Super-Orthogonal Double Space-Time Trellis Code

Super-Orthogonal Double Space-Time Trellis Code

Mohammed A. Tubaila, Ammar M. Abu-Hudroussa, Mohammed Taha O. ElAstalb

aDepartment of Electrical Engineering, Islamic University of Gaza, Gaza, Gaza Strip,Palestine

bCTRC, P-ICTRA, Gaza, Gaza Strip, Palestine

Abstract

This study develops a new class of super-orthogonal trellis code for four trans-

mit antennas based on double space-time codes. The transmit antennas are

divided into two groups, each having two transmit antennas. The information

bits are demultiplexed into two streams; each is encoded independently using

a super-orthogonal trellis code and then is transmitted from the corresponding

antenna group. The resultant parallel-trellis code structure offers a higher data

rate and, at the same time, it has a smaller number of parallel branches in the

trellis encoder compared to a single stream encoder. The decoding is done using

a maximum likelihood decoder with an interference cancellation algorithm.

It has been shown that the proposed scheme reduces the required number of

overall calculations by about half compared with super-orthogonal space-time

trellis codes (SO-STTC) and super-orthogonal trellis coded spatial modulation

(SOTC-SM).

The performance of the designed codes is simulated and shows that an im-

provement in the frame error rate is achieved at 4 and 5 b/s.Hz compared with

SO-STTC and SOTC-SM, while at 6 b/s.Hz, it achieved an improvement in the

lower and medium range of SNR (< 22).

Keywords: Trellis, MIMO, STBC, STTC, SO-STBC

Email addresses: [email protected] (Mohammed A. Tubail),[email protected] (Mohammed Taha O. El Astal), [email protected] (AmmarM. Abu-Hudrouss)

Preprint submitted to AEU - International Journal of Electronics and CommunicationsMay 9, 2020

1. Introduction

Alamouti’s code is the first space-time block code (STBC) that was designed

to give full diversity to a MIMO system with 2 transmit antennas [1]. It was

generalised in [2] to accommodate any number of transmit antennas. Based

on Alamouti’s code, the ‘Double space-time transmit diversity’ (DSTTD) was

proposed in [3], [4]. It consists of two Alamouti STBCs at the transmitter and

with interferer-resistance decoder at the receiver. Thus, the spectral efficiency

improved compared to Alamouti’s code and it benefits from the same diversity

gain. However, the decoder’s complexity of DSTTC increases. This can be miti-

gated as demonstrated in [3, 5], by using a cancellation technique that separates

the two STBC codes and decreases the needed operations for the decoder.

Space-time trellis coding, STTC, was first introduced in 1998 by Tarokh, Se-

shadri and Calderbank in [6]. This technique offers better reliability for wireless

communications. In [7], another scheme was realised by concatenating Alam-

outi’s STBC symbols drawn from the phase shift keying (PSK) constellation

with an outer trellis code. This scheme is called ‘super-orthogonal space-time

trellis code’ (SO-STTC). The SO-STTC has an improved performance of more

than 2 dB compared to STTC. The authors also provided a systematic method

to maximise the coding gain for a given rate, constellation, and number of states.

However, for high data rates (≥ 4b/s.Hz), the SO-STTC either should have a

high number states or a high number of parallel branches which negatively im-

pact the performance or the complexity of the system, respectively [8].

Spatial modulation (SM) concept was first introduced in [9], and modified with

trellis coded spatial modulation (TCSM) in [10], [11]. In the TCSM scheme

the incoming sequence of bits is divided into two groups. The second group

directly enters the SM mapper while the first enters the SM mapper after being

coded by a 4-state convolutional encoder. In this scheme, the improvement in

performance occurs only in the correlated channels whereas there is no error

performance advantage in uncorrelated channels compared to uncoded SM. In

[12], the authors directly combined the trellis coding and SM by passing all the

2

incoming bits through a convolutional encoder before entering the SM mapper.

Therefore, this scheme benefits from the trellis coding in both correlated and

uncorrelated channels by fully coding all the incoming bits.

Moreover, another method in [13] is proposed to enhance the overall spectral effi-

ciency of the SM technique while retaining all the advantages of SM system. The

proposed technique, called quadrature spatial modulation (QSM), succeeded in

increasing the spectral efficiency of its systems over SM and improving the error

performance without any increase in cost or receiving complexity. Also, trellis

coded quadrature spatial modulation enhanced spatial (TC-QSM) was proposed

in [14]. The TC-QSM has a better error performance when compared with the

TCSM.

Many novel schemes were proposed based on combining the advantages of the

STBCs and the SM concept in one scheme. For example, a novel design, called

“Space-time block coded spatial modulation” (STBC-SM) was proposed in [15].

In this scheme, both the STBC code and the indices of the active pair of trans-

mit antennas carry the information. STBC-SM offered an improvement on the

error performance over SM and vertical-Bell laboratories layered space-time (V-

BLAST) with a low-complexity maximum likelihood decoder. An improvement

in spectral efficiency over STBC-SM was proposed in a new scheme called space-

time block coded spatial with cyclic structure (STBC-CSM) [16]. In this scheme,

as in STBC-SM, both the STBC symbols and the indices of the active antennas

carry information. In addition, the active pair of transmit antennas is chosen

circularly along the total transmit antennas.A modified version of SOTC-SM is

introduced in [17]. The code is denoted as SOTC-CSM is created by expanding

the codebook using the cyclic space-time spatial codes. For eight state trellis

structure, the proposed SOTC-CSM schemes achieve significantly better error

performance than the SOTC-SM with the same decoding complexity.

A new class of STTC, called ‘super-orthogonal trellis-coded spatial modulation’

(SOTC-SM), was proposed in [18]. This code applies set-partitioning on the

super-set of STBC-SM, which was proposed in [15]. Meanwhile, SOTC-SM uses

a super-set of STBC-SM which results in an increase in the distance spectrum

3

of the trellis codes, which in turn yield in an improvement in the error perfor-

mance for the same spectral efficiency. As in SO-STTC, SOTC-SM suffers from

a high number of parallel branches and a high complexity decoder.

Here, a novel super-orthogonal double space-time trellis code (SO-DSSTC) is

designed. It offers better performance because of the coding and diversity gains

of SO-STTCs inherited in the new design. Moreover, the receiving complexity is

reduced by dividing the overall encoding system into two symmetrical indepen-

dent SO-STTC with a half rate for each. Each sub-system employs a different

pair of transmit antennas.

A small number of states (≤ 8) in the Trellis is used to reduce the decoding com-

plexity of SO-STTC and SOTC-SM at the expense of having parallel branches.

The subset of data in the parallel branches is not coded but it is protected

by the large minimum Euclidian distance within the subset as a result of the

set-partitioning. However, as the data rate becomes higher, a larger number of

parallel branches is needed to maintain a small number of states. As a result, the

minimum Euclidian distance for the parallel subset inevitably becomes smaller.

It is worth mentioning that even with a small number of states, the complexity

of the decoding of both SO-STTC and SOTC-SM increases dramatically with

the data rate.

The division of the encoding system into two separate SO-STTCs with half of

the rate for each reduces the number of parallel branches in each state in the

code. At the same time, it reduces the complexity of the maximum-likelihood

decoder.

To elaborate on the idea of the new scheme, assume that we have a 4-state

MIMO system with spectral efficiency 4 b/s.Hz. In SO-STTC, 256 transitions

diverge from each state and merge into the next states; thus, the number of

parallel branches is 64. While in SO-DSTTC, there are two systems with 2

b/s.Hz for each. For each state in both systems, there are 16 transitions diverg-

ing from it and there are only four parallel branches. This significant decrease

in the number of overall transitions from each state and the resultant number

of parallel branches enhance the error performance of the system, especially in

4

high data rate systems, and also in reducing the complexity of the maximum

likelihood (ML) decoder.

The remainder of this paper is organised as follows: In section 2, the SO-DSTTC

is illustrated. In section 3, the decoding criteria and the related complexity cal-

culations are presented. In section 4, the simulation results and the performance

comparison are given. Finally, in section 5, the conclusions of the paper are pre-

sented.

2. Super-orthogonal double space-time trellis codes

In this section, the system model of the new scheme is introduced and the

set partitioning of SO-STTC is presented. Also, the related rotating angles to

produce the desired design are listed.

2.1. System model

A MIMO with four-transmitting antennas L = 4 and N ≥ 2 receive antennas

is considered. A block diagram describing the introduced code transmitter is

shown in Fig. 1. The system consists of two symmetrical SO-STTC sub-systems

each with 2 transmit antennas and with k/2 b/s.Hz spectral efficiency. Each

sub-system employs a different pair of transmit antennas.

