With the development of economy and technology, the requirement of information transmission rate and service quality becomes higher and higher. However, the scarcity of spectrum resource limits the further development of wireless communication. The openness of the wireless channel and the time-varying characteristics of channel parameters also bring serious damage to the transmission of wireless signals [1]. With the characteristics of high spectral efficiency (SE) and anti-multipath interference capability, etc., OFDM technology [2] can satisfy the demand of wireless communication for high rate, wide broadband and mobility. It has become the core modulation transmission technology of the next generation broadband wireless communication system.

OFDM [3-6] is a particular multicarrier transmission technology. The main idea of it is to transform high rate information into parallel low rate symbols and then transmit them parallel in a number of orthogonal sub-carriers, thereby reducing the effect of frequency selective fading (FSF). In OFDM, the entire channel is divided into many narrow sub-channels which can be utilized in parallel transmission; the carriers of the sub-channels are orthogonal to each other resulting in overlap of the subcarriers in frequency spectrum, thereby reducing the effect of mutual interference between the subcarriers and greatly improving the SE simultaneously. How to improve the SE of the OFDM communication system has been a main research focus. The most common way is to increase the modulation orders; however, doing so will increase the bit error rate (BER) and symbol error rate (SER) simultaneously. SE and BER seem to be a pair of mutually exclusive performance indexes. At present, several modulation methods have been proposed to get better data transfer rate for improving SE. A rotated quadrature phase shift keying (R-QPSK) technique was proposed in [7]; this scheme can transmit 3 bits per symbol period, effectively achieving higher throughput albeit at the cost of increased complexity. An improved scheme was proposed in [8] and [9] where one additional bit can be transmitted by adopting two R-QPSK constellations with different phases. This technique can get the gain in throughput without sacrificing BER. Based on [9], Ref. [10] proposed a quad state-paired QPSK (QS-PQPSK) scheme. Simulation results showed that its performance is better than 8PSK.

Inspired by [8] and [9], this paper proposes a rotated four leaves clover (R-FLC) constellation whose Euclidean distance is larger than 8PSK; therefore, its BER performance is better than 8PSK. Adopting the new constellation, the system can transmit additional bits by employing rotation mechanism; therefore, the SE can be improved. In addition, we apply the rotated constellations mechanism into the traditional OFDM system, putting forward a universal rotated constellation aided OFDM system. Simulation results show that the comprehensive performance of this system is much better than the traditional quadrature amplitude modulation (QAM) based OFDM system.

The remaining part of this paper is organized as follows: In section 2, after a brief review on how to transmit additional bits by R-QPSK constellation, an R-FLC constellation is proposed. Then, a rotated constellation aided OFDM system model is introduced in Section 3, where the SE of this new system is discussed. In Section 4, extensive simulation results about BER and ESE performances are given and analyzed. Finally, Section 5 concludes the whole work.

Ref. [8] and [9] proposed an R-QPSK constellation scheme capable of transmitting additional information. As shown in Figure 1, R-QPSK scheme utilizes two QPSK constellations: Q₀ and Q₁. The phase difference between Q₀ and Q₁ is 45 degrees and the Minimum Euclidean distance (MED) of those two constellations is same.

The basic principle of R-QPSK is as follows. In the transmitter, 2Nbits information are modulated by different constellations Q_k, where $k\in \left\{ 0,1 \right\}$, constellation Q₀ represent sone bit information “0”, while constellation Q₁ represents the other bit information “1”.Thus, the transmitter can send (2N+1) bits information duringN symbol periods.

In Figure 1, the constellation points $S_{{{Q}_{k}}}^{n}$ of Q₀ and Q₁ do not overlap with each other in the Euclid space, where $n\in \left\{ 1,\text{ }2,\text{ }3 \right\}$, thereby making the receiver detect and determine the received signal belonging to Q₀orQ₁. The extraction of the additional bits carried by the group of information can be determined by comparing the accumulated distance between constellation Q_k and the received N symbols.

Inspired by the scheme of R-QPSK constellation, a rotated 8 points constellation is proposed. As shown in Figure 2, the shape of this constellation is similar to the four leaves clover (FLC); therefore, we name it the R-FLCconstellation.

From Figure 2, it can be seen that any two adjacent points in the inner circle and a point in the big circle constitute a regular triangle. This arