OFDM dominates the current broadband wireless communication systems but it falls short to address the requirements of 5G networks satisfactorily. ⢠As a result ...
Generalized Frequency Division Multiplexing with Space and Frequency Index Modulation Ersin Öztürk, Ertugrul Basar, Hakan Ali Çırpan Faculty of Electrical and Electronics Engineering Istanbul Technical University 34469, Maslak, Istanbul, Turkey Email: {ersinozturk, basarer, cirpanh}@itu.edu.tr Sayfa 1
GFDM - Main Properties & Benefits •
OFDM dominates the current broadband wireless communication systems but it falls short to address the requirements of 5G networks satisfactorily
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As a result, alternative multicarrier transmission schemes are currently being evaluated as potential candidates for the 5G wireless networks
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GFDM is a promising candidate for 5G PHY
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Transmits a block composed by K subcarriers with M time slots on each of it •
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Circular pulse shaping of individual sub-carriers •
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permits flexible time and frequency partitioning
reduces OOB emission and tolerates loose time and frequency synchronization
Uses only one CP per GFDM block •
enables low-complexity frequency domain equalization
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increase spectral efficiency
Uses circular convolution for filtering to prevent long filter tail
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 2 June, Istanbul, Turkey
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Spatial Modulation & Index Modulation •
Spatial Modulation (SM) employs the transmit antenna indices to carry additional information
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In SM, single transmit antenna is activated at each time interval by the input bit sequences and other antennas remain silent
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For SM multicarrier schemes, only one transmit antenna is activated at any subcarrier
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Activating single transmit antenna at a time or subcarrier eliminates interchannel interference (ICI) and relaxes inter-antenna synchronization requirements
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OFDM-IM is an extension of the SM concept to subcarrier indices
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In OFDM-IM, active subcarriers are selected by the input bit sequences
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The information bits are conveyed by both the activated subcarrier indices and the conventional modulation symbols
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Dual-mode OFDM-IM (DM-OFDM) scheme has been proposed to prevent throughput loss in OFDM-IM due to unused subcarriers
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In the DM-OFDM scheme, two different constellation modes have been used to modulate the selected subcarrier indices and the remaining subcarriers in a subcarrier group
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 3 June, Istanbul, Turkey
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The Proposal – GFDM with SFIM • Any physical layer proposal for 5G wireless networks is expected to be compatible with MIMO transmission • IM concept for OFDM has attracted significant attention during recent times • Thus, applicability of MIMO and IM techniques will be a critical milestone for GFDM • In this study, a novel MIMO-GFDM system, which combines GFDM with SFIM, is proposed • In order to enhance the error performance in a spectrum-efficient manner while preserving the advantages of the SM, combination of dual mode IM scheme with SM-GFDM is considered • An enhanced MIMO-GFDM receiver based on joint MIMO detection and GFDM demodulation is presented
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 4 June, Istanbul, Turkey
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GFDM-SFIM Transmitter • A MIMO-GFDM system with 𝑇 transmit and 𝑅 receive antennas is considered • A GFDM block consists of 𝐾 subcarriers with M time slots on each of it • The total number of symbols becomes 𝑁 = 𝐾𝑀
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 5 June, Istanbul, Turkey
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GFDM-SFIM Transmitter (cont.) • Step-1: Bit splitting • 𝐺 information bits are taken as input and divided into 𝐿 groups each containing 𝑞 bits, i.e., 𝑞 = 𝐺/𝐿 • Step-2: Space and Frequency Index Modulation
• Each group of 𝑞 bits is mapped to a subcarrier group with 𝑢 elements • In this mapping operation, antenna and subcarrier indices as well as Q-ary quadrature amplitude modulation (Q-QAM) constellations are used • Transmit antenna selection • The first 𝑞1 = log2(𝑇) bits of the 𝑞 bits sequence are used to select the transmitting antenna index of the subcarrier group
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 6 June, Istanbul, Turkey
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GFDM-SFIM Transmitter (cont.) • Step-2: Space and Frequency Index Modulation (cont.) • Subcarrier index selection • The first 𝑞2 = 𝑙𝑜𝑔2 (𝐶(𝑢, 𝑣))⌋ bits of the remaining bits are fed into index selector to partition the indices of each subcarrier group into two index subgroups 𝐴 𝐴 𝐴 𝐼𝑙𝐴 = 𝑖𝑙,1 , 𝑖𝑙,2 , … , 𝑖𝑙,𝑣
𝐵 𝐵 𝐵 𝐼𝑙𝐵 = 𝑖𝑙,1 , 𝑖𝑙,2 , … , 𝑖𝑙,𝑢−𝑣
𝐴 𝐵 𝑖𝑙,𝛾 ∈ {1,… , 𝑢}, for 𝛾 = 1, … , 𝑣 , 𝑖𝑙,𝛾 ∈ {1,… , 𝑢}, for 𝛾 = 1, … , 𝑢 − 𝑣,
𝑙 ∈ {1,… , 𝐿}
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 7 June, Istanbul, Turkey
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GFDM-SFIM Transmitter (cont.) • Step-2: Space and Frequency Index Modulation (cont.)