The incoming data stream is divided into two independent streams. For each

sub-system, k bits are encoded by SO-STTC and produce an Alamouti’s STBC

according to the trellis structure of the employed code. The number of branches

leaving each state is 2k and the number of parallel branches is equal to (2k/ total

number of states). Each SO-STTC encoder uses phase rotation to maximise the

coding gain of the encoder. In the case of a 4 × 2 SO-DSTTC MIMO system,

the code matrix is given by,

X =

s1ejθ11 s2e

jθ12 s3ejθ21 s4e

jθ22

−s∗2e−jθ12 s∗1e−jθ11 −s∗4e−jθ22 s∗3e

−jθ21

, (1)

where (s1, s2) are the transmitted symbols from the first antenna group,

while (s3, s4) are transmitted from the second antenna group. The transmitted

5

Figure 1: SO-DSTTC encoder’s block diagram

symbols si,i=0,1,. . . ,M -1 are drawn from M -PSK/QAM with phase rotations

of {θ11, θ12} for (s1, s2) and (θ21, θ22) for {s3, s4}, respectively. In the proposed

scheme, the rotating angles of the other sets of the constellation points were

optimised to ensure maximum diversity and coding gain.

The received signal, assuming flat-fading channel during two-time intervals, can

be expressed as,

Y = HX + Z (2)

where,

Y =

y11 y21 . . . yN1

y12 y22 . . . yN2

T

, (3)

ynk denotes the received signal by the nth receive antenna at a timeslot k (in

Alamouti’s STBC, k = 1,2),

H =

h11 h12 h13 h14

h21 h22 h23 h24...

......

...

hN1 hN2 hN3 hN4

, (4)

where hnm denotes the channel coefficient between the mth transmit antenna

and the nth receive antenna, and

Z =

z11 z21 . . . zN1

z12 z22 . . . zN2

T

, (5)

6

where znt represents the noise element in the nth receive antenna at a times-

lot t.

The system model in (2) can be changed to the following equivalent form,

y =

y11

y∗12...

yN1

y∗N2

= Hex + Z, (6)

where,

He =

h11 h12 h13 h14

h∗12 −h∗11 h∗14 −h∗13...

......

...

hN1 hN2 hN3 hN4

h∗N2 −h∗N1 h∗N4 −h∗N3

, x =

s1e

jθ11

s2ejθ12

s3ejθ21

s4ejθ22

, (7)

and Z is the modified noise matrix.

2.2. SO-STTC set-partitioning

The set-partitioning of the super-set of Alamouti’s code is performed to en-

sure that the constructed trellis structure achieves the needed coding gain. The

set-partitioning of these codes is based on the CGD metric, which is expressed

as,

d = det(A(Ci,Cj)) (8)

where

A(Ci,Cj) = D(Ci,Cj)HD(Ci,Cj) (9)

and D is the difference matrix between the transmission matrices Ci and Cj

and can expressed as,

D(Ci,Cj) = Ci −Cj , i 6= j (10)

The set partitioning of STBC codewords for 8-PSK is illustrated in Fig. 2 and

the set partitioning of STBC codewords for QPSK is illustrated in Fig. 3, while

7

the set partitioning of STBC codewords for 16-QAM is based on the criteria in

[19].

Figure 2: The set-partitioning of STBC codewords for QPSK

Figure 3: The set-partitioning of STBC codewords for 8-PSK

2.3. Trellis structure

After the set-partitioning process, the trellis structure for the code can be

constructed by assigning different STBC codewords for transitions originating

from every state. Fig. 4 demonstrates different examples of the proposed SO-

DSTTC scheme. In these figures, C(s1, s2, θ11, θ12) represents the particular

codewords from the set-partitioning for the state with rotating angles θ11 and

8

θ12 for the symbols s1 and s2, respectively. Similarly, the rotating angles θ21

and θ22 are used for the symbols s3 and s4, respectively. The As symmetric

codes are used, each example shows the trellis structure of one of the parallel

codes.

Fig. 4 illustrates examples of 4-state SO-DSTTC for a rate of 4 b/s.Hz, 5 b/s.Hz,

and 6 b/s.Hz. Fig. 4(a) shows a trellis structure of rates of 4 b/s.Hz and 6 b/s.Hz

using the QPSK and 8-PSK modulation schemes, respectively. In the trellis

structure of a rate of 4 b/s.Hz, each state has 16 diverging branches. While in

the case of a 6 b/s.Hz rate, the number of branches originating from each state

is equal to 64 and these branches merge into 4 states only. Therefore, there are

16 parallel branches in each state. In these structures, four pairs of optimised

rotating angles are used to ensure the maximum coding gain is achieved.

