sub.,l(2), . . . ,s.sub.t.sub.l.sub.R.sub.,l(u)].sup.T,  (10)
s.sub.t.sub.l.sub.I.sub.,l=[s.sub.t.sub.l.sub.I.sub.,l(1),s.sub.t.sub.l.sub.I.sub.,l(2), . . . ,s.sub.t.sub.l.sub.I.sub.,l(u)].sup.T.  (11)

(64) TABLE-US-00003 TABLE 3 Subcarrier Active Index Determining Table for u = 4, v = 2 Bits Indexes Sub carrier Index Subgroups [0 0] {1, 2} [s.sub.l.sup.A (1) s.sub.l.sup.A (2) s.sub.l.sup.B (1) s.sub.l.sup.B (2)] [0 1] {2, 3} [s.sub.l.sup.B (1) s.sub.l.sup.A (1) s.sub.l.sup.A (2) s.sub.l.sup.B (2)] [1 0] {3, 4} [s.sub.l.sup.B (1) s.sub.l.sup.B (2) s.sub.l.sup.A (1) s.sub.l.sup.A (2)] [1 1] {1, 4} [s.sub.l.sup.A (1) s.sub.l.sup.B (1) s.sub.l.sup.B (2) s.sub.l.sup.A (2)]

(65) Here, s.sub.t.sub.l.sub.R.sub.,l(γ)∈{Re{S.sup.A}, Re{S.sup.B}, 0}, t.sub.l.sup.R=1, . . . , T, s.sub.t.sub.l.sub.I.sub.,l(γ)∈{Im{S.sup.A}, Im{S.sup.B}, 0}, t.sub.l.sup.I=1, . . . , T, γ=1, . . . , u. On the other hand, when the QSM mode is not active, which means EN.sub.QM=0, both the in-phase and quadrature phase of s.sub.l is assigned to t.sub.l.sup.R. Then, the FIM block generator (7) makes assignment to the subcarriers of the non-selected antennas as 0 and arranges the transmission signals for the lth block as D.sub.l, which is a T×u type matrix. Here, the t.sub.l.sup.Rth row of D.sub.l is s.sub.t.sub.l.sub.R.sub.,l and the t.sub.l.sup.Ith row is s.sub.t.sub.l.sub.I.sub.,l. Then, the GFDM block generator (8) combines FIM blocks and obtains
D=[D.sub.1,D.sub.2, . . . D.sub.L].  (12)

(66) Here, the dimension of the D matrix is T×N. As a result, the GFDM symbol for tth transmission antenna is shown as
d.sub.t=[d.sub.t,0,0, . . . ,d.sub.t,K-1,0,d.sub.t,0,1, . . . ,d.sub.t,K-1,1, . . . ,d.sub.t,0,M-1, . . . ,d.sub.t,K-1,M-1].  (13)

(67) Here, (13) is the tth row vector of the D matrix and d.sub.t,k,m is the data symbol of mth timeslot on kth subcarrier belonging to tth antenna. The next stage is the block interleaving stage which takes place at the block inter leaver (9). Block interleaving is used for rendering the channel without memory by segmenting the interdependent errors at the channel. For this reason, when the IM mode is active, which means when EN.sub.IM=1, L×u dimension block interleaving is applied to d.sub.t, which is the GFDM symbol for each antenna and {tilde over (d)}.sub.t is obtained. After the block interleaving, {tilde over (d)}.sub.t vector is modulated by the GFDM modulator (10) and the final GFDM transmission signal of the tth antenna is obtained as
x.sub.t(n)=Σ.sub.k=0.sup.K-1Σ.sub.m=0.sup.M-1{tilde over (d)}.sub.t,k,mg.sub.k,m(n).  (14)

(68) Here, n∈{0, . . . , N−1} is the sampling index and

(69) $\begin{array}{cc}{g}_{k,m}\left(n\right)=g\left({\left(n-\mathrm{mK}\right)}_{\mathrm{modN}}\right)\exp \left(j2\pi \frac{\mathrm{kn}}{K}\right)& \left(15\right)\end{array}$
is a transmission filter circularly shifted to the mth timeslot and modulated to the kth subcarrier. If the filter samples are collected in a vector such as g.sub.k,m=[g.sub.k,m(0), . . . g.sub.k,m(N−1)].sup.T, (14) equation can be rephrased as
x.sub.t=A{tilde over (d)}.sub.t.  (16)

