Near optimum OSIC-based ML algorithm in a ...

Digital Signal Processing 40 (2015) 250–257

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Digital Signal Processing www.elsevier.com/locate/dsp

Near optimum OSIC-based ML algorithm in a quantized space for LTE-A downlink physical layer Mohamed G. El-Mashed ∗ , S. El-Rabaie Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt

a r t i c l e

i n f o

Article history: Available online 23 February 2015 Keywords: LTE-A MIMO OSIC ML Quantized space and complexity

a b s t r a c t In this paper, we propose a scalable and implementation efficient OSIC-based ML algorithm in a quantized space with higher performance for MIMO detection, which can be applied to the LTE-A downlink physical layer system. It is characterized by dividing the overall OSIC detector into small dimension blocks to reduce complexity. The proposed algorithm utilizes ML algorithm in a quantized space to detect the first data streams and overcome error propagation problem. Then, it applies small dimension OSIC block to detect other data streams. The mathematical analysis is illustrated and derived. This paper shows BER performance of the proposed algorithm and compares its performance with other algorithms. This paper also presents the computational complexity to show that it gives lower complexity close to optimal ML algorithm. Simulation results show that the proposed algorithm provides a better performance and low BER values compared to OSIC algorithm. Finally, the proposed algorithm enhances the detection in LTE-A system and gives results close to optimum ML. © 2015 Elsevier Inc. All rights reserved.

1. Introduction A 3GPP LTE-A promises high data rates for uplink and downlink transmission, low bit error rates, spectral efficiency and low latency [1–5]. MIMO techniques are applied to provide the better link quality and increase the transmission data rate. These systems require detection algorithms with high probability of detection, high performance and low complexity [6–9]. There are a variety of detection algorithms such as ML, ZF, MMSE and Ordered Successive Interference Cancellation (OSIC). The ML detection achieves a full diversity gain. The BER performance of ML can be used as the lower bound to measure the performance of other detection algorithms [20,21]. Its complexity is high because it depends on the number of antennas and signal constellation size [22]. ZF and MMSE algorithms are more practical due to their lower complexity. They are very easy to be realized with low computation and implementation costs [23,24]. They give lower performance compared to ML algorithm. In [27], approximate ML algorithm is based on reducing the search set. The symbol constellation points are replaced with the quadrant constellation (i.e., signal constellation for 16QAM is represented by four quadrant signal points). The ML Euclidean distances are calcu-

*

Corresponding author. E-mail address: [email protected] (M.G. El-Mashed).

http://dx.doi.org/10.1016/j.dsp.2015.02.007 1051-2004/© 2015 Elsevier Inc. All rights reserved.

lated using l2 -norm approximation. The complexity in [27] is still large and close to optimal ML. The OSIC algorithm gives better performance than ZF and MMSE [25,26]. The OSIC is a bank of ZF or MMSE algorithms [23, 24], each of which detects one of the parallel data streams, with the detected signal components successively canceled from the received signal at each stage. The detected signal in each stage is subtracted from the received signal so that the remaining signal with the reduced interference can be used in the next stages [26]. When the detection error occurred in the previous stages, it will be propagated to the next stages by the process of subtraction, which is called error propagation problem [26]. Therefore, if the detection accuracy in the previous stages improves, the detection performance will be better. Also, its complexity is high because it processes the matrix inversion several times that found in ZF or MMSE [31–34]. The reliability of the OSIC detection in the first stage is important and dominates the overall detection performance. To reduce error propagation problem, near optimum OSIC-based ML algorithm in a quantized space is proposed in this paper. In the proposed scheme, the OSIC architecture is divided into five subsections namely: Ordering, Group Interference Suppression, ML algorithm in a quantized space, Interference Cancelation and OSICMMSE algorithm. In the proposed algorithm, the block for ML algorithm in a quantized space is applied in the first stage of OSIC algorithm. The computational complexity of first block in proposed

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Fig. 1. LTE-A downlink physical layer transmitter structure [7–9].