Fig. 4(b) shows a 4-state example with a rate of 5 b/s.Hz. In this example, the

8-PSK modulation scheme is used with the corresponding set-partitioning as

illustrated in Fig. 3. In the proposed code, each state in the parallel structure has

only 32 diverging branches. However, both SO-STTC and SOTC-SM with same

data rate and number of trellis states, each state has 1024 diverging branches as

the 32 QAM are used. In this example, only 2 pairs of optimised rotating angles

are used. C(s1, s2, 0, 0) is assigned for the first two states and C(s1, s2, θ11, θ12)

is assigned for the last two states in order to increase the coding gain.

2.4. Rotating angle optimisation

Rotating angles pairs {θ11, θ12} and {θ21, θ22} are optimised to ensure the

maximum coding and diversity gains. These angles are related directly to the

minimum CGD, so this optimisation is performed to maximise the minimum

CGD of codewords that will be assigned to the different states of the code.

The optimised rotating angles pairs are calculated by a linear optimisation al-

gorithm with a cost function that maximises the minimum CGD and the results

are recorded in Table 1. In Table 1, the symbols are assigned according to Fig. 4

where θ ∈ {−π, π} and k represents the index of the angle pair according to the

trellis figure.

9

Figure 4: A 4-state SO-DSTTC (the first code trellis structure (a) r = 4 b/s.Hz and 6 b/s.Hz

using QPSK and 8PSK, respectively, (b) r = 5 b/s.Hz using 8PSK

3. ML decoding with interference cancellation (IC)

SO-DSTTC receiver uses the Viterbi algorithm to perform a soft ML decod-

ing process and find the most likely valid path for a specific frame length. In

general, the decoding process passes through four stages to decode the symbols

(s1, s2, s3, s4). Then, these stages are repeated in two-step decoding to minimise

the mean squire error (MSE). Fig. 5 and Fig. 6 describe the mechanism of the

decoding process.

3.1. Decoding process

The SO-DSTTC decoding process passes through the following stages, which

also are described in Fig. 5. The decoding process is done using the minimum

10

mean square error interference cancellation (MMSE-IC) method [3].

Figure 5: Decoding process step stages

Table 1: The optimised rotating angles of SO-DSTTC in Fig. 4

Spectral Num. Num. of

Figure efficiency of rotating θ1k θ2k

(b/s.Hz) states angle pairs (rad) (rad)

0 0

0.9163 -2.4871

4(a) 4 4 4 -1.4399 -0.9163

-2.7489 -1.4399

0 0

4(a) 4 4 42.5133 1.2566

0 0

-2.3562 -1.8850

4(a) 4 4 4 2.8274 -0.6283

-1.8850 0.6283

11

3.1.1. Calculate the weights (α1, α2) for MMSE-IC

: The weights α1 and α2 are used in the interference canceller that min-

imises the MSE. These weights are used in the decoding process of (s1, s2), the

transmitted symbols from the first structure. According to the system model in

(6), α1 and α2 can be calculated as the following,

M = HeHHe +

2.5

ρI2N (11)

α1 = M−1h1, α2 = M−1h2 (12)

where hi in (12) is the ith column of He in (7), ρ is the signal to noise ratio

(SNR) and I2N represents an identity matrix of size 2N × 2N .

3.1.2. First structure decoding (s1, s2)

The Viterbi algorithm is used to perform the MMSE decoding to find the

most likely path. The metric used in the Viterbi process is MMSE-IC based on

the weights of α1 and α2, which are calculated in the previous step.

At each state, we should find the best transition among all transitions. Then,

we use the best transition to calculate the path metric in the Viterbi process.

According to the system model in (6), the branch metric used in the Viterbi

algorithm is

J(s1, s2) =∥∥αH1 y− s1ejθ11

∥∥2 +∥∥αH2 y− s2ejθ12

∥∥2 (13)

Due to the orthogonality of Alamouti’s STBC, the previous metric can be de-

composed into two separated metrics where

J(s1, s2) = J1(s1) + J2(s2) (14)

and

J1(s1) =∥∥αH1 y− s1ejθ11

∥∥2 (15)

J2(s2) =∥∥αH2 y− s2ejθ12

∥∥2 (16)

12

J1 is a function of s1 only and J2 is a function of s2 only. This separation

simplifies the search for the branch with the minimum metric among all branches

and thus reduces the complexity of the decoding process [8].

3.1.3. Second structure decoding (s3, s4)

After decoding (s1, s2) for the whole frame, we can eliminate the impact of

the first sub-system using the following equation,

y = y −(h1 h2

)s1s2

(17)

where y represents the received vector after cancelling the contribution of the

first sub-system and hi in (17) is the ith column of He in (7). Thereafter,

the decoding process can be performed as the first structure with modification

on the branch metric. The branch metric after cancelling the first sub-system

contribution is,

J(s3, s4) =

N∑m =1

(∥∥ym1 − hm3s3ejθ21 − hm4s4e

jθ22∥∥2 +

∥∥y∗m2 + h∗m3s4ejθ22 − h∗m4s3e

jθ21∥∥2) (18)

By expanding (18) and removing the constant terms, the branch metric results

in the following,

J(s3, s4) =

N∑m =1

2<(y∗m2hm3s

∗4e

−jθ22 − y∗m2hm4s∗3e

−jθ21−

ym1h∗m3s

∗3e

−jθ21 − ym1h∗m4s

∗4e

−jθ22) (19)

Now, (19) can be rewritten as two separated functions,

J(s3, s4) = J1(s3) + J2(s4) (20)

where

J1(s3) = −N∑

m =1

<([ym2h

∗m4 + y∗m1hm3]s3e

jθ21)

(21)

J2(s4) =

N∑m =1

<([ym2h

∗m3 − y∗m1hm4]s4e

jθ22)

(22)

13

Note that J1 is a function of s3 only and J2 is a function of s4 only. The simplified

ML decoding can be done now in the same way as for the first sub-system.

3.1.4. First structure re-decoding (s1, s2)

At this stage, we will re-decode the first structure symbols (s1, s2) after

eliminating the impact of the channels of the second system. This stage will be

evaluated in the same way as illustrated in the previous section.

3.2. Two-step interference cancellation with ML

In this work, a two-step decoding stage is performed to enhance the overall

performance of the system. In the first step we get the decoded vector d0

by decoding (s1, s2) first and (s3, s4) later using the process described in the

previous section. In the second step, we assume decoding (s3, s4) first and then

(s1, s2) after the cancellation. The decoded vector d1 is then obtained. For each

step, we calculate the sum of MSE of the decoded vectors which are denoted by

40 and 41, respectively. The receiver chooses d0 if 40 < 41 or d1 if 40 > 41.

Fig. 6 describes the two-step decoding process.

Figure 6: Two-step decoding process

3.3. Complexity calculations

Based on the illustrated decoding criteria in the previous section, one can

estimate the degree of the complexity of the new scheme. SO-STTC decoding

complexity and calculations are explained in [20] and based on these calculations

the new scheme complexity will be illustrated.

In the following example, we will elaborate on the complexity degree of the

14

decoding algorithm described in the previous section by calculating the required

real multiplications (RM) and real additions (RA) for each stage. Suppose that

we have the 4-state trellis structure shown in Fig. 4(a) with a rate of 4 b/s.Hz.

The system uses a QPSK modulation with the set-partitioning of Fig. 2.

We can divide the needed calculations over the five stages described previously:

1. Calculate the weights (α1, α2): Calculating the weights (α1, α2) requires

128 RM and 135 RA [21]. But this step is calculated once for each frame,

so the complexity of this stage is divided by the frame length.

2. First system decoding: By the same criteria used in calculating the branch

metric in SO-STTC [20], this step requires 32 RM and 24 RA for a tran-

sition that includes the transmission of two symbols.

3. Second system decoding: This stage needs the same calculations used in

the previous stage in addition to the calculations caused by the eliminating

of the impact of the first system. For this example, this stage needs 48

RM and 40 RA. First system re-decoding: As in the previous stage, this

stage needs 48 RM and 40 RA.

4. The two-step decoding: The previous steps are repeated two times to

perform the two-step MMSE. So, by comparison with SO-STTC, the new

scheme needs 262 RM and 215 RA while SO-STTC needs 542 RM and

296 RA.

Table 2 represents the complexity comparison between the SO-STTC [20], SOTC-

SM [18] and SO-DSTTC scheme for a 4-state trellis structure at different spec-

tral efficiencies. In Fig. 7, the comparison for the needed RA and RM calcula-

tions for the different schemes is presented.

4. Simulation and results

In this section, the simulation results for the proposed SO-DSTTC are

demonstrated using four transmit antennas and two receive antennas. The error

performance of the new scheme is compared with that of SO-STTC and SOTC-

SM schemes. The frame error rates (FER) of these schemes are evaluated using

15

the Monto Carlo simulation for various spectral efficiencies. In all cases, the

simulation is done using a frame length of 40k bits for a spectral efficiency of k

b/s.Hz. All simulations are evaluated in a MATLAB simulation environment.

We assume a quasi-static flat Rayleigh fading model for the channel. Therefore,

the path gains are independent complex Gaussian random variables and fixed

during the transmission of one frame. In addition, we assume that the perfect

Channel State Information (CSI) is available at the receiver.

The FER of the simulation results for SO-DSTTC scheme at 4 b/s.Hz is com-

pared with the results from SOTC-SM and SO-STTC schemes at the same rate

in Fig. 8. In this case, the FER performance of the 4-state SO-DSTTC is bet-

ter than that of a 4-state SOTC-SM and SO-STTC by about 1 dB at FER of

3×10−3. Also, the decoding complexity of a SO-DSTTC is lower than that of a

SOTC-SM and SO-STTC with a similar number of states, as shown in section

3.3.

In Fig. 9, the FER of the simulation results for SO-DSTTC scheme at 5 b/s.Hz

compared with the results from SOTC-SM and SO-STTC schemes at the same

rate is presented. As seen in Fig. 9, an improvement is achieved by the new

Table 2: Complexity comparison of different schemes

Spec. Transmission Modulation No. of No. of parallel RM RA

effi. scheme scheme branches/state branches/state

SO-DSTTC QPSK 16 4 262 215

4 SO-STTC 16-QAM 256 64 542 296

SOTC-SM 16-QAM 256 64 448 240

SO-DSTTC 8-PSK 32 8 662 419

5 SO-STTC 32-QAM 1024 256 1056 548

SOTC-SM 32-QAM 1024 256 960 496

SO-DSTTC 8-PSK 64 16 1142 659

6 SO-STTC 64-QAM 4096 1024 2066 1052

SOTC-SM 64-QAM 4096 1024 1984 1008

16

Figure 7: Complexity comparison for different schemes, (a) RA comparison, (b) RM compar-

ison

scheme compared with SO-STTC and SOTC-SM. From Fig. 9, we can observe

that the SNR gain starts to increase firstly as the SNR increases, then, after

a certain limit, it begins to decrease. This observation can be explained as a

result of the error propagation due to the interference cancellation process.

Fig. 10 shows the FER performance of the SO-DSTTC scheme compared

with SO-STTC and SOTC-SM at 6 b/s.Hz. The results in Fig. 10 shows that

the new scheme achieved an improvement in the lower and medium range of

SNR (< 22 dB), while in higher SNR, the result worsened due to the high

interference that occurred between the systems.

17

5. Conclusion

In this paper, a novel MIMO transmission scheme called SO-DSSTC has

been proposed. The encoding process and the technique which has been used

to construct a new code for a given spectral efficiency have been illustrated.

Also, the simplified decoding criteria and the related complexity degree have

been showed and compared with that of SO-STTC and SOTC-SM. The FER

performance of the proposed scheme has been simulated and compared with

SO-STTC and SOTC-SM. It has been shown from the complexity calculations

that the new scheme has reduced the total amount of overall calculations by

approximately half compared with SO-STTC and SOTC-SM. Also, the FER

simulation has shown that the new scheme achieved an improvement in the FER

Figure 8: FER performance for 4-state SO-DSTTC, SOSTTC and SOTC-SM at 4 b/s.Hz

18


performance at 4 and 5 b/s.Hz, while at 6 b/s.Hz it achieved an improvement

in the lower and medium range of SNR (< 22 dB).

6. Acknowledgments

Thanks to Dr. Gemma Nicholson for proofreading the article.