(70) Here, A matrix is a GFDM transmitter matrix in KM×KM dimensions in the following structure:
A=[g.sub.0,0, . . . g.sub.K-1,0,g.sub.0,1, . . . g.sub.K-1,1, . . . ,g.sub.0,M-1, . . . ,g.sub.K-1,M-1].  (17)

(71) The final stage at the transmitter is the N.sub.CP-length cyclic prefix addition (11) stage in order to convert the linear convolution effect of the channel to the cyclic convolution. After the cyclic prefix addition (11), the final GFDM symbols of
{tilde over (x)}.sub.t=[x.sub.t(KM−N.sub.CP+1:KM).sup.T,x.sub.t.sup.T].sup.T  (18)
are obtained. Finally, {tilde over (x)}.sub.t is transmitted over a frequency selective Rayleigh fading channel. The receiver block scheme used in the subject method is shown in FIG. 2. Cyclic prefix removal (12) is performed as the first stage at the receiver. Following the cyclic prefix removal (12), by accepting that the wireless transmission channel features do not change during the GFDM symbol transmission, the cyclic prefix (CP) length is longer than the channel coefficients (N.sub.Ch) and that full synchronization is provided, the signal coming to the receiver can be shown as

(72) $\begin{array}{cc}\left[\begin{array}{c}{y}_1\\ \mathrm{.Math.}\\ y_R\end{array}\right]=\left[\begin{array}{ccc}{H}_{1,1}& \mathrm{.Math.}& H_{1,T}\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ H_{R,1}& \mathrm{.Math.}& H_{R,T}\end{array}\right]\left[\begin{array}{c}{x}_1\\ \mathrm{.Math.}\\ x_T\end{array}\right]+\left[\begin{array}{c}{w}_1\\ \mathrm{.Math.}\\ w_R\end{array}\right].& \left(19\right)\end{array}$

(73) Here, y.sub.r=[y.sub.r(0), y.sub.r(1), . . . , y.sub.r(N−1)] is the signal received at the rth receiver antenna, H.sub.r,t, t=1, . . . , T, r=1, . . . , R is the N×N dimension circular convolution matrix generated by the channel impulse response coefficients given by h.sub.r,t=[h.sub.r,t(0), h.sub.r,t(1), . . . , h.sub.r,t(N.sub.Ch−1)].sup.T between the tth transmitter antenna and rth receiver antenna and w.sub.r is the additive white Gaussian noise (AWGN) vector whose NT×1 dimension elements have CN (0,σ.sub.w.sup.2) distribution. Here, h.sub.r,t(n), has CN (0, 1) distribution. If Eq. 16 is put in place in the Eq. 19,

(74) $\begin{array}{cc}\left[\begin{array}{c}{y}_1\\ \mathrm{.Math.}\\ y_R\end{array}\right]=\left[\begin{array}{ccc}{H}_{1,1}A& \mathrm{.Math.}& H_{1,T}A\\ \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ H_{R,1}A& \mathrm{.Math.}& H_{R,T}A\end{array}\right]\left[\begin{array}{c}{\tilde{d}}_1\\ \mathrm{.Math.}\\ {\tilde{d}}_T\end{array}\right]+\left[\begin{array}{c}{w}_1\\ \mathrm{.Math.}\\ w_R\end{array}\right]& \left(20\right)\end{array}$
is obtained. Eq. 20 can simply be shown as
y={tilde over (H)}{tilde over (d)}+w.  (21)

(75) Here, dimensions of y, {tilde over (H)}, {tilde over (d)} and w are NR×1, NR×NT, NT×1 and NR×1, respectively.

(76) The most critical part of the receiver is the part where the MIMO signal detection, GFDM and space-frequency index demodulation (13) procedures are realized.