• Q-ary modulation • The remaining 𝑞3 and 𝑞4 bits are fed into mappers A and B to modulate the subcarriers selected by two index subgroups • Use the first 𝑞3 = 𝑣𝑙𝑜𝑔2(𝑇) bits of the remaining bits to modulate the subcarriers selected by 𝐼𝑙𝐴 • Constitute symbol vector for 𝐼𝑙𝐴 𝐬𝑙𝐴 = [𝑠𝑙𝐴 1 , 𝑠𝑙𝐴 2 ,…, 𝑠𝑙𝐴 𝑣 ]𝑇
𝑠𝑙𝐴 (𝛾) ∈ 𝑆 𝐴 , for 𝛾 = 1, … , 𝑣
• Use the remaining 𝑞4 = (𝑢 − 𝑣)log2(𝑇) bits to modulate the subcarriers selected by 𝐼𝑙𝐵 • Constitute symbol vector for 𝐼𝑙𝐵 𝐬𝑙𝐵 = [𝑠𝑙𝐵 1 , 𝑠𝑙𝐵 2 ,…, 𝑠𝑙𝐵 𝑢 − 𝑣 ]𝑇
𝑠𝑙𝐵 (𝛾) ∈ 𝑆 𝐵 , for 𝛾 = 1, … , 𝑢 − 𝑣
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 8 June, Istanbul, Turkey
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GFDM-SFIM Transmitter (cont.) • Step-3: SFIM block creation • SFIM block creator combines symbol vectors of index subgroups, 𝐬𝑙𝐴 and 𝐬𝑙𝐵 , and creates the vector of the modulated symbols for the subcarrier group (𝑡𝑙 , 𝑙), which will be assigned to the transmit antenna 𝑙 𝐬𝑡𝑙,𝑙 = [𝑠𝑡𝑙,𝑙 1 , 𝑠𝑡𝑙,𝑙 2 ,…,𝑠𝑡𝑙,𝑙 𝑢 ]𝑇 𝑠𝑡𝑙,𝑙 (𝛾) ∈ {𝑆 𝐴 , 𝑆 𝐵 }, for 𝑡𝑙 ∈ {1, … T} 𝑎𝑛𝑑 𝛾 = 1, … , 𝑢 • SFIM block creator sets the subcarriers of the inactive antennas to zero • Arranges the transmit symbols for block 𝑙 in a 𝑇 x 𝑢 matrix 𝐃𝑙 𝐬𝑡𝑙,𝑙 is the 𝑡𝑙 th row of 𝐃𝑙
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 9 June, Istanbul, Turkey
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GFDM-SFIM Transmitter (cont.) • Step-4: GFDM block creation • GFDM block creator combines the SFIM blocks in a 𝑇 x 𝑁 matrix 𝐃 = [𝐃1 , 𝐃2 , … 𝐃𝐿 ] • The GFDM symbol for the transmit antenna 𝑡, which is 𝑡th row vector of 𝐃, can be expressed by 𝐝𝑡 = [𝑑𝑡,0,0 , … 𝑑𝑡,𝐾−1,0 , 𝑑𝑡,0,1 , … , 𝑑𝑡,𝐾−1,1 , … , 𝑑𝑡,0,𝑀−1 , … , 𝑑𝑡,𝐾−1,𝑀−1 ] 𝑑𝑡,𝑘,𝑚 : The data symbol of 𝑚th timeslot on 𝑘th subcarrier belonging to 𝑡th transmit antenna 𝐾 and 𝑀 stand for the number of subcarriers and subsymbols • Step-5: Block interleaving • A block interleaver is used to render the channel memoryless
• 𝐿 x 𝑢 block interleaving is applied to each 𝐝𝑡 and 𝐝𝑡 is obtained 5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 10 June, Istanbul, Turkey
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GFDM-SFIM Transmitter (cont.) • Step-6: GFDM modulation • GFDM modulator modulates the each data block 𝐝𝑡 and overall GFDM transmit signal 𝑥𝑡 (𝑛) of 𝑡th transmit antenna is obtained 𝐾−1 𝑀−1
𝑑𝑡,𝑘,𝑚 𝑔((𝑛 − 𝑚𝑘)𝑚𝑜𝑑 𝑁 ) exp(𝑗2𝜋
𝑥𝑡 (𝑛) = 𝑘=0 𝑚=0
𝑘 𝑛) 𝐾
𝑛 = 0, … , 𝑁 − 1
𝑔((𝑛 − 𝑚𝑘)𝑚𝑜𝑑 𝑁 ) : the transmit filter circularly shifted to the mth subsymbol
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 11 June, Istanbul, Turkey
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GFDM-SFIM Transmitter (cont.) • Step-7: Cyclic Prefix adding • Add a CP with length 𝑁CP in order to avoid intersymbol interference (ISI) 𝐱 𝑡 = 𝐱 𝑡 𝐾𝑀 − 𝑁CP + 1 ∶ 𝐾𝑀 T ,
𝐱𝑡 T
T
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 12 June, Istanbul, Turkey
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GFDM-SFIM Receiver
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 13 June, Istanbul, Turkey