References

[1] Alamouti, S.M.: ’A simple transmit diversity technique for wireless com-

munications’ IEEE Journal on Selected Areas in Communications, 1998,

16, (8), pp. 1451–1458

19


[2] Tarokh, V., Jafarkhani, H., and Calderbank, A.R.: ’Space-time block

codes from orthogonal designs’, IEEE Transactions on Information The-

ory, 1999, 45, (5), pp. 1456–1467

[3] Naguib, A.F., Seshadri, N., and Calderbank, A.R.: ’Applications of space-

time block codes and interference suppression for high capacity and high

data rate wireless systems’. Proc. of the IEEE the 32th Asilomar Conf.

on Signals, Sys. and Comp., Pacific Grove, CA, USA, Nov. 1998

[4] Naguib, A.F., Seshadri, N., and Calderbank, A.R.: ’Increasing data rate

over wireless channels’, IEEE Signal Processing Magazine, 2000, 17, (3),

pp. 76–92.

[5] Lee, Y., and Shieh, H.-W.: ’A simple layered space-time block nulling

technique for DSTTD systems’, IEEE Communications Letters, 2011, 15,

(12), pp. 1323–1325

20

[6] Tarokh, V., Seshadri,N., and Calderbank, A.R.: ’Space-time codes for

high data rate wireless communication: performance criterion and code

construction’, IEEE Transactions on Information Theory, 1998, 44, (2),

pp. 744–765

[7] Jafarkhani, H. and Seshadri,N.: ’Super-orthogonal space-time trellis codes’,

IEEE Transactions on Information Theory, 2003, 49, (4), pp. 937–950

[8] Sterian,C. E. D., Linga,S., Singh, H., and Patzold,M.: ’New super-orthogonal

space-time trellis codes with 32QAM and two transmit antennas for five

bits per signalling interval’, Transactions on Emerging Telecommunica-

tions Technologies, 2007, 18, (2), pp. 205-215, .

[9] Mesleh, R.Y., Haas, H., and Sinanovic, S.: ’Spatial Modulation’, IEEE

Transactions on Vehicular Technology, 2008, 57, (4), pp. 2228–2241

[10] Mesleh, R., Stefan, I., Haas H., and Grant, P. M.: ’On the performance of

trellis coded spatial modulation’. Proceedings of Int. Workshop on Smart

Antenna.,Berlin, Germany, Feb, 2009

[11] Mesleh, R., Renzo, M. D., Haas. H., Grant, P. M.: ’Trellis coded spatial

modulation’, IEEE Transaction Wireless Communications, 2010, 9, (7),

pp. 2349–2361

[12] Basar, E., Aygolu, U., Panayirci, E., Poor,H .V.: ’New trellis code design

for spatial modulation’, IEEE transactions on Wireless Communications,

2011, 10, no. (8) pp. 2670–2680

[13] Mesleh, R., Ikki, S.S., and Aggoune, H.M.: ’Quadrature Spatial Modula-

tion’, IEEE Transactions on Vehicular Technology, 2015, 64, (6) pp. 2738-

2742.

[14] Yigit, Z., Basar, E., Mesleh, R.: ’Trellis coded quadrature spatial modu-

lation’, Physical Communication, 2018, 29, (4), pp. 147–155

[15] Basar, E., Aygolu, U., Panayirci, E., Poor, H .V.: ’Space-time block coded

spatial modulation’, IEEE Transactions on Communications, 2011, 59,

(3), pp. 823–832

[16] Li, X., and Wang, L.:’High rate space-time block coded spatial modula-

tion with cyclic structure’ IEEE Communications Letters, 2014, 18, (4),

21

pp. 532–535

[17] Abu-Hudrouss, A.: ’Improved Super-Orthogonal Trellis-Coded Spatial

Modulation Using STBC-CSM’, Journal of Computer and Communica-

tion, 2018, 6, pp. 149–156.

[18] Basar, E., Aygolu, U., Panayirci, E., Poor,H .V.: ’Super-orthogonal trellis-

coded spatial modulation’, IET Communications, 2012, 6, (17), pp. 2922–

2932.

[19] Wang, D., and Xia, X.-G.: ’Space–time trellis code design based on QAM-

MTCM with trellis shaping,’ IEEE Transactions on Communications,

2007, 55, (1), pp. 76–82

[20] Jafarkhani, H.: ’Space-time coding: theory and practice’, Cambridge Uni-

versity Press, 2005.

[21] Jung, S., and Lee, J.: ’A new ML based interference cancellation technique

for layered space-time codes’, IEEE Transactions on Communications,

2009, 57, (4), pp. 930–936

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