• Introduction

The unprecedented increase of mobile communications, wireless Internet access and multi-media applications has been driven by telecommunications companies and re-searchers to conceive new transmission technologies, proto-cols, and network infrastructure solutions in order to max-imize both throughput and spectral efficiency [1]. For the next generation of wireless communication, it has become necessary to provide higher data rate and improve spectral efficiency. Employing multi–antennas at transmitter and re-ceiver has shown to be an effective technique to achieve spectral efficiency over the past few years. The use of spatial multiplexing using multiple input multiple output (MIMO) was first proposed in [2]. MIMO technology is one of the techniques employed to attain high spectral effi-ciency by transmitting multiple data streams from multiple antennas [3]. However, the MIMO transmission is depen-dent on transmit and receive antenna spacing [4, 5], syn-chronization of the transmit antenna [6], as well as the al-gorithm needed for inter-channel interference (ICI) reduc-tion at the receiver input. The Bell Labs Layered Space-Time Architecture (BLAST) in [7] proposed MIMO detection algorithms, named vertical BLAST (V-BLAST) [8]. In V-BLAST, multiple data streams are transmitted separately and detected successively by employing both an array pro-cessing (nulling) and interference cancelation techniques.

OFDM is another promising technique proposed for transmitting high speed data over wireless channels in fu-ture mobile communication systems [9]. OFDM has been useful in several wireless standards, for example, digital audio and video broadcasting (DAB) and (DVB-T), IEEE 802.11a [10], the IEEE 802.16a metropolitan area network (MAN), and the local area standard (LAN) [11]. Although, OFDM features seems attractive, there is still technical challenges that needs to be addressed for future wireless transmission [12, 13].

Recently, a new extension to OFDM has been proposed, namely, F-OFDM in [12, 13]. The most significant differ-ence of F-OFDM, as opposed to the conventional OFDM, is that the former total bandwidth has been divided into mul-tiple subband. In addition, each subband have a distinct subcarrier spacing with its own cyclic prefix (CP) and filter. On the other, in conventional OFDM, total bandwidth con-sists of a single block and has the same subcarrier spacing between the individual subcarriers. Note that, there is de-The proposed architecture of SM F-OFDM system is depicted in

Figure 1, with the F-OFDM transmitter showing in Figure 2, while F-OFDM receiver is illustrated in Figure 3. Suppose the input Q(k) is m n matrix which represents the transmitted symbols, where m is the total number of bits per symbol per subcarrier and n denotes the total number of

gree of flexibility in F-OFDM than its counterpart OFDM.		subcarriers of the multiple subband of F-OFDM system. By
The details can be found in [12, 13].		using the SM mapping rule as listed in Table I, this matrix
Therefore, in this paper, SM is applied to F-OFDM,		is mapped into X(k) of size Nt   n.
namely,  spatial  modulation  F-OFDM  (SM  F-OFDM),		From Table I, the SM mapping rule, maps each col-
which provides higher spectral efficiency as a result of both		umn in Q(k) into 4QAM and BPSK signal constellations
SM and F-OFDM advantages. The main contributions of		respectively. In addition, one transmit antenna from a set of
this work can be summarized as follows: (i) Analogue to		two (QPSK) and four (BPSK) antennas is assumed. Herein,
[9], SM F-OFDM is designed for wireless transmission. (ii)		4QAM and BPSK modulation schemes were adopted in this
Binary phase shift keying (BPSK) and quadrature ampli-		work. As can be seen in Table I, the encoding mechanism
tude modulation (QAM) modulation schemes were adopted		are Nt = 2 and M = 4 when QAM is adopted. Note that,
for SM mapping rule.		three information bits can be mapped onto 4-QAM with
The remaining sections are organized as follows:	In	two transmit antennas selected.  Similarly, for BPSK, the
Section II, the system model of SM-F-OFDM is presented.		same spectral efficiency can be achieved with Nt = 4 and
Simulation results are provided in Section III and conclud-		M = 4.  Thus the F-OFDM system can convey three bits
ing summaries are drawn in Section IV.		in each time slots. The number of information bits that can
Throughout the paper, the following notations are used.		be transmitted on each F-OFDM subcarriers is given in (1).
Bold lowercase and bold uppercase letters denote vectors		According to the SM mapping rule, the matrix Q(k) has
and matrices, respectively.  We use [:]T  and k:kF to de-		one nonzero element in each column at the position of the
note transpose and Frobenius norm of a matrix or a vector,		mapped transmit antenna number.  All the other elements
respectively.  iˆ(k) is the estimated transmit antenna index		in that column are defined as zero. It is worth mentioning
(number) and xˆiˆ(k) is the estimated transmitted symbol. F-		that, when Nt = 1 simplifies SM F-OFDM to conventional
OFDM modulator-1 contains data belong to first antenna		single antenna communications.
and so forth and   denotes time convolution.		Supposing  in  Figure  1,	an  input  bit	sequence  of
		[0 0 1]T (column vector in Q(k)) from Table I, is mapped
2  System Model of SM F-OFDM		to the QAM symbol – 1 + j and the first transmit antenna
		by using SM mapping. Thus only the first antenna trans-
In this section, SM is discussed briefly. Suppose the total		mits this symbol on the first F-OFDM subcarrier, whereas
		other antenna remains silent (zero power). As a result, the
number of transmit and receive antennas is denoted by Nt		first column vector in X(k) is [	1 + j  0]T . The second bit
and Nr respectively, M being the cardinality of the signal		sequence is [1 1 0]T and is mapped to [0		1  j]T , and
constellation. Hence, the rate of SM (bits per channel use		so on. Similarly, the same approach is adopted for BPSK
– (bpcu)) for arbitrary Nt and M respectively, can be given		symbols. The resultant symbols in each row vector xv (k)
by [14],[15]
		are the data that will be transmitted on all subcarriers from
RSM = log2(Nt) + log2(M)	(1)	transmit antenna v. And F-OFDM modulator will be used
		to modulate each row vector xv (k).
where log2(Nt) defines the single active transmit antenna		At the F-OFDM modulator output, sv (t) vector is gener-
and log2(M) is the transmitted QAM/BPSK modulation		ated. Each sv (t) vector generated has a unique and disjoint
symbols.  Note that the Nt, Nr and M, respectively, can		set of F-OFDM subcarriers. The resulting output vectors at
be chosen independently [16]. The basic principle of SM is		the F-OFDM modulator will be transmitted simultaneously
that, it maps multiple information bits into one information		from the Nt over the channel H(t). At the receiver, the re-
symbol with respect to their corresponding transmit antenna		ceived matrix Y(t) can be expressed as
number. The number of information bits that can be trans-		Y(t) = H(t)	S(t) + G(t)	(2)
mitted in SM technique depends on the signal constellation
diagram employed as well as the given number of transmit		where S(t) is a matrix that has all F-OFDM symbols that
antennas. It is important to note that the SM utilizes the dis-		are transmitted from all transmit antennas. G(t) is the ad-
tinctiveness and random nature of the wireless channel for		ditive noise matrix, in which each element is assumed to be
communication. The following summarized SM character-		an independent and identically distributed (iid) zero mean
istics [14]:		complex Gaussian random variable with variance  N2 . H(t)
1) At any signaling time instance, only one transmit an-		is the Nr   Nt channel matrix between transmit antennas v
tenna is active for data transmission while the other		and receive antennas k, respectively and can be expressed
antennas remains silent.		as (3)

	0
	B h1;1 (t)
H (t) =	B	h2;1::: (t)
	B
	B
	B
	B
	B	h	Nr ;1	(t)
	B
	B
	B

B

B

B

B

B

@

h_1;2 (t)

h_2;2 (t)

where h_k;v is a complex fading coefficient between the v^th transmit antenna and k^th the receive antenna. h_k;v is as-

		F-OFDM
		Modulator -1
q(k)	Spatial	F-OFDM
	Modulation
		Modulator -2
		X(k)
		F-OFDM
		Modulator -M

					H(t)		F-OFDM
s			(t)
	1						Demodulator-1
									ˆ
									i(k )
s			(t)				F-OFDM		ML	Spatial
		2					Demodulator-2		Detection	Demodulation
									xˆ	(k)
									ˆ
								Y(k)	i
					H(t)
					N	r
							F-OFDM
					Y(t)
s				(t)			Demodulator-M
		N
			t

 q(k)ˆ

Figure 1: Proposed architecture of Spatial Modulation F-OFDM System for wireless transmission.

