Generalized Quadrature Spatial Modulation Scheme Using Antenna Grouping
2017; Electronics and Telecommunications Research Institute; Volume: 39; Issue: 5 Linguagem: Inglês
10.4218/etrij.17.0117.0162
ISSN2233-7326
AutoresFrancisco R. Castillo‐Soria, Joaquín Cortez, Raymundo Ramirez-Gutierrez, F. M. Maciel-Barboza, Leonel Soriano-Equigua,
Tópico(s)Satellite Communication Systems
ResumoETRI JournalVolume 39, Issue 5 p. 707-717 ArticleFree Access Generalized Quadrature Spatial Modulation Scheme Using Antenna Grouping Francisco Rubén Castillo-Soria, Francisco Rubén Castillo-Soria fsoria@fc.uaslp.mx Search for more papers by this authorJoaquín Cortez-González, Joaquín Cortez-González joaquin.cortez@itson.edu.mx Search for more papers by this authorRaymundo Ramirez-Gutierrez, Raymundo Ramirez-Gutierrez raymundo.ramirez.gutierrez@intel.com Search for more papers by this authorFermín Marcelo Maciel-Barboza, Fermín Marcelo Maciel-Barboza fermin_maciel@ucol.mx Search for more papers by this authorLeonel Soriano-Equigua, Leonel Soriano-Equigua lsoriano@ucol.mx Search for more papers by this author Francisco Rubén Castillo-Soria, Francisco Rubén Castillo-Soria fsoria@fc.uaslp.mx Search for more papers by this authorJoaquín Cortez-González, Joaquín Cortez-González joaquin.cortez@itson.edu.mx Search for more papers by this authorRaymundo Ramirez-Gutierrez, Raymundo Ramirez-Gutierrez raymundo.ramirez.gutierrez@intel.com Search for more papers by this authorFermín Marcelo Maciel-Barboza, Fermín Marcelo Maciel-Barboza fermin_maciel@ucol.mx Search for more papers by this authorLeonel Soriano-Equigua, Leonel Soriano-Equigua lsoriano@ucol.mx Search for more papers by this author First published: 11 October 2017 https://doi.org/10.4218/etrij.17.0117.0162Citations: 24 Francisco Rubén Castillo-Soria (corresponding author, fsoria@fc.uaslp.mx) is with the Department of Telecommunications Engineering, Autonomous University of San Luis Potosí, SLP, México. Joaquín Cortez-González (joaquin.cortez@itson.edu.mx) is with the Electronics and Electrical Engineering Department, Technologic Institute of Sonora, México. Raymundo Ramirez-Gutierrez (raymundo.ramirez.gutierrez@intel.com) is with the DSP and algorithms research group, Intel Labs, Guadalajara, México. Fermin Marcelo Maciel-Barboza (fermin_maciel@ucol.mx) and Leonel Soriano-Equiga (lsoriano@ucol.mx) are with the Faculty of Mechanical and Electrical Engineering, University of Colima, Colima, México. AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This paper presents a novel generalized quadrature spatial modulation (GQSM) transmission scheme using antenna grouping. The proposed GQSM scheme combines QSM and conventional spatial multiplexing (SMux) techniques in order to improve the spectral efficiency (SE) of the system. Analytical and simulation results show that the proposed transmission scheme has minimal losses in terms of the average bit error probability along with the advantage of an increased SE compared with previous SM and QSM schemes. For the case studies, this advantage represents a reduction of up to 81% in terms of the number of required transmit antennas compared with QSM. In addition, a detection architecture based on the ordered successive interference cancellation scheme and the QR decomposition is presented. The proposed QRD-M adaptive algorithm showed a near-maximum-likelihood performance with a complexity reduction of approximately 90%. 1 Introduction Spatial modulation (SM) is a transmission technique that is designed to work on multiple-input multiple-output (MIMO) systems 1. In general, SM schemes exhibit advantages in terms of the bit error rate (BER) and complexity when compared to conventional spatial multiplexing (SMux) techniques such as Vertical-Bell Laboratories Layered Space-Time (V-BLAST) 2. In addition, SM schemes are energy efficient because a reduced number of radiofrequency (RF) chains are used 3. New research in this topic has been oriented to improve sub-optimal low-complexity detection algorithms 4. Furthermore, some multiuser schemes that employ the SM technique have been proposed in 5. In 6, the SM transmission technique has been considered as a key technology for future wireless communication systems. However, a major concern of SM is its suboptimal log2(Ntx) data-rate enhancement, while for the SMux technique, the data rate increases linearly with the number of transmit (Tx) antennas Ntx. Recently, 7 proposed a transmission scheme for SM signals known as quadrature spatial modulation (QSM). The QSM scheme can be considered as a generalization of the bi-space shift keying (BiSSK) scheme proposed in 8. It should be noted that these schemes have roughly the same BER performance as the basic SM scheme, but with the advantage of doubling the number of bits that can be transmitted in the spatial constellation, which results in an improved spectral efficiency (SE). This technique has motivated a new study that is oriented to improve the system performance while reducing the detection complexity 9, 10. However, the number of Tx antennas required for the QSM scheme is still much higher than that required by the conventional SMux scheme, especially when high spatial constellations are considered. To overcome this drawback, this paper proposes a novel generalized QSM (GQSM) scheme based on antenna grouping. In the proposed scheme, the total number of Tx antennas Ntx is divided into small groups, each with two Tx antennas, in order to obtain a high SE; however, this idea can easily be extended to form groups with more than two Tx antennas. Using the principle of the QSM technique, each group transmits a different M-order quadrature amplitude modulation/phase-shift keying (M-QAM/M-PSK) symbol at each period. As a result, the proposed scheme has a significant SE improvement, which is reflected in a reduction in the total number of required Tx antennas, Ntx. Analytical and simulation results show that the proposed GQSM scheme using Ntx = 4 or Ntx = 6 and 4-QAM modulation requires an additional 1 dB to 2 dB in order to achieve the QSM performance; nevertheless, when Ntx = 4 and 16-QAM modulation is used, the proposed scheme shows a slightly better performance than the QSM scheme. The proposed scheme has a reduction of up to 81% over the required Ntx when compared to that of the reference scheme (QSM). Moreover, a low-complexity/near-maximum-likelihood (ML) architecture for the detection of GQSM signals is presented. The proposed detection architecture is based on ordered successive interference cancellation (OSIC) and the QR decomposition. The proposed QRD-M adaptive algorithm shows a near-ML performance with a complexity reduction of approximately 90%. Throughout this paper, the following notation is used: bold and lowercase letters denote vectors, whereas bold and capital letters denote matrices. The notations (·)T, (·)H, and ||·|| denote the transpose, conjugate transpose, and the norm of a vector or matrix, respectively. is used to represent the complex Gaussian distribution of a random variable with mean n and variance σ2. P(·) represents the event probability, while E[·] denotes the statistical expectation. The rest of this paper is organized as follows: Section 2 describes in detail the proposed system and the channel model under consideration. Section 3 presents a theoretical analysis of ML detection for the proposed scheme. In Section 4, the complexity of the ML criterion is analyzed, while in Section 5, low-complexity algorithms are proposed for the GQSM signal detection. In Section 6, the simulation results are analyzed, and conclusions are presented in Section 7. 2 System Model 2.1 Channel Model It is assumed that the channel propagation between each pair of Tx and Rx antennas can be modeled as a Rayleigh narrowband stationary stochastic process. It is also considered that the channel provides rich scattering on both sides, that is, the transmitter and receiver sides. The simulation considers that a realization of the MIMO channel can be expressed as a random matrix H of size Nrx × Ntx, where Ntx and Nrx are the number of Tx and Rx antennas, respectively. The elements of H are denoted by hij, for i = 1, 2, … , Nrx, j = 1, 2, … , Ntx. With this model, each entry of H at any time is a complex Gaussian random variable with zero mean and a variance of σ2/2 per dimension. It is assumed that the temporal channel fading is slow compared with the symbol period T, where a quasi-static block-fading model is sufficient to characterize the temporal correlation. Therefore, the channel matrix H is randomly generated, but remains constant during the transmission of one space-time code word of length T. In addition, a perfect channel state information (CSI) is assumed at the receiver. 2.2 Proposed System Model Figure 1 shows the GQSM system model, which is composed of Ntx and Nrx antennas. Let us consider small groups of two Tx antennas. Then, the GQSM system comprises nB = Ntx/2 blocks or groups, where each group transmits one different symbol at T using the QSM technique. Let us consider an incoming data string of bits, where M represents the M-QAM constellation size. Considering only two Tx antennas per group, each group can transmit mg = 2 + log2(M) bits per channel use (bpcu). For the l-th group, the first two bits are modulated using a spatial constellation; the second log2(M) bits are modulated using the M-QAM constellation. First, the M-QAM symbol x is divided into its real and imaginary parts: x = xℜ + jxℑ. Then, xℜ is transmitted using the spatial constellation in the l-th group using one Tx antenna, and xℑ is transmitted by another or the same Tx antenna within the same group. Each selected antenna transmits the signal . Figure 1Open in figure viewerPowerPoint GQSM system model. The normalized transmission vector , where l = {1, 2, … , nB} has elements , which represent the signal transmitted by the l-th group and the k-th Tx antenna in the GQSM constellation. Because only two Tx antennas are used per group, the signals and are transmitted by the first and second Tx antennas, respectively. The constant e(l) is the normalization factor for the l-th group, which is calculated to maintain a unitary power transmission. Table 1 shows the symbol mapping for only one group using the QPSK constellation. is the antenna that transmits the real part of the M-QAM symbol, and is the antenna that transmits the imaginary part. For example, in Table 1, for the input sequence a = [0000], both real and imaginary parts of the symbol (+1 +j) are transmitted by the first Tx antenna, while the second Tx antenna remains silent. A detailed explanation of the QSM scheme can be found in 8. Table 1. GQSM constellation for 4-QAM and two Tx antennas a = [a1 a2 a3 a4] (Axℜ, Axℑ), QPSK symbol [0 0 0 0] [(1, 1), (+1 + j)] [1 + j, 0] [0 0 0 1] [(1, 1), (−1 + j)] [–1 + j, 0] [0 0 1 0] [(1, 1), (+1 − j)] [1 − j, 0] [0 0 1 1] [(1, 1), (−1 − j)] [–1 – j, 0] [0 1 0 0] [(1, 2), (+1 + j)] [1, j] [0 1 0 1] [(1, 2), (−1 + j)] [–1, j] [0 1 1 0] [(1, 2), (+1 − j)] [1, –j] [0 1 1 1] [(1, 2), (−1 − j)] [–1, –j] [1 0 0 0] [(2, 1), (+1 + j)] [j, 1] [1 0 0 1] [(2, 1), (−1 + j)] [j, –1] [1 0 1 0] [(2, 1), (+1 − j)] [–j, 1] [1 0 1 1] [(2, 1), (−1 − j)] [–j, –1] [1 1 0 0] [(2, 2), (+1 + j)] [0, 1 + j] [1 1 0 1] [(2, 2), (−1 + j)] [0, –1 + j] [1 1 1 0] [(2, 2), (+1 − j)] [0, 1 − j] [1 1 1 1] [(2, 2), (−1 − j)] [0, −1 − j] Consider the GQSM scheme with nB blocks of Tx antennas (antenna grouping). The complete transmission block: is composed of a concatenated output of all groups. The transmission vector sB is conveyed over the random complex wireless channel H defined in Section 2-1. For simplicity, it is assumed that all of the Tx antennas convey information symbols from the same constellation map; it is also assumed that the receiver is perfectly synchronized. The number of bpcu that can be transmitted for the complete transmission vector sB in the proposed GQSM scheme is bpcu. The number of bits that can be transmitted using QSM is mQSM = log2(M) + 2log2(Ntx) bpcu 8. The number of bits that can be transmitted using SM is mSM = log2(M) + log2(Ntx) 1. The number of bits that can be transmitted using SMux is mSMux = Ntxlog2(M) 2. Figure 2 shows a comparison of the SE in bpcu for SM, QSM, GQSM, and SMux transmission schemes for different configurations. For the proposed GQSM scheme, the improvement in the SE can be seen in terms of the required number of Tx antennas. For example, considering a transmission of 8 bpcu and 4-QAM, the proposed GQSM scheme requires four Tx antennas, the GSM scheme proposed in 11 requires at least eight Tx antennas, and the SM-SMux scheme 12 requires at least four Tx antennas. Figure 2Open in figure viewerPowerPoint Comparison of spectral efficiency in bpcu. At the receiver, the CSI and are assumed to be known. In addition, it is assumed that H is full-rank. During every T, the sequence of symbols is transmitted and multiplexed over the Ntx antennas. Therefore, the system equation can be expressed as (1) or equivalently, (2) where y is the received signal vector, ρ is the signal-to-noise-ratio (SNR) at the receiver, hi,j. is the channel gain for i = 1, 2, … , Nrx and j = 1, 2, … , Ntx, and n is the noise vector at the receiver. The noise samples ni are independent identically distributed (i.i.d.) complex Gaussian random variables with CN(0, ). At the receiver, the signals of all groups are detected at the same time. The optimal detection for GQSM signals is given by the ML criterion, which is defined as (3) Finally, the original sequence of bits can be detected by employing the mapping rule used for