(77) The optimum decision rule for the proposed method is to select the ones which have the greatest likelihood from the antenna index, subcarrier index and QAM signals used in the transmission by observing the received signal and channel coefficients. In the MIMO-OFDM application, the orthogonality between the subcarriers enables for applying the optimum decision rule independently for each subcarrier. In GFDM, the interference between the subcarriers prevents the independent operation of the optimum decision rule for each subcarrier, therefore, in MIMO-GFDM application, the optimum decision rule is needed to be operated by considering all the subcarriers. However, in this case, a processing complexity which cannot be handled takes place. The ML-SIC (Maximum Likelihood-Successive Interference Cancellation) detection technique proposed as a part of the proposed method reduces this complexity and enables for operating a near-optimal decision rule which jointly decides the antenna index, subcarrier index and QAM signals used in the transmission and which processes all the subcarriers together.

(78) The block scheme of the proposed ML-SIC detection method is in FIG. 3. QR decomposition of the channel matrix {tilde over (H)} is
{tilde over (H)}=QRP.sup.T,  (22)
where Q matrix is an NR×NT dimension unitary matrix, R matrix is a NT×NT dimension upper triangular matrix, P matrix is a permutation matrix which enables arranging the rows of the {tilde over (H)} matrix before analysis in order to provide for deciding the transmitted signals based on the “space-frequency index modulation block” (UFIMB). If block interleaving is applied at the transmitter, before arranging the H matrix rows based on UFIMB, block deinterleaving should be applied. The process presented in the block scheme is described below.

(79) QR decomposer (20) combines the signals received from the antennas first and obtains the y=[y.sub.1.sup.T, y.sub.2.sup.T, . . . , y.sub.R.sup.T].sup.T vector. Then obtains the
{tilde over (y)}=Q.sup.Hy=R{tilde over (d)}+{tilde over (w)}  (23)
vector which is the received signal vector altered by applying multiplication from left with Q.sup.H.

(80) Here, {tilde over (w)}=Q.sup.Hw, {tilde over (d)} is the arranged form of the transmission vector d based on UFIMB:
{tilde over (d)}=P.sup.Td=[z.sub.1.sup.T,z.sub.2.sup.T, . . . ,z.sub.L.sup.T].sup.T.  (24)

(81) Here, z.sub.l the space-frequency index modulation block is (UFIMB):
z.sub.l=[s.sub.1,l,s.sub.2,l, . . . ,s.sub.T,l].  (25)

(82) In the Eq. 25, s.sub.t,l (t=1, . . . , T and l∈{1, . . . , L}) is a u×1 dimension vector:
s.sub.t,l=[s.sub.t,l[1],s.sub.t,l[2], . . . ,s.sub.t,l[u]]=[d.sub.t((l−1)u+1:lu),  (26)
which means UFIMB is a vector which is formed by lining the index modulation samples of each antenna under one another. Since the index modulation group has u number of elements, in UFIMB, u*T numbers of samples are present. As indicated before, when the IM mode is disabled, u=1, s.sub.t,l includes only one element.

(83) In the next step, the detection procedure is started by making use of the upper triangle feature of the R matrix on the Eq. 23. First, space-frequency block (UFIM) ML (maximum likelihood) detector (21) finds the most likely solution for the last UFIMB, UFIM block recreator (22) uses this solution and obtains the transmit signal of the related UFIMB. Then, this signal is extracted from the signal coming to the receiver and the interference caused by UFIMB is eliminated. After that, system reduces its dimension by uT times and skips to the UFIMB second to the last. This procedure is applied for all UFIMBs. During the procedure, the outputs of each UFIMB are stored by the UFIM block dispatcher (23).

(84) The ML-SIC detection algorithm of the proposed method is given in Algorithm-1.

(85) In this algorithm, uT shows the last uT part, uT shows the part outside the last uT part and: shows all the elements of the indexed object. When running the algorithm is completed, for each UFIMB, the transmitter antennas, subcarrier index sub-groups and transmission constellation signals corresponding to the in-phase and quadrature phase transmission signals for each UFIMB are respectively detected as {circumflex over (t)}.sub.l.sup.R, {circumflex over (t)}.sub.l.sup.I, Î.sub.l.sup.A, ŝ.sub.l.sup.A, ŝ.sub.l.sup.B.