algorithm is reduced because of two reasons. First, ML is applied to a small part of the detector which reduces complexity. Second, the multiplications of the difference in ML algorithm are replaced with readings from a Look-Up Table (LUT) [28,29]. For fast vector quantization encoding, [28] and [29] present Approximated LookUp Table (ALUT) method to speed up the calculation of the squared Euclidean distance between two vectors. In the proposed algorithm, we use LUT technique to simplify the calculation of squared Euclidean distances in ML algorithm. After quantization process for the received vector, the detection problem is sub-optimally solved. Then, a LUT with pre-stored components provides the distance metrics. The number of pre-stored components can be made as small as the number of quantization levels per dimension. This procedure eliminates the multiplications involved in the calculation of the squared Euclidean distances. We apply the proposed algorithm to LTE-A downlink physical layer system and compares with OSIC-ZF and OSIC-MMSE algorithms. The paper is organized as follows. Section 2, gives a brief review of the LTE-A downlink physical layer. The proposed algorithm is described in Section 3. The analysis of computational complexity is calculated in Section 4. The simulation parameters and results are given in Section 5. Finally, the concluding remarks are given in Section 6. 2. The LTE-A downlink physical layer The LTE-A physical layer uses MIMO OFDM technique for high data transmission. The LTE-A standard uses OFDMA for the downlink transmission and SC-FDMA for the Uplink transmission due to its low PAPR characteristics [10–12]. It supports both TDD and FDD operation [13,14]. LTE-A supports scalable bandwidths of 1.25, 2.5, 5, 10 and 20 MHz. In 20 MHz channel, the peak data rates of the downlink and the Uplink are 100 Mbps and 50 Mbps respectively. The standard specifies full performance within a cell up to 5 km radius and slight degradation from 5–30 km. It also supports highspeed mobility with high performance at speeds up to 120 km/h. LTE-A also specifies very low latency operation with control plane

(C-plane) latency of less than 50–100 ms and user plane (U-plane) latency of less than 10 ms [14,15]. In the downlink, the operations on the signaling information from the transmitter to the receiver are coding, HARQ, scheduling, and precoding operations [8,9]. In the Uplink, Channel Quality Indicator (CQI), Precoding Matrix Indicator (PMI), and Rank Indicator (RI) are signaled. These parameters give information about channel state. In this simulation scenario, the feedback of CQI, PMI, and RI are supported [12]. Setting fixed values to these parameters is required for specific simulations such as throughput evaluation of an individual Modulation and Coding Scheme (MCS). The LTE-A downlink physical layer transmitter structure is shown in Fig. 1. This structure is basically a graphical representation of the transmitter description defined in the TS36 standard series [7–9]. Based on User Equipment (UE) feedback values, a scheduling algorithm allocates Resource Blocks (RBs) to UEs and sets an appropriate MCS (i.e., coding rates between 0.076 and 0.926 with 4, 16, or 64-QAM symbol alphabet), the MIMO transmission mode and the precoding/number of spatial layers for all served users [10,11]. There are different MIMO transmission modes, which are Transmit Diversity (TxD), Open Loop Spatial Multiplexing (OLSM), and Closed Loop Spatial Multiplexing (CLSM). The benefits of the channel adaptive scheduling are frequency diversity, time diversity, spatial diversity and multi-user diversity. After the layer mapping, the reference symbols are inserted into the precoded data stream and OFDM symbols are assembled. The assembled OFDM symbols are transformed via IFFT into the time domain. The Cyclic Prefix (CP) is added to avoid Inter-Symbol Interference (ISI) between consecutive OFDM symbols [2–4]. Fig. 2 shows the LTE-A downlink physical layer receiver structure. First, the samples of CP are removed and then the received signal is transformed into the frequency domain using the FFT process. After that, the reference symbols are extracted and the channel is estimated. There are different types of channel estimators such as Least Squares (LS), Linear Minimum Mean Squared Error (LMMSE), Approximate LMMSE [17,18], genie-driven perfect channel knowledge based on all transmitted symbols, and perfect channel knowledge. The estimated channel coefficients are used to

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Fig. 2. LTE-A downlink physical layer receiver structure [7–9].