sB. 3 Average Bit Error Probability Derivation The average bit error probability (ABEP) can be derived by using the well-known bounding technique. Considering that , the probability of deciding on given that gi is transmitted is upper bounded as (4) where E[·] represents the expected value and is the pairwise error probability (PEP) of deciding on the signal given that gi is transmitted. The conditional PEP can be calculated as (5) where Q[·] is the Q function, which is defined as , and v = 3ρ/(Nrx + 5). Considering a probability density function p(v), the total PEP for the fading channel can be calculated using the mathematical expectation as follows: (6) Considering a single Rx antenna, the probability of error can be solved as 7 (7) If the receiver is equipped with Nrx > 1 Rx antennas, , which has a closed-form expression that is obtained as (8) where γ is the PEP for a single Rx antenna 13. Using (4), the ABEP for a general GQSM scheme can be computed as (9)where N(i, j) is the number of bits in error associated with the corresponding PEP, and M′ is the spatial constellation size. Note that if nB = 1, the ABEP for QSM is obtained. Substituting (8) into (9) and considering a spatial constellation of size M′ = 4 (groups of two Tx antennas), the ABEP for the proposed GQSM scheme can be computed as (10) Figure 3 illustrates the analytical upper bound in (10) using the ML criterion and 4-QAM for different configurations of nB and Nrx. Figure 3Open in figure viewerPowerPoint Analytical and simulation results of the GQSM scheme utilizing the ML criterion and 4-QAM. 4 Complexity The receiver complexity η for the ML criterion in (3) is measured in terms of complex operations (CO). One arithmetic operation is considered as one CO, and one comparison is considered as one CO. The lattice in the system has 2m points. After performing subtraction, obtaining the square, and finding the minimum in (3), the result obtained is (3 + D)2m CO. Considering Nrx Rx antennas, the complexity of the ML in (3) can be approximated by (11) where m is the number of bpcu for each system defined in Section I, and D is a factor that depends on the number of COsx that are required to generate one symbol in the constellation in (3). The SM scheme requires only one multiplication (D = 1), and QSM requires two multiplications, but with only one QAM symbol (D = 1), GQSM requires a combination of nB groups (D = nB = Ntx/2 CO), and SMux requires that all transmitted signals be combined (D = 2Ntx − 1). This result shows that the complexity of the proposed scheme is between that of QSM and SMux, and that it depends on nB. Table 2 shows a comparison of the complexity for ML detection considering the three case studies. Table 2. Complexity comparison for the ML criterion in CO Transmission scheme 8 bpcu (4-QAM) Nrx = 4 12 bpcu (16-QAM) Nrx = 4 12 bpcu (4-QAM) Nrx = 6 SM 4,096 65,536 98,304 QSM 4,096 65,536 98,304 GQSM 5,120 81,920 147,456 SMux 10,240 163,840 344,064 5 Low-Complexity Detection Algorithms for GQSM Signals The ML criterion is the optimal detector; however, its high complexity may be restrictive for real implementations. To overcome this drawback, in this section, two different detection algorithms are proposed for the GQSM scheme. Both algorithms follow three similar steps, where the system equations are rewritten to obtain a more convenient representation, the QR decomposition of H is carried out, and the decoding problem is set as a search tree. Using OSIC techniques based on the zero-forcing (ZF) solution in V-BLAST systems, the order of detection is very important because an optimum order can reduce the risk of error propagation in the estimation of the transmitted symbols. Reference 14 proposes a very efficient method to obtain an optimal order based on the minimum mean-square error (MMSE) sorted QR decomposition of H. The algorithm is presented as an extension to the modified Gram-Schmidt (MGS) algorithm 15 by reordering the blocks of the GQSM system, and this is done by reordering the columns of the channel matrix prior to each orthogonalization step. Reordering the channel matrix H results in matrix , with rows sorted from the highest to the lowest SNR 14. In order to reduce the complexity of the QR decomposition process, the norm pre-computing of columns in the matrix was introduced and updated according to the MGS algorithm proposed in 16. The complete MMSE SQRD-GQSM algorithm is shown in Table 3. Table 3. MMSE SQRD-GQSM algorithm (1) = 0, = H, order = 1:1:nB, ind = 1 (2) for i = 1, … , Ntx (3) normbi = ‖qi‖2 (4) end for (5) index = 1 (6) for i = 1, … , Ntx (7) if(mod(i, 2) ≠ 0) (8) [ind block] = (normbl) (9) exchange columns i and i + 1 for ind and ind + 1 in , normb and in the first Nr + i – 1 rows of exchange columns index and block of order index = index + 1 (10) end (11) ri,i = ‖qi‖2 (12) qi = qi/ri,i (13) for k = i + 1, … , Ntx (14) ri,k = qiH qk (15) qk = qk − ri,k · qi (16) normbk = normbk − ǀri,kǀ2 (17) end for (18) end for 5.1 OSIC-MMSE Sorted QR Decomposition Detector for GQSM Scheme (OSIC MMSE SQRD – GQSM) In order to extend the QR-based detection with respect to the MMSE criterion, the QR decomposition is carried out for the extended , which is defined as: (12) where the (Ntx + Nrx) × Ntx matrix with orthonormal columns is partitioned into (Nrx × Ntx) matrix Q1 and (Ntx × Ntx) matrix Q2, with (Nrx × Ntx) matrix . The algorithm proposed in 14 (see Table 3) was modified in order to implement the OSIC process in the detection of the GQSM scheme. After calculation of the MMSE SQRD-GQSM decomposition for the channel matrix , that is, , where Q1 is a unitary matrix and is an upper triangular matrix. By multiplying the received signal in (2) by , the modified received vector is (13) if vector sGQSM is transmitted. Note that the statistical properties of the noise remain unchanged. The OSIC block detector was proposed considering the GQSM constellation for one block of two Tx antennas. The constellation has a size of (see Table 1); therefore, it is possible to achieve a complexity reduction with respect to the ML detector. Then, it is necessary to rewrite (1) as a block system (14) which can be expressed as a matrix equation (15) where block matrix is called a block matrix GQSM, and each block of B is given by (16) for m = 1, 2, … , nB, k = 1, 2, … , nB, and m = k. In the case with m > k, B is given by (17) Now, each block of , , and for k = 1, 2, … , nB is (18) Owing to the upper block triangular structure of B, the k-th element of is (19) The blocks are estimated in sequence, from the lower to the higher stream, using OSIC. Assuming that all previous block decisions are correct, the interference can be perfectly cancelled at each step except for the additive noise. The estimated vector is given by (20) where is the estimate of sk and D(·) is a decision device that maps its argument to the closest signal in the GQSM constellation. A full description of the OSIC detector is shown in Table 4. Table 4. OSIC MMSE SQRD-GQSM (1) INPUT: , Q1, y, ΩGQSM, order, nB (2) OUTPUT: (3) = y (4) dt = 0 (5) for k = nB:−1:1 (6) Calculate and sort the metrics B = ‖nB – nBnBxnB‖2 of value in ascending order with its corresponding position, for all possible values of xnB ∈ ΩGQSM. Store the values in dist and ord, respectively. (7) = ΩGQSM(ord(1),:) (8) dt = dt + dist(1) (9) for m = k − 1:−1:1 (10) m = m − mk (11) end for (12) (k) = (13) end for (14) permutate according order (15) return The algorithms were written using MATLAB notation. Variables in bold represent either vectors (lowercase) or matrices (uppercase). Vector and matrix indexing are indicated using square brackets. ΩGQSM is a matrix whose rows elements are the GQSM constellation symbols. 5.2 Near-ML MMSE Sorted QR Decomposition for GQSM Scheme (Near-ML MMSE SQRD – GQSM) In this section, the advantages of combining QRM-algorithm 17 and the sphere detector (SD) 18 with MMSE-sorted QR decomposition are presented. In the proposed approach, a search was carried out in breadth-first (QRM algorithm), after which a depth-first search tree algorithm based on SD was used. As a result, a similar performance in terms of BER compared to that of the ML criterion is obtained, with an important reduction in the detection's complexity. In this work, the GQSM scheme with nB = 2 and three blocks was considered. The near-ML detector operates for Nrx ≥ Ntx/2. The aim of the near-ML detector is to find the optimum solution to the ML in (3) using the distances calculated during the process to find the closest vector in (20). For clarity, the next metric to select the estimated symbol vector is defined as (21) where with nB = 2 are given by (22) (23) and with nB = 3 are given by (24) (25) (26) (27) where xi ∈ ΩGQSM is a vector that contains all of the psible constellation symbols. Consider a breadth-first tree search. The full description of the near-ML detection algorithm for nB = 3 is shown in Table 5. Table 5. Near-ML MMSE SQRD-GQSM detector for nB = 3 (1) INPUT: , Q1, y, ΩGQSM, order, Nc = length (ΩGQSM) (2) OUTPUT: (3) = y (4) Compute and sort the metrics = ‖3 − 33x3‖2 in ascending order with its corresponding position, for all possible values of x3 ∈ ΩGQSM. Store the values in dist3 and ord3, respectively. (5) D = ∞; (6) for k = 1: Nc, (7) = ΩGQSM(ord3(k),:) (8) Compute and sort the metrics = ‖2 − 22x2 − 23x3‖2 in ascending order with its corresponding position, for all possible values of x2 ∈ ΩGQSM. Store the values in dist2 and ord2, respectively. (9) dt1 = dist2(1) + dist3(k) (10) for m = 1: Nc, (11) = ΩGQSM(ord2(m),:) (12) Compute and sort the metrics = ‖1 − 11x1 − 12 – 13 ‖2 in ascending order with its corresponding position for all possible values of x1 ∈ ΩGQSM. Store the values in dist1 and ord1, respectively. Compute DT = dist1(1) + dist2(m) + dist3(k) (13) if DT < D (14) dt2 = dist1(1) + dist2(m) (15) D = DT (16) = ΩGQSM(ord1(1),:) (17) = ΩGQSM(ord2(m),:) (18) = ΩGQSM(ord3(k),:) (19) = (20) end if (21) if m < Nc (22) if dist2(m + 1) > dt2 (23) break (24) end if (25) end if (26) end for (27) if k < Nc (28) if dist3(k + 1) > dt1 (29) break (30) end if (31) end if (32) end for (33) Permute according to order (34) return However, this procedure can be improved in several ways. First, the iteration between step 5 and step 32 does not need to be over all vectors , , and . Because the vectors are sorted in order of increasing distance, the likelihood of vectors being in the optimal solution decreases as the algorithm progresses, mainly for high SNRs. This suggests that some pairs of vectors may be skipped, and that the search can be stopped early according to some criterion, resulting in a significant reduction in complexity. The criterion should maximize the probability of the optimum solution, which has to be included in the search, while minimizing the number of vector pairs that are examined. This is the main reason for which the algorithm improves the complexity. The algorithm for nB = 2 can be easily obtained by making minimal changes to this pseudo code. 6 Results and Discussion 6.1 Simulation Results In this section, results of the proposed scheme are compared in terms of BER performance and complexity. The performance is compared considering a BER of 10–3 for the study cases. Figure 4 shows the performance comparison for a transmission of 8 bpcu with Nrx = 4 and 4-QAM modulation. It can be observed that the proposed GQSM scheme requires an additional SNR gain of around 1 dB and < 2 dB to obtain a performance similar to the QSM and SM schemes, respectively. In this case, the number of Tx antennas required by SM is Ntx = 64, QSM requires = 8, and GQSM Ntx = 4, which represents a reduction in Ntx of 93% and 50%, respectively. Figure 4Open in figure viewerPowerPoint BER performance versus SNR for 8 bpcu using 4-QAM. Figure 5 shows the performance comparison for a transmission of 12 bpcu, Nrx = 4, and 16-QAM modulation. In this case, the GQSM and SM schemes have a slightly better performance than the QSM scheme for the ML detection. The SM scheme requires Ntx = 256, QSM requires Ntx = 16, and GQSM requires Ntx = 4, which represents a reduction in Ntx of 98% and 75%, respectively. Figure 5Open in figure viewerPowerPoint BER performance versus SNR for 12 bpcu using 16-QAM. Figure 6 shows the performance comparison for a transmission of 12 bpcu, Nrx = 6, and 4-QAM modulation. In this case, the number of Tx antennas required by SM is Ntx = 1,024, QSM requires Ntx = 32, and GQSM requires Ntx = 6, which represents a reduction in Ntx of 99% and 81%, respectively. Figure 6Open in figure viewerPowerPoint BER performance versus SNR for 12 bpcu using 4-QAM. Table 6 compares the computational complexity of the proposed detectors. This complexity is measured in terms of the CO used per decoded symbol. Table 6. Complexity comparison in COs for the OSIC and near-ML algorithms Detection scheme 8 bpcu (4-QAM) nB = 2, Nrx = 4 12 bpcu (16-QAM) nB = 2, Nrx = 4 12 bpcu (4-QAM) nB = 3, Nrx = 6 ML 5,120 81,920 147,456 OSIC 1,039 1,999 2,860 Near ML Min Max Min Max Min Max 1,049 1,366 2,046 5,206 2,938 5,146 In this comparison, the complexity required to carry out the MMSE SQRD-GQSM algorithm has been included, and it was calculated using the polynomial defined in 14. In addition, the number of COs required for the algorithms are included in Table 4 and Table 5. The OSIC algorithm has the lowest complexity. Considering 12 bpcu and 4-QAM, this reduction represents 98%. The near-ML algorithm achieves almost the same reduction in its minimum. Figure 7 shows a comparison of the variation in the number of COs for ML, near-ML, and OSIC detection algorithms for a (4 × 4), nB = 2 transmission. (a) Shows the configuration with 8 bpcu and 4-QAM, and (b) shows the configuration with 12 bpcu and 16-QAM. The proposed near-ML algorithm achieves almost the same complexity for SNR values higher than 15 dB and 20 dB, respectively. Figure 7Open in figure viewerPowerPoint Variation in the number of complex operations for the OSIC and the near-ML algorithms for the (4 × 4), nB = 2: (a) 8 bpcu and 4-QAM configuration and (b) 12 bpcu and 16-QAM configuration. 