(86) After the MIMO signal detection, GFDM and space-frequency index demodulation (13) are complete, information bits corresponding to {circumflex over (t)}.sub.l.sup.R, {circumflex over (t)}.sub.l.sup.I, Î.sub.l.sup.A, ŝ.sub.l.sup.A, ŝ.sub.l.sup.B are obtained by the demapping procedure. First, {circumflex over (t)}.sub.l.sup.R and {circumflex over (t)}.sub.l.sup.I estimation values are converted to p.sub.T number of bits by the Tx Ant. demapper (14). The Î.sub.l.sup.A estimation value is converted to p.sub.IM number of bits by index demapper (15). The v number of QAM symbols in the ŝ.sub.l.sup.A vector is converted to p.sub.A number of bits by the Q-ary demapper A (16). The u−v number of QAM symbols in the ŝ.sub.l.sup.B vector is converted to p.sub.B number of bits by the Q-ary demapper B (17). Then, the secondary bit combiner (18) obtains the p-bit array for each space-frequency index modulation block. The last stage is obtaining P bit input information bits by combining p-bit arrays with the primary bit combiner (19).

(87) TABLE-US-00004 Algorithm 1: ML-SIC detection  8. Input = {tilde over (y)}, R  9. Output = {circumflex over (t)}.sub.l.sup.R, {circumflex over (t)}.sub.l.sup.I, Î.sub.l.sup.A, Î.sub.l.sup.B, ŝ.sub.l.sup.A, ŝ.sub.l.sup.B for l = 1, ..., L 10. For l←L to 1 do  ${\hat{z}}_l=\underset{t,I^A,S^A,S^B}{\arg \min }{.Math.{\tilde{y}}_{\mathrm{uT}}-R_{\mathrm{uT},\mathrm{uT}}{z}_l.Math.}^2$ 12.  ŷ.sub.l = R.sub.:,uT{circumflex over (z)}.sub.l, {tilde over (y)} ← {tilde over (y)} − ŷ.sub.l 13.  {tilde over (y)} ← {tilde over (y)}.sub.uT, R ← R.sub.uT,uT 14. end for

(88) Computer Simulation Results:

(89) The bit error rate (BER) performance of the proposed method belong to the invention is obtained through Monte Carlo simulations. The algorithm of the proposed method for computer simulations which realizes the technical features described above in detail is written and the bit error rate calculation has been realized in computer environment. In the simulations, Extended Pedestrian Model-A, (EPA-A) channel model prepared for the Rayleigh channel is used.

(90) The error performance of the MIMO-GFDM-FIM method proposed by the computer simulations realized, have been compared with the OFDM system having the ML receiver structure and the GFDM systems having the ZF-SDD and MMSE-JDD receiver structures present in the literature. In the simulations, binary phase shift keying (BPSK), 4-ary quadrature amplitude modulation (4-QAM), 8-ary quadrature amplitude modulation (8-QAM) and 16-ary quadrature amplitude modulation (16-QAM) in the present standards have been used. The T transmitter and R receiver antenna (T×R) MIMO systems considered are 2×2 and 4×4 (two-each and four-each transmitter/receiver antenna systems). The coded channels and uncoded channels in the method of the invention have been dealt with separately. Simulation parameters shown in Table 4.

(91) TABLE-US-00005 TABLE 4 Other parameters used in the simulations Description Parameter Value GFDM subcarrier number K 128 GFDM sub-symbol number M 5 Pulse Shaping Filter g Raised Cosine (RC) Cyclic prefix length N.sub.CP 32 Roll-Off factor a 0.1

(92) In FIG. 4-9, the uncoded BER performances for SM, QSM, SFIM, QSFIM, SFDMIM and QSFDMIM MIMO-GFDM structures of the subject method respectively by using 4-QAM in the 2×2 and 4×4 transmitter-receiver antenna configurations are given. The dimensions of the MIMO system used and the spectral efficiency values have been indicated in the related figures. With the purpose of comparison, BER performances of the same MIMO-OFDM applications for the same modulation and transmitter/receiver antenna numbers are shown in the figures. The receiver structure proposed in the method of the invention ML-SIC and the signal to noise ratio (SNR) gains provided for 10.sup.−4 BER value (in decibel, dB) is given in Table 5.