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GFDM-SFIM Receiver (cont.) • In OFDM, due to orthogonality in the frequency domain, joint MIMO detection and demodulation can be performed at the subcarrier level
• In GFDM, the inherent intercarrier interference prevents the frequency domain decoupling of GFDM subcarriers for both SISO and MIMO schemes • Therefore, in order to realize joint MIMO detection and GFDM demodulation, all subcarriers belonging to all GFDM subsymbols must be processed together in time domain
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 14 June, Istanbul, Turkey
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GFDM-SFIM Receiver (cont.) • Step-1: Cyclic prefix removal • We assume CP is longer than 𝑁ch and perfect synchronization is ensured
• Stacking the received signals enables the linear system model in matrix form which combines GFDM modulation and MIMO 𝐲𝟏 𝐇𝟏,𝟏 𝐀 ⋯ ⋮ = ⋮ ⋱ 𝐲𝑹 𝐇𝑹,𝟏 𝐀 ⋯
𝐇𝟏,𝑻 𝐀 𝐝𝟏 ⋮ ⋮ +𝐰 𝐇𝑹,𝑻 𝐀 𝐝𝑻
𝐲 = 𝐇𝐝 + 𝐰 𝐲 is 𝑁𝑅 x 1 vector
𝑟 = 1, … 𝑅 : receive antenna index 𝑡 = 1, … 𝑇 : transmit antenna index 𝐲𝑟 : The vector of received signals at the 𝑟th antenna 𝐡𝑟,𝑡 : The channel impulse response coefficients between 𝑡th transmit antenna and 𝑟th receive antenna, 𝐡𝑟,𝑡 = [ℎ𝑡,𝑟,1 , … , ℎ𝑡,𝑟,𝑁ch ] , ℎ𝑡,𝑟,𝑛 follows CN (0,1)
𝐇 is 𝑁𝑅 x 𝑁𝑇 matrix 𝐝 is 𝑁𝑇 x 1 vector 𝐰 is 𝑁𝑇 x 1 vector
𝐇𝑟,𝑡 𝐀
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 15 June, Istanbul, Turkey
: The circular convolution matrix constructed from 𝐡𝑟,𝑡 : 𝑁 x 𝑁 transmitter matrix 15
GFDM-SFIM Receiver (cont.) • Step-2: Joint MIMO detection and GFDM demodulation • Since GFDM modulation and MIMO channel is linearly modeled, 𝐲 = 𝐇𝐝 + 𝐰 joint MIMO detection and GFDM demodulation through MMSE filtering can be performed:
𝐃 = (𝐇 H 𝐇 + 𝜎𝑤2 𝐈)−1 𝐇H 𝐲 • This method is named as MMSE-JDD (joint detection and demodulation) • MMSE-JDD is also applicable for SM and SSK based GFDM systems
• Step-3: Block deinterleaving • 𝐿 x 𝑢 block deinterleaving is applied to each 𝐝𝑡 and obtain 𝐝𝑡
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 16 June, Istanbul, Turkey
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GFDM-SFIM Receiver (cont.) • Step-4: SFIM block splitting
• SFIM Block Splitter partitions each 𝐝𝑡 into 𝐿 groups with 𝑢 elements • Arranges these groups in a 𝑇 x 𝑢 matrix 𝐬1,𝑙 𝐝1,𝑙 ( 𝑙 − 1 𝑢 + 1: 𝑙𝑢) 𝐃𝑙 = ⋮ = ⋮ 𝐬 𝑇,𝑙 𝐝 𝑇,𝑙 ( 𝑙 − 1 𝑢 + 1: 𝑙𝑢) • Step-5: SFIM Demodulation • For each 𝑇 x 𝑢 matrix, SFIM Demodulator makes a joint decision on the active transmit antenna index, subcarrier index subgroups as well as constellation symbols considering all possible realization of 𝐃𝑙 by minimizing the following metric {𝑡𝑙 , 𝐼𝑙𝐴 , 𝐬𝑙𝐴 𝐬𝑙𝐵 } = arg
min 𝐴
𝑡,𝐼𝐴 ,𝑆 ,𝑆 𝐵
𝐃 𝑙 − 𝐃𝑙
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 17 June, Istanbul, Turkey
2 𝐹
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GFDM-SFIM Receiver (cont.) • Step-6: Demapping and Bit Combining • Original information bits are retrieved • For each group,
• Convert 𝑡𝑙 to 𝑞1 - bits • Convert 𝐼𝑙𝐴 to 𝑞2 - bits • Convert 𝐬𝑙𝐴 to 𝑞3 - bits
• Convert 𝐬𝑙𝐵 𝑡𝑜 𝑞4 - bits • Combine 𝑞1 - bits, 𝑞2 - bits, 𝑞3 - bits and 𝑞4 - bits and obtain 𝑞-bits • Combine all 𝑞- bits and obtain 𝐺 - bits