• IFFT

SUBBAND-1

SUBBAND-Z

PAR	ADD CP	FILTER
		1
SER

M	M	M	S	I	(T)
PAR	ADD CP	FILTER
SER		Z

Figure 2: Block diagram of F-OFDM Transmitter.

FILTER	REMOVE

• CP

Y(T)	M	M
	FILTER	REMOVE
	Z	CP

Figure 3: Block diagram of F-OFDM Receiver.

Table 1: Adopted SM F-OFDM Mapping Rule (3 bpcu).

		QAM			BPSK
Input bits	Antenna Number		Transmit Symbol	Antenna Number		Transmit Symbol
000	1		+1+j	1		-1
001	1		-1+j	1		+1
010	1		-1-j	2		-1
011	1		+1-j	2		+1
100	2		+1+j	3		-1
101	2		-1+j	3		+1
110	2		-1-j	4		-1
111	2		+1-j	4		+1

Four bits transmission using spatial modulation

	10-1
	10-2
Error Rate	10-3
	10-4
Bit
	10-5
		SM-4bits 2×4 8QAM -ZF
	10-6	SM-4bits 4×4	4QAM -ML
		SM-4bits 2×4	8QAM -ML
		SM-4bits 4×4	4QAM -ZF
	10-7	5	10	15	20	25	30
	0

SNR (dB)

Figure 4: Illustration of BER performance for 4 bits per subcarrier employing ML and ZF detectors.

Three bits transmission using spatial modulation

						SM-3bits 2×4 4QAM -ML
	10-1					SM-3bits 4×4	BPSK -ML
						SM-3bits 4×4	BPSK -ZF
						SM-3bits 2×4	4QAM -ZL
	10-2
Error Rate	10-3
	10-4
Bit
	10-5
	10-6
	10-7	5	10	15	20	25	30
	0

Figure 5: Illustration of BER performance for 3 bits per subcarrier employing ML and ZF detectors.

sumed to be iid complex zero mean Gaussian with variance one.

The receiver uses maximum likelihood detector to esti-mate the index, i^ˆ(k) and the transmitted symbol, xˆ_iˆ(k) can be expressed as

where x denotes the transmitted symbol vector, H^T (t) is the transpose of the channel matrix in (3) and denotes the convolution.

ˆ@

xˆ@

= arg max Pr Y

H (

)

xˆ

iˆ

3  Simulation Results and Discussions

hi ;

i

i;x

@

t

;

(4)

In this section, simulation results for the proposed SM F-

= arg min

2

OFDM transmission is shown. Monte Carlo simulations is

Y@   H (t) ;xˆˆ

F

i;x

i

used to evaluate bit error rate (BER) performance utilizing

maximum likelihood (ML) detector at the receiver. In ad-

where Y@ is the output matrix from the ML for the sub-

dition, zero forcing (ZF) detector was employed for com-

carrier @, i.e. (@ : 1;2; :::; n) and

parison.  Herein, it was considered that the receiver have

2

3

full channel knowledge and the receive antennas are sepa-

1

Y@   H (t) ;xˆˆ

2

rated wide enough to avoid correlation. Flat Rayleigh fad-

F

Pr Y@ H (t) ;xˆiˆ

=

exp

i

ing channel was also assumed.

Nr

2Nr

2

N

6

N

7

6

7

6

7(5)

6

7

6

7

6

7

is the conditional probability density

4function (PDF) of

5Y@

3.1  Three Bits Transmission

given H(t) and xiˆ. Equation (4) estimates both the transmit

By using different configurations, a three bits per subcarrier

antenna number and the transmitted symbols jointly. The

SM demodulator, then used these two estimates to extract

transmission can be achieved. For SM, a 4  4 BPSK and

the transmitted information bits on this subcarrier by taking

2  4 4QAM configuration convey three bits per subcarrier.

an inverse mapping process adopted by the same mapping

In Figure 4, SM 4  4 BPSK shows performance degrada-

table used at the transmitter.

tion as compared to SM 2  4 4QAM when ML detector

Similarly, the zero forcing (ZF) detector can be written

is used.  A similar trend can be observed for ZF detector

as

as the same degradation performance is seen with the same

_@	_@	=  HT (t) H (t)	1	x		configurations. The results in Figure 4 shows that the ML
i	; x		H (t)		(6)	detector estimation outperforms ZL detector estimation.