(93) As can be seen from this table and figures, the ML-SIC method proposed in all scenarios considered reduces the SNR value (transmitter transmission power) which is necessary in order to reach a target BER value according to the receiver structures in the literature. The considerable BER gains obtained by the proposed ML-SIC method results from deciding the antenna index, active subcarrier index and QAM symbols jointly with a near optimum decision rule and the high diversity value of the ML-SIC method. In addition, almost the same BER performance can be obtained with the same MIMO-OFDM configuration. By this means, thanks to the lower out-of-band emission and reduced cyclic prefix compared to MIMO-OFDM, a higher spectral efficiency is obtained. For the reference values in Table-4, the spectral efficiency increases obtained thanks to the cyclic prefix reduced in comparison to OFDM with GFDM is 19%.

(94) In order for the method proposed and the other methods to be realized at the receiver, the complex multiplication numbers are given in Table-6. According to Table-6, while the ML and ZF-SDD receiver structure have the highest and lowest complexity, respectively, ML-SIC and MMSE-JDD methods are intermediate solutions in terms of complexity. From these results, it is seen that the ML-SIC method provides a trade-off between complexity and BER performance.

(95) TABLE-US-00006 TABLE 5 Signal to noise ratio (SNR) gains the method of the subject invention enables a 10.sup.−4 bit error rate (BER) value compared to the other methods (in decibel (dB)) Gain Obtained Against Gain Obtained Against Structure/Method ZF-SDD Method MMSE-JDD Method 2 × 2 SM 18.1 13.7 4 × 4 SM 28.7 21 2 × 2 QSM 18.2 13.8 4 × 4 QSM 28.8 21.2 2 × 2 SFIM 25.7 13.4 4 × 4 SFIM 32.8 15.8 2 × 2 QSFIM 25.8 13.5 4 × 4 QSFIM 32.9 15.9 2 × 2 SFDMIM 21.2 15.9 4 × 4 SFDMIM 29.2 20.4 2 × 2 QSFDMIM 21.3 16.0 4 × 4 QSFDMIM 29.3 20.5

(96) TABLE-US-00007 TABLE 6 Complex multiplication numbers necessary for realizing the methods at the receiver Structure/Method ZF-SDD MMSE-JDD ML-SIC ML 2 × 2 SM 2.49 × 10.sup.6 6.31 × 10.sup.9  4.21 × 10.sup.9  1 × 10.sup.581 4 × 4 SM 5.09 × 10.sup.6 5.04 × 10.sup.10 3.36 × 10.sup.10 1 × 10.sup.783 2 × 2 QSM  2.5 × 10.sup.6 6.31 × 10.sup.9  4.21 × 10.sup.9  1 × 10.sup.783 4 × 4 QSM 5.21 × 10.sup.6 5.04 × 10.sup.10 3.36 × 10.sup.10 .sup. 1 × 10.sup.1157 2 × 2 SFIM 2.64 × 10.sup.6 6.30 × 10.sup.9  4.21 × 10.sup.9  1 × 10.sup.341 4 × 4 SFIM  5.7 × 10.sup.6 5.04 × 10.sup.10 3.36 × 10.sup.10 1 × 10.sup.389 2 × 2 QSFIM  2.8 × 10.sup.6 6.31 × 10.sup.9  4.21 × 10.sup.9  1 × 10.sup.389 4 × 4 QSFIM 7.67 × 10.sup.6 5.04 × 10.sup.10 3.36 × 10.sup.10 1 × 10.sup.485 2 × 2 SFDMIM  5.1 × 10.sup.6 6.31 × 10.sup.9  4.22 × 10.sup.9  1 × 10.sup.533 4 × 4 SFDMIM 1.55 × 10.sup.7 5.04 × 10.sup.10 3.37 × 10.sup.10 1 × 10.sup.581 2 × 2 QSFDMIM 7.72 × 10.sup.6 6.31 × 10.sup.9  4.23 × 10.sup.9  1 × 10.sup.581 4 × 4 QSFDMIM  4.7 × 10.sup.7 5.04 × 10.sup.10 3.38 × 10.sup.10 1 × 10.sup.677

(97) In the method of the subject invention, the SM, IM and QAM modulations can be positioned as three distinct layers. As can be seen in FIG. 10, the SM part consumes 2 dB less power according to the total bit error performance and enables to reach 1×10.sup.−4 bit error rate. By this means, with the proper conditioning of the primary bit splitter (1) and secondary bit splitter (2) blocks at the transmitter, the bits which need to be transmitted with high safety are directed at the antenna indexes and an additional gain can be provided.