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 18 June, Istanbul, Turkey
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Computational Complexity • Computational complexities of ZF-SDD based SM-GFDM receiver and MMSEJDD based GFDM-SFIM receiver are analyzed in terms of total number of complex multiplications (CMs) and presented in below table • The complexity of the GFDM-SFIM receiver increases with the increasing value of the number of transmit and receive antennas, subcarriers, subsymbols and constellation size ZF-SDD: Zero-Forcing based separate MIMO detection and demodulation MMSE-JDD: MMSE based joint MIMO detection and demodulation Computational Complexity
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 19 June, Istanbul, Turkey
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Spectral Efficiency • Active antenna selection for each subcarrier group instead of each subcarrier reduces the spectral efficiency with respect to classical SM scheme • This loss can be compensated by increasing either the modulation order or the transmit antenna size • In GFDM, using a single CP for the entire symbol block provides spectral efficiency gain over OFDM • Spectral efficiency gain of GFDM-SFIM over OFDM-SFIM with the same system parameters: 𝜌 = 100
𝑁𝐶𝑃 (𝑀 − 1) % 𝐾𝑀 + 𝑁𝐶𝑃
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 20 June, Istanbul, Turkey
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Results and Discussion (cont.) • • •
The BER performance of the proposed GFDM-SFIM scheme has been compared with SM-GFDM and OFDM-SFIM schemes for Rayleigh multipath fading channels Perfect synchronization and perfect channel state information is assumed Simulation parameters are shown below
Description Number of subcarriers Number of subsymbols Pulse shaping filter Length of cyclic prefix Exponent of power delay profile Number of channel taps
Parameter 𝐾 𝑀 𝑔 𝑁𝐶𝑃 ∅ 𝑁𝑇𝐴𝑃
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 21 June, Istanbul, Turkey
Value 128 5 RRC 32 0.1 10
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Results and Discussion (cont.) •
In order to determine the subcarrier index subgroups look-up table method is used
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Constellations BPSK
4-QAM
𝐒A = {−1, +1}
𝐒A = {−1 − 𝑗, 1 − 𝑗, 1 + 𝑗, −1 + 𝑗}
𝐒B = {−𝑗, +𝑗}
𝐒B = { 1 + 3 , 1 + 3 𝑗, −1 − 3 , − 1 + 3 𝑗}
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 22 June, Istanbul, Turkey
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Results and Discussion (cont.) BER performance of the proposed GFDM-SFIM scheme and the ZF-SDD based SM-GFDM scheme for a 2 x 2 MIMO configuration with roll-off factor (α) of 0.1 and 0.5 • For BPSK, GFDM-SFIM achieves approximately 15 dB better BER performance at the cost of a slightly decreased spectral efficiency • For 4-QAM, GFDM-SFIM BER achievement is 7 dB • Computational complexity: GFDM-SFIM ~O(4.2 x 109) ZF-SDD SM-GFDM ~O(4.1 x 106)
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 23 June, Istanbul, Turkey