6.2 Discussion In this study, a perfect CSI was assumed at the Rx; however, the channel estimation requires additional bandwidth, and a larger number of errors can occur in the detection owing to imperfect channel estimation, especially for systems with a large number of Tx antennas. The results obtained in this study show that the SM and some configurations of the QSM scheme have a better BER performance than the proposed GQSM scheme; however, the number of Tx antennas required for the transmission of high data rates may be impractical. Further, the CSI estimation for this system is challenging 19. The conventional SMux scheme requires a reduced number of Tx antennas and has a slightly better performance compared to the GQSM scheme; however, in this case, its high detection complexity is impractical. The proposed GQSM scheme inherits advantages and disadvantages of both the QSM and the SMux schemes. The main advantage of the proposed scheme is the flexibility of its system design, which enables the optimization of Ntx, performance, and complexity parameters. The proposed scheme can be easily generalized for groups with more than two Tx antennas. While this option reduces the detection complexity of the system, it also reduces the SE. On the other hand, the main disadvantage of the proposed scheme is that the number of RF chains required in the transmitter increases linearly with the number of groups of nB. The proposed OSIC algorithm has the lowest complexity; nevertheless, it has important losses in terms of its performance. The proposed Near ML algorithm shows a similar performance to the ML scheme, but with reduced complexity. This complexity is reduced to the OSIC complexity around SNR = 20 dB, which is close to the SNR used for the target BER of 10−3. 7 Conclusions In this paper, a spectrally efficient GQSM scheme has been proposed. In the GQSM scheme, the total Ntx is divided into small groups of two Tx antennas, where each group uses the QSM technique. Analytical and simulation results show that the ABEP performance of the proposed scheme has losses of < 2 dB when compared to the QSM scheme, but has the advantage of reducing the required Ntx by up to 81% for the analyzed cases. Compared with the SMux scheme, the proposed GQSM scheme has roughly the same performance, but with a reduction in detection complexity. In addition, a new efficient algorithm was proposed for the detection of GQSM signals. The proposed Near ML detection architecture performs with a complexity reduction of approximately 90%. The proposed GQSM scheme introduces many enhancement opportunities that can be considered in future work. For example, i) the incorporation of antenna selection into the grouping process, ii) the effects of imperfect CSI and correlated channels on the system performance, iii) combining the proposed scheme with other techniques such as block diagonalization, which can result in a general performance improvement and/or reduction in complexity detection. The proposed scheme may be an alternative for future wireless communication systems using the spatial constellations, where space limitations and detection complexity are crucial factors to be considered. Acknowledgements This work was supported by the projects PRODEP / SEP UASLP-PTC-598, 2017-2018, the PFCE 2016 and the Sonora Institute of Technology through internal funding for research groups (CAs). Biographies Francisco Rubén Castillo-Soria received his MS in Telecommunications Engineering from IPN-ESIME, Mexico City, in 2004 and his Ph.D. degree in Electronics and Telecommunications from the CICESE Research Center, Ensenada, Mexico, in 2015. Since 2017, he has been a research-professor at Autonomous University of San Luis Potosí, SLP, México. His current research interests include SM, STF coding and MIMO-OFDM. Joaquín Cortez-González received the MS and the Ph.D. degrees in Electrical Engineering from CINVESTAV- Guadalajara, Mexico, in 2001 and 2008 respectively. He is currently an electrical and electronics engineering professor