(98) In FIG. 11, a convolutional channel coded bit error rate performance of the method of the invention in 4×4 MIMO configurations for ML-SIC method using 4-QAM is seen. The generator sequence of the channel coding is [133, 171, 165]. As can be seen from FIG. 11, when channel coding is applied, a BER gain between 5.4 and 8.1 dB based on the uncoded condition is obtained.

(99) In FIG. 12, the coded BER performance of the subject method is observed for 3.81 bit/s/Hz spectral efficiency. As can be seen from FIG. 12, BER performance in the subject method is better at 4×4 configurations as independent from the modulation level. From this point of view, it can be said that in the ML-SIC method BER performance, the receiver antenna number is the main determinant.

(100) From these results, it can be seen that the SM, QM, IM, DMIM modes are applicable to the GFDM system. The proposed ML-SIC method provides a significant BER gain compared to the present methods in the literature. This gain results from the near optimal detection structure of the ML-SIC method.

(101) In the method of the subject invention, by means of the pulse shaping applied in GFDM, the out-of-band emission is lower compared to OFDM. In OFDM, rectangular pulse is used as the pulse form in the time domain. The equivalent of the rectangular pulse in the frequency domain is in the “sinc” signal form. For this reason, the out-of-band emission in OFDM is disturbingly high and a space should be left between neighboring systems at the frequency spectrum. This causes the inefficient use of the frequency spectrum. In GFDM, pulse shaping which has a low out-of-band emission such as Raised Cosine (RC) or Root Raised Cosine (RRC) is used. By this means, the need to leave a space between neighboring systems is eliminated.

(102) In the method of the subject invention, since one cyclic prefix is used for more than one timeslot in GFDM, spectral efficiency is higher compared to the OFDM method which uses equivalent time-frequency resources. In OFDM, only one timeslot is used on a subcarrier and CP is added to this timeslot. In GFDM, one CP is added per block composed of more than one timeslot. By this means, the spectral efficiency increases in GFDM based systems.

(103) The method of the subject invention is a multicarrier method making use of the spatial modulation. In the multicarrier applications of the spatial modulation, for each subcarrier, only one antenna is activated.

(104) In the method of the subject invention, both spatial modulation and the subcarrier index modulation can be applied together according to the system configuration. Activating a single antenna per subcarrier the subcarrier group prevents inter-antenna interference and the receiver complexity is reduced by this means.

(105) The method of the subject invention is a multi-layered method which brings the GFDM, spatial modulation, subcarrier index modulation and QAM/PSK modulations together. In this type of multi-layered applications, while deciding the symbol sent in order to obtain high error performance at the receiver, a common decision rule needs to be used which considers all the layers. In this case, the optimum receiver structure is used. The optimum receiver, antenna index, subcarrier index and QAM/PSK symbol for the proposed method should be decided under a common decision rule.

(106) Because of the pulse shaping applied at GFDM, the orthogonality between subcarriers is lost. For this reason, the optimum decision rule cannot be operated subcarrier-base, all the subcarriers should be considered. This brings a considerably high process complexity. With the maximum likelihood-successive interference cancellation (ML-SIC) detection method as a part of this invention, the antenna index, subcarrier index and QAM/PSK symbol can be decided by a common decision rule without increasing complexity. Therefore, the bit error rate value targeted by the proposed method can be reached by a lower signal to noise ratio (lower transmitter transmission power).

(107) In the method of the subject invention, on the contrary of the classical method, the number of the active subcarriers of the multicarrier system can be changed and thus, a trade-off between spectral efficiency and performance is presented by providing a dynamic communication.

(108) The method of the subject invention combines the spatial modulation and subcarrier index modulation in a configurative manner and enables the channel to adapt onto the proper structure without the transmitter and receiver structure being changed when the channel conditions change. Therefore, the trade-off between band efficiency and performance can be used in an adaptive way according to factors such as the channel conditions, application requirements, etc.

(109) The method of the subject invention combines the spatial modulation and subcarrier index modulation and QAM/PSK modulations. These modulations have different error performances in their own right.

(110) The most important advantage of the invention is that it provides to have energy efficiency provided by the space and frequency index modulation systems with GFDM without complicating the transmitter and receiver structure.