Six bits transmission using spatial modulation

					SM-6bits 4×4		16QAM -ML
	10-1				SM-6bits 4×4		16QAM -ZL
					SM-6bits 2×4		32QAM -ZF
					SM-6bits 2×4		32QAM -ML
	10-2
Error Rate	10-3
	10-4
Bit
	10-5
	10-6
	10-7	5	10	15	20	25		30
	0

SNR (dB)

Figure 6: Illustration of BER performance for 6 bits per subcarrier employing ML and ZF detectors.

100
				3 bits (2×4 4 QAM − ML)
				4 bits (2×4 8 QAM − ML)
−1				6 bits (2×4 32 QAM − ML)
10
10−2
10−3
BER
10−4
10−5
10−6
10−7	5	10	15	20	25	30
0
			SNR(dB)

Figure 7: BER comparison performance for SM bits transmission, namely, 3, 4 and 6 bits, respectively when ML is adopted.

3.2    Four Bits Transmission

Four bits transmission can be achieved by the employment of SM 4 4 4QAM or 2 4 8QAM configuration. The com-parison BER results in Figure 5 shows that the ZF demon-strates the worst performance as compared to ML detector.

3.3    Six Bits Transmission

Figure 6 results extended the simulation to a spectral efficiency of 6 bits transmissions ML detection outperforms ZF detection.

It can be observed that the likelihood of errors for an-tenna detection increases with an increase in the number of transmit antennas. Therefore, the 2 4 SM system outper-forms 4 4 system at high SNR. An interesting feature of SM can be noticed in Figure 6, where the 2 4 32QAM for ZF detector BER curve crosses the 4 4 16QAM ML detec-tor at around 16 dB. This effect is a result of two estimation processes which is performed in SM, thus antenna number and transmitted symbol. Note that, the error level is dom-inated by the estimation of the transmitted symbol for low SNR, while the error level is dominated by the estimation of the transmit antenna number for a relatively high SNR. Hence, the scenario shown in Figure 6, for SN R < 16dB, lower constellation size and higher number of transmit an-tenna array is better for improved performance. On the other hand, for SN R > 16dB, higher constellation size and lower number of transmit antenna array is better. So there is a flexible tradeoff in this regard.

Figure 7 illustrates the BER comparison for distinct SM bits transmission, namely, 3 bits, 4 bits and 6 bits, respec-tively, for QAM modulation scheme.

It can be observed that the 6 bits SM transmission performs better than the 3 bits and 4 bits. Thus 6bits > 4bits > 3bits. This is because higher data rate can be achieved in the SM 6 bits transmis-sion leading to a higher spectral efficiency.

• Conclusion

In this paper, spectral efficient multiple antenna transmis-sion technique, namely, spatial modulation (SM) is applied to F-OFDM for wireless transmission. The antenna pat-tern is considered as a spatial constellation in an innovative fashion by using SM technique to increase the spectral effi-ciency. By computer simulation, BER performance for the proposed scheme was evaluated for uncorrelated Rayleigh fading channel and compared with ZF detector. The pro-posed SM F-OFDM achieves a constant spectral efficiency in bits per subcarrier. Another significant merit of employ-ing SM is the possibility of interchanging the constellation size and number of transmit antenna array to achieve better performance with respect to the operating SNR. In a follows up work, this feature will be further exploited. Furthermore, the performance improvement of the system increases as the transmission rate increases, which makes it a potential candidate for high data rate transmission systems. In addition, due to the estimation processes in SM approach, it is worth investigating further new algorithms for detection to improve the performance.

Conflict of Interest The author declare no conflict of in-terest.

Acknowledgment The author would like to thank Re-spected Professor Wen-Qin Wang (Senior Member – IEEE) of UESTC for his great contributions, support and encour-agement.

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