at the Technologic Institute of Sonora. His research interests include digital communications and digital signal processing. Raymundo Ramirez-Gutierrez received the MEng. and Ph.D. degrees from the School of Electronic and Electrical Engineering, University of Leeds, Leeds, U.K., in 2009 and 2015, respectively. He is currently a DSP and algorithm researcher at Intel Labs in Guadalajara, Mexico. His research interests lie in the areas of wireless communications and signal processing, coding and modulation, massive MIMO systems, and mmWave technology. Fermín Marcelo Maciel-Barboza received his MEng degree in communications and electronics engineering, from the Universidad de Colima, Mexico, in 2010 and 2012, respectively. He is currently a professor with the Faculty of Mechanical and Electric Engineering, Universidad de Colima. His research interests include multiuser MIMO communications and cooperative networks. Leonel Soriano-Equigua received his MS and Ph.D. degrees in Electronics and Telecommunications from the CICESE Research Center, Ensenada, Mexico, in 2000 and 2011, respectively. Since 2000, he has been an assistant professor with the Faculty of Mechanical and Electric Engineering, Universidad de Colima. His area of interest is MIMO communications. References 1R.Y. Mesleh et al., "Spatial Modulation," IEEE Trans. Veh. Technol., vol. 57, no. 4, 2008, pp. 2227– 2241. 2P.W. Wolniansky et al., "V-BLAST: An Architecture for Realizing Very High Data Rates Over the Rich-Scattering Wireless Channel," in URSI Int. Symp. Signals, Syst. Electron., Pisa, Italy, Oct. 2, 1998, pp. 295– 300. 3A. Stavridis et al., "An Energy Saving Base Station Employing Spatial Modulation," in IEEE Int. Workshop Comput. Aided Modeling Des. Commun. Links Netw., Barcelona, Spain, Sept. 17–19, 2012, pp. 231– 235. 4M. Wen et al., "A Low–Complexity Near–ML Differential Spatial Modulation Detector," IEEE Signal Process. Lett., vol. 22, no. 11, 2015, pp. 1834– 1838. 5F.R. Castillo-Soria et al., "Multiuser MIMO Downlink Transmission Using Block Diagonalization and Generalized Spatial Modulation Techniques," AEU–Int. J. Electron. Commun., vol. 70, no. 9, Sept. 2016, pp. 1228– 1234. 6C.-X. Wang et al., "Cellular Architecture and Key Technologies for 5G Wireless Communication Networks," IEEE Commun. Mag., vol. 52, no. 2, 2014, pp. 122– 130. 7R. Mesleh, S.S. Ikki, and H.M. Aggoune, "Quadrature Spatial Modulation," IEEE Trans. Veh. Technol., vol. 64, no. 6, 2015, pp. 2738– 2742. 8H.-W. Liang et al., "Bi-Space Shift Keying Modulation for MIMO Systems," IEEE Commun. Lett., vol. 16, no. 8, 2012, pp. 1161– 1164. 9J. Li et al., "Generalized Precoding-Aided Quadrature Spatial Modulation," IEEE Trans. Veh. Tech., vol. 66, no. 2, 2017, pp. 1881– 1886. 10S. Kim, "Antenna Selection Schemes in Quadrature Spatial Modulation Systems," ETRI J., vol. 38, no. 4, Aug. 2016, pp. 606– 611. 11A. Younis et al., "Generalised Spatial Modulation," Conf. Record Asilomar Conf. signals, Syst. Comput., Pacific Grove, CA, USA, Nov. 7–10, 2010, pp. 1498– 1502. 12F.R. Castillo Soria et al., "Improved Detection of SM-SMux Signals for MIMO Channels," IEEE Latin Am. Trans., vol. 13, no. 1, Jan. 2015, pp. 43– 47. 13M.S. Alouini and A.J. Goldsmith, "A Unified Approach for Calculating Error Rates of Linearly Modulated Signals over Generalized Fading Channels," IEEE Trans. Commun., vol. 47, no. 9, 1999, pp. 1324– 1334. 14R. Böhnke et al., "MMSE Extension of V-BLAST Based on Sorted QR Decomposition," in IEEE Veh. Technol. Conf., Orlando, FL, USA, Oct. 6-9, 2003, pp. 508– 512. 15G.H. Golub and C.F. Van Loan, Matrix Computations, 3rd edition, Baltimore, MD, USA: John Hopkins University Press, 1996. 16M. Mohaisen, H. An, and K. Chang, "Detection Techniques for MIMO Multiplexing: A Comparative Review," KSII Trans. Internet Inform. Syst., vol. 3, no. 6, 2009, pp. 647– 666. 17B. Kim and K. Choi, "A Very Low Complexity QRD-M Algorithm Based on Limited Tree Search for MIMO Systems," in IEEE Veh. Technol. Conf., Singapore, May 11–14, 2008, pp. 1246– 1250. 18R. Wang and G. Giannakis, "Aproaching MIMO Channel Capacity with Soft Detection Based on Hard Sphere Decoding," IEEE Trans.Commun., vol. 54, no. 4, 2006, pp. 587– 590. 19O. Longoria-Gandara and R. Parra-Michel, "Estimation of Correlated MIMO Channels Using Partial Channel State Information and DPSS," IEEE Trans. Wirel. Commun., vol. 10, no. 11, 2011, pp. 3711– 3719. Citing Literature Volume39, Issue5October 2017Pages 707-717 FiguresReferencesRelatedInformation
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