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Results and Discussion (cont.) BER performance of the proposed GFDM-SFIM scheme, MMSE-JDD based OFDM-SFIM scheme, ZF-SDD based SM-GFDM scheme and MMSE-JDD based SM-GFDM scheme for a 4 x 4 MIMO configuration with roll-off factor (α) of 0.1 •
GFDM-SFIM scheme with 4-QAM transmission achieves approximately 14 dB better BER performance than the ZF-SDD based SM-GFDM scheme with BPSK transmission at the same spectral efficiency
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MMSE-JDD based SM-GFDM scheme achieves approximately 8 dB better BER performance than the ZF-SDD based SM-GFDM scheme
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GFDM-SFIM scheme still achieves 6 dB better BER performance than the MMSE-JDD based SM-GFDM scheme at the same computational complexity
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BER performance of the GFDM-SFIM scheme and the MMSE-JDD based OFDM-SFIM scheme is approximately same
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 24 June, Istanbul, Turkey
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Results and Discussion (cont.) BER performance of the proposed GFDM-SFIM scheme for a 4 x 4 MIMO configuration and the ZFSDD based SM-GFDM scheme for a 2 x 2 MIMO configuration with a roll-off factor of 0.1
• For BPSK, GFDM-SFIM achieves approximately 22 dB better BER performance at the same spectral efficiency • For 4-QAM, GFDM-SFIM BER achievement is 12 dB
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 25 June, Istanbul, Turkey
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Results and Discussion (cont.) • The reason behind improvements are • Increased diversity order due to MMSE detector, • Joint MIMO detection and GFDM demodulation, • Improved Euclidean distance spectrum due to IM, • GFDM-SFIM scheme provides 19% spectral efficiency gain over the OFDMSFIM schemes
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 26 June, Istanbul, Turkey
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Conclusion •
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We propose a novel MIMO-GFDM system, which combines GFDM with SFIM
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The system model of the GFDM-SFIM has been presented
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BER performance has been compared to SM-GFDM and OFDM-SFIM systems under Rayleigh multipath fading channels
It has been shown that: •
SFIM is applicable to MIMO-GFDM
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Provides significant BER improvements compared to SM-GFDM
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Provides spectral efficiency gain compared to OFDM-SFIM
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IAI in spatial multiplexing transmission scheme is avoided
GFDM-SFIM can be considered as a promising scheme for future 5G wireless networks
5th International Black Sea Conference on Communications and Networking, Sayfa 5-8 27 June, Istanbul, Turkey
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Thank you
Sayfa 28