Fig. 3. The layout of MIMO systems.

calculate feedback values, in particular, the supported CQI, the optimum PMI, and the RI [19]. After disassembling the RBs according to UE resource allocation, a MIMO OFDM detection process using the estimated channel is carried out. There are different types of detectors such as the ZF, the MMSE, the OSIC and the SD decoding. The detected soft bits are decoded to obtain the data bits, coded/uncoded BER and throughput. The UE feedbacks (i.e., CQI, RI and PMI) are required in order to adapt the transmission to the current channel conditions [7]. The function of the CQI is choosing an appropriate MCS in order to achieve a predefined target BER, whereas the RI and the PMI are used for MIMO pre-processing. The simulator provides algorithms that utilize the estimated channel coefficients to evaluate these feedback parameters [19]. 3. The proposed OSIC-based ML in a quantized space algorithm Consider the N × M MIMO system as shown in Fig. 3. Let H denote a channel matrix with it ( j, i)th entry h ji for the channel gain between the ith transmit antenna and the jth receive antenna, j = 1, 2, . . . , M and i = 1, 2, . . . , N. The transmitted user data streams and the corresponding received signals are given by s = [s1 , s2 , . . . , s N ] T and r = [r1 , r2 , . . . , r M ] T , respectively, where si and r j denote the transmitted signal from the ith transmit antenna and the received signal at the jth receive antenna, respectively. The received signal vector with N transmits and M receives antennas is given by [26]:

r = Hs + z

(1)

where H is the channel matrix with M by N dimension and z is the AWGN noise vector. The channel matrix can be written as:

⎡

h11 ⎢ h21 ⎢

h12 h22

h M1

h M2

H=⎢

. ⎣ ..

.. .

· · · h1N · · · h2N .. .. . . · · · hM N

⎤ ⎥ ⎥ ⎥ ⎦

(2)

The proposed OSIC-based ML detection algorithm in a quantized space achieves the scalability because the whole detector is partitioned into basic building blocks that can be modified to different size. It uses Group Interference Suppression method [16] to divide the whole detector into small blocks. The processing time of each small block can be minimized, and then the detection can be applied in each block to reduce the whole detection complexity. The proposed algorithm consists of five blocks with smaller dimension. The blocks are ordering, Group Interference Suppression, ML algorithm in a quantized space, Interference Cancelation and OSICMMSE as in Fig. 4. We will analysis mathematically the proposed algorithm in the case of 4T × 4R antennas (i.e. T refers to transmits and R refers to receives). The blocks are followed as shown in Fig. 4. 3.1. Ordering The first step in the proposed algorithm is the ordering. It is done by the received power strength of each transmitter antenna:

Ho1 2 ≥ Ho2 2 ≥ . . . ≥ Ho N 2

(3)

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253

3.3. 2 × 2 ML algorithm in a quantized space The first part contains the first two transmitted streams after ordering for detecting. Now the 2 × 2 ML can be applied to detect the transmitted streams. The ML algorithm finds the minimum Euclidean distance between the received signal vector and the transmitted signal vectors. Let C , denote a set of signal constellation symbol points. Then, the detection of the ML algorithm is represented mathematically by the relation [27–29]:

sˆ ML = [ sˆ ML1

Fig. 4. The structure of the proposed OSIC-based ML in a quantized space algorithm.

Fig. 5. The structure of the Group Interference Suppression.

where Hi is the ith column of H and o1 , o2 , . . . , o N  is the detection order. 3.2. Group interference suppression

sˆ ML2 ] T = arg min r − Hs2

(8)

S ∈C 2

The Euclidean distance computation is the square of the difference between the received signal vector and the transmitted signal vectors which is basically a multiplication operation. If the range of the two integers to be multiplied is known, then all the possible product terms can be pre-computed and stored in a LUT. A LUT with pre-stored components provides the distance metrics. The number of pre-stored components can be made as small as the number of quantization levels per dimension. This procedure eliminates the multiplications involved in the calculation of the squared Euclidean distances. The total complexity required is reduced by replacing multiplications with readings from a LUT [27–29]. After quantization process, the resulting received quantized vector is:

 [˜r1 , r˜2 , . . . , r˜ N R ]T = Q θ [r1 , r2 , . . . , r N R ]T

(9)

The received quantized components r˜i ∈ {c 1 , c 2 , c 3 , . . . , c Θ }, with quantization levels Θ = 2b , (i.e., b is the number of bits) have a uniform step size, which is given by:

The next step is the Group Interference Suppression, which limits the dimension of the channel matrix. It minimize the effect of interference in the detection process, such as noise amplification, loss and fading of desired signals energies in the channel while combating the outside interference. It consists of splitter, null space finder and the Gram–Schmidt Orthogonalization (GSO) [30]. The channel matrix H can be divided into [H1 H2 ]. For 4T × 4R case, the H1 consists of [Ho1 Ho2 ] w, and H2 consists of [Ho3 Ho4 ] as shown in Fig. 5. The null space finder is used to find the null space of the group which is eliminated for the ML block. The null space of H2 is [30]:



I − H2 H2H H2

− 1

H2H

(4)

where I is the identity matrix. Then, choose two row vectors in this set due to the rank of left null space is two for MIMO case, and then apply the GSO to obtain two orthonormal vectors to form the matrix P. The matrix P consists of a set of orthogonal vectors selected in left null space of H2 such that:

P[ H1

H2 ] = [ PH1

˜ PH2 ] = [ H

0]

(5)

Then, we multiply both sides of Eq. (1) by matrix P as follows:

Pr = PHs + Pz

(7)

˜ = PH1 , r˜ = Pr, z˜ = Pz, and s˜ = [s1 s2 ] T . where H Then, the proposed detector is divided into two parts, one is a 2 × 2 part which is detected by ML after quantization process and the second part is a 4 × 2, which is detected by OSIC-MMSE as shown in Fig. 4.

i ∈ {1, 2, . . . , Θ}

(10)

The values of {c 1 , c 2 , c 3 , . . . , c Θ }, is given by:

{c 1 , c 2 , c 3 , . . . , c Θ } 

= −(Θ − 1), . . . , −3, −1, +1, +3, . . . , (Θ − 1)

(11)

Fig. 6(a) shows the bipolar quantizer with Θ = 8 levels (b = 3 bits). The Euclidean distances needed to solve ML equation are given by: n

 (l) 2 r − Hs(l) 2 = r˜i − H s˜ , i

l = 1, 2, . . . , M n

(12)

i =1

(l)

For a particular lattice point Hs(l) , and letting Δi = (˜r i − H s˜ i ), each particular squared Euclidean distance is:



2

d2 = r − Hs(l) =

n

Δ2i

(13)

i =1

The major computation in the Euclidean distance between r and Hs(l) is the square of a difference. The squares of all the possible difference components Δ2i , can be arranged in a 2-D LUT as follows [27–29]:

⎛

(6)

After applying the Group Interference Suppression, the received signal vectors become:

˜ s˜ + z˜ r˜ = H

q = c i − c i +1 ,

(c 1 − c 1 )2 (c 1 − c 2 )2 (c 1 − c 3 )2 ⎜ (c 2 − c 1 )2 (c 2 − c 2 )2 (c 2 − c 3 )2 ⎜ ⎜ (c 3 − c 1 )2 (c 3 − c 2 )2 (c 3 − c 3 )2 ⎜ T 1 = ⎜ (c 4 − c 1 )2 (c 4 − c 2 )2 (c 4 − c 3 )2 ⎜ ⎜ .. .. .. ⎝ . . . (c Θ − c 1 )2 (c Θ − c 2 )2 (c Θ − c 3 )2

⎞ . . . (c 1 − c Θ )2 . . . (c 2 − c Θ )2 ⎟ ⎟ . . . (c 3 − c Θ )2 ⎟ ⎟ . . . (c 4 − c Θ )2 ⎟ ⎟ ⎟ .. .. ⎠ . . 2 . . . (c Θ − c Θ ) (14)

It is shown from the above LUT that (cm − cm ) = 0, and (cm − cn )2 = (cn − cm )2 = (c |m−n| )2 , for all m = n (m, n = 1, 2, 3, . . . , Θ). Therefore, the T 1 can be rewritten as follows: 2

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Table 1 The 4 × 2 OSIC-MMSE algorithm. W1 = [(H2H H2 + σz2 I)−1 H2H ]1T ; y1 = W1T r ; sˆ 1 = Q (y1 ); r = r − (H2 )1 sˆ 1 ; W2T = [((H2 (:, 2)) H H2 (:, 2) + σz2 I)−1 (H2 (:, 2)) H ]; y2 = W2T r ; sˆ 2 = Q (y2 );

{Nulling} {Slicing} {Cancelation} {Nulling} {Cancelation}

(l)

(l)

coming from upper bounds of [− max(Hsi ), + max(Hsi )] does not introduce any degradation in the ML problem. So we assume these errors are negligible. 3- The granular noise is the only noise that affect on the performance. We also assume that the quantization in each dimension is a uniform error distribution, and then the quantization noise variance is:

q/2

1

2 q

σ =

q

−q/2

Fig. 6. (a) Bipolar quantizer with Θ = 8 levels (b = 3 bits) in each dimension normalizing the input to Hs(l) and (b) Quantization error for the squared Euclidean distance as a function of the number of quantization bits obtained by simulation.

⎛

2

2

0 (c 1 ) (c 2 ) ⎜ (c 1 )2 0 (c 1 )2 ⎜ 2 ⎜ (c 2 )2 (c 1 ) 0 ⎜ 2 2 T 2 = ⎜ (c 3 )2 ( c ) ( c 2 1) ⎜ ⎜ .. .. .. ⎝ . . . (c Θ−1 )2 (c Θ−2 )2 (c Θ−3 )2

... ... ... ... .. . ...

2

⎞

(c Θ−1 ) (c Θ−2 )2 ⎟ ⎟ (c Θ−3 )2 ⎟ ⎟ (c Θ−4 )2 ⎟ ⎟ ⎟ .. ⎠ .

2

2

2

 2 T

T 3 = 0, (c 1 ) , (c 2 ) , (c 3 ) , . . . , (c Θ−2 ) , (c Θ−1 )

(15)



|cm − cn | q

(16)



+1

(17)

The value of the distance component can be determined from the values pre-stored in a LUT. The use of LUT does not produce any errors because it is an exact method in the quantized space. The lattice and received signal are bounded to (l) (l) [− max(Hsi ), + max(Hsi )] in the ith real dimension, corresponding to the clipping imposed by Q θ ( ). To reduce quantization noise, we assume that: 1- All data symbols are uncorrelated and quantization noise nq , is component-wise independent. These assumptions make the total noise variance in a quantized vector is:

σt2 = σn2q ,1 + σn2q ,2 + · · · + σn2q ,i + · · · + σn2q ,N R where

 

E [nq ] = E 1 −

 ˜r − H s˜ (l) 2 − r − Hs(l) 2   · 100 r − Hs(l) 2

σs2 σs2 σ2 = 2= s 2 = 2 n qi n σt σq i =1 12

The squared difference of cm ∈ r and cn ∈ Hs(l) is given by T 2 (cm , cn ) = (c |m−n| )2 = T 3 (|cm − cn | + 1). In order to approximate the absolute separation between the distances components to an integer number of intervals, we divide by a uniform step size q as follows:

T 2 (cm , cn ) = (c |m−n| )2 = T 3

(19)

12

Independently of the number of dimensions n, the percentage of mean error per dimension is obtained by simulation using:

0

2

q2

(20)

and the result is shown in Fig. 6(b). The signal to total quantization noise ratio is:

Note that the first column of the above 2-D LUT contains all the n distinct scalars. Then, the above entries in reduced to T 3 as follows:



s2 ds =

(18)

σn2q ,i is the noise variance in the ith dimension.

2- The complex lattice of possible points in each receive antenna is a combination of N T constellation symbols weighted by the complex channel coefficients. If the quantized space with sides (l) of length max(Hsi ) contains all the lattice points, then the error

= n

3Θ 2 σs2

i =1



σs2 σt2

 dB

(l) max(Hs )2

σs2 (l)

i =1

(2 max(Hsi )/Θ)2

= n

i

12 3(2b )2 s2

σ

(21)

(l) 2 )

i =1 max(Hsi

 = 4.77 + 6.02b + 20 log n



σs2 (l) 2 )

(22)

i =1 max(Hsi

From above equation, SNR may be limited by the quantization error, which is a function of both the lattice and of the number of bits per dimension. Every extra bit used in the quantization of each component improves the signal to quantization noise on that real component by 6 dB. 3.4. Interference cancelation After that, the Interference Cancelation subtracts the interference of the detected signals by the ML detector as follows [25,26]:

r = r − H1 sˆ ML

(23)

3.5. 4 × 2 OSIC-MMSE The second part of the proposed algorithm is a 4 × 2 OSICMMSE algorithm. The process for detecting the signals is listed in Table 1. The matrices H1 and H2 are defined in Eq. (5), [H]1 denotes the first row of matrix H and H2 (:, 2) denotes the second column of matrix H2 . 4. Computational complexity The complexity of ML is C N M ( N + 1), where C N M N is for matrix multiplication and C N M is for square operation (i.e., C is the constellation size). The computation complexity of pseudo-inverse

M.G. El-Mashed, S. El-Rabaie / Digital Signal Processing 40 (2015) 250–257

Table 2 Complexity comparison between OSIC-ZF, OSIC-MMSE and proposed algorithm in the case of 4T × 4R. Total complexity

ML OSIC-ZF OSIC-MMSE Proposed

QPSK, M = 4, N = 4, C = 4

16QAM, M = 4, N = 4, C = 16

64QAM, M = 4, N = 4, C = 64

5120 712 1032 316

1 × 106 712 1032 556

3 × 108 712 1032 4396

matrix [(H H H)−1 H H ] putation needs to be sion. The complexity  N −1 i =0 [ N ( N − i ) + 2N ] by: N





4i 3 + 2Mi 2 +

i =0



= N4 +

for OSIC-ZF is 4N 3 + 2M 2 [38]. This comcalculated N times with decreasing dimenof ordering and interference cancelation is [39]. The total complexity of OSIC-ZF is given

N −1



N ( N − i ) + 2N

i =0

5

+

2

2 3





M N3 +

7 2

255

Table 3 LTE-A downlink physical layer parameters. Parameter

Value

Bandwidth Modulation Number of resource blocks FFT size Cyclic prefix No. of transmit and receive antennas Detection algorithms Transmission mode Channel estimator Channel type SNRs

5 MHz QPSK, 16QAM and 64QAM 25 512 Normal 4T×4R OSIC-ZF, OSIC-MMSE, ML and proposed Open Loop Spatial Multiplexing (OLSM) MMSE ITU VehA [37] 0–35 dB



 1 + M N2 + M N

(24)

3

where i represents the index of summation. Also, the total complexity of OSIC-MMSE is given by:

 4

N +

5 2

+

2 3



 3

M N +

7 2

 +M+M

2

 2

N +

1 3

 + M M N (25)

The complexity analysis of the proposed algorithm is computed for each part. The computational complexity for ordering (M , N) process is M N. The complexity of Group Interference Suppression part is given by [39]:





2( M + 1)2 + 2M + M ( N − 2)

 + M ( M − 2)( N − 2) + M ( M − 2) 

(26)

The complexity of 2 × 2 ML in quantized space part is C 2 . The complexity of interference cancelation part is 2M. Two important steps of the 4 × 2 OSIC-MMSE detector involve generation of two nulling vectors, W1 and W2 which are derived from (H2H H2 + σz2 I)−1 H2H and (((H2 (:, 2)) H (H2 (:, 2)) + σz2 I)−1 )(H2 (:, 2)) H respectively. Note that the pseudo inverse operation is very simple in this OSIC detector because (H2H H2 ) is only 2 × 2. For QPSK, the complexity of proposed algorithm is calculated from above equations as follows: a) b) c) d) e)

Ordering: 16 Group Interference Suppression: 90 2 × 2 ML Algorithm in a Quantized Space: 16 Interference Cancelation: 8 4 × 2 OSIC-MMSE: 186

The total complexity of the proposed algorithm is: 16 + 90 + 16 + 8 + 186 = 316. The respective computational complexities of ML, OSIC-ZF, OSIC-MMSE and proposed algorithm in the case of 4T × 4R are listed in Table 2. The results show that the complexity of the proposed algorithm is much lower than the OSIC-ZF and OSICMMSE in the case of QPSK and 16QAM. For QPSK, the complexity reduction of OSIC-ZF and OSIC-MMSE algorithm is 86% and 79.8% respectively. The proposed algorithm gives 93.8% complexity reduction compared to ML. It also gives lower complexity in the case of 16QAM. In the case of 64QAM, it gives low complexity compared to ML and high complexity compared to OSIC-ZF and OSIC-MMSE algorithms.

Fig. 7. Comparison of the BER performance for different detection algorithms in the case of QPSK.

5. Simulation parameters and results The performance of the proposed OSIC-based ML in a Quantized Space algorithm was evaluated through link-level simulations under the LTE-A specifications [36]. The simulation parameters for a LTE-A standard are listed in Table 3. We considered the Vehicular-A channel environment at different mobile speed [35]. We compare BER performance of the proposed algorithm with those of the OSIC-ZF, the OSIC-MMSE, and the ML. Our simulation setup corresponds to the spatial multiplexing MIMO systems with the case of 4T×4R antennas. Fig. 7 shows the performance of the proposed algorithm in the case of QPSK. The proposed scheme gives low BER values compared to others. The performance of the proposed algorithm for different values of the number of bits per component is compared to other detection algorithm. The ML detection in a quantized space for different levels of quantization per dimension improves the performance of the OSIC algorithm as illustrated in Figs. 7, 8 and 9 for QPSK, 16QAM and 64QAM respectively. It is observed from figures that the BER performance changes when the number of quantization levels (b) changes. The results show that for b = 4, the performance of the proposed algorithm is close to the OSIC-MMSE. For b increased to 5, the performance of the proposed algorithm enhanced compared to b = 4 as shown in Fig. 7. For b = 6, the performance of the proposed algorithm is close to ML. When of the number of quantization bits (b) increased, the quantization error for the squared Euclidean distance is increased. The performance of the proposed detector is best for b = 4, 5, and 6 bits. The number of bits needed to represent both the received vectors and the lattice associated with each channel realization is shown to be small. The near optimum proposed algorithm close clearly to the optimum ML detection in the case of 64QAM as shown in Fig. 9.

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ulation results show that the proposed algorithm gives low BER values compared to OSIC-ZF and OSIC-MMSE algorithm. Finally, it improves the detection in LTE-A system. References

Fig. 8. Comparison of the BER performance for different detection algorithms in the case of 16QAM.

Fig. 9. Comparison of the BER performance for different detection algorithms in the case of 64QAM.

At SNR = 15 dB, the proposed detector gives BER values 2 × 10−4 (b = 6), 4 × 10−3 (b = 5), 7 × 10−3 (b = 4) which are low compared to 3 × 10−2 and 1.5 × 10−2 for the OSIC-ZF and the OSIC-MMSE detectors respectively as shown in Fig. 7. The optimum ML algorithm is taken reference to other algorithms. The BER value for ML at SNR = 15 dB is 2.5 × 10−5 , which is close to 2 × 10−4 for the proposed algorithm (b = 6). The proposed algorithm gives low complexity and achieves much better BER performance in the QPSK and 16QAM cases. For 64QAM, the complexity increase but performance is still high. The results show that the proposed technique outperforms the other detection techniques. Finally, the proposed OSIC-based ML algorithm in a quantized space is applicable in LTE-A systems. 6. Conclusion In this paper, a scalable and applicable OSIC-based ML algorithm in a quantized space has been proposed. The proposed algorithm divides the whole detector into small blocks to reduce complexity. It uses ML algorithm in a quantized space to detect the first data streams and overcome error propagation problem in OSIC. Then, it applies small dimension OSIC block to detect other data streams. The ML block with small dimension uses LUT to save a lot of computation time and speed up the calculation of the squared Euclidean distance between transmitted and received signals. The proposed algorithm has been applied in the application for LTE-A downlink physical layer. It achieves better performance, which approaches to optimal ML. Its complexity is low compared to OSIC-ZF and OSIC-MMSE in the case of QPSK and 16QAM. Sim-

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Mohamed G. El-Mashed received the B.Sc. (Honors) and M.Sc. from the Faculty of Electronic Engineering, Menofia University, Menouf, Egypt, in 2008 and 2012, respectively. He is currently a Ph.D. student and assistant lecturer in the Dept. of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University. His research areas of interest include: Ultra-Wide Band (UWB) radar applications, radar signal processing and imaging, MIMO radar system, SAR imaging techniques, digital signal processing, advanced digital communication systems, wireless communication systems, WiMAX, LTE, LTE-A and FPGA implementation in communication systems. Prof. S. El-Rabaie is involved now in different research areas including CAD of nonlinear microwave circuits, nanotechnology, digital communication systems, and digital image processing. He has authored and co-authored more than 180 papers and eighteen books. He was awarded several awards (Salah Amer Award of Electronics in 1993, the best researcher on CAD from Menoufia University in 1995). He acts as a reviewer and member of the editorial board for several scientific journals. He has shared in translating the first part of the Arabic encyclopedia. Professor El-Rabaie was the head of the Electronic and Communication Engineering Dept., Faculty of Electronic Engineering, Menoufia University, then the vice dean of Postgraduate Studies and Research in the same faculty. Now he is member of the Electronic and Communication Eng. Promotion Committee and reviewer of Quality Assurance and Accreditation of Egyptian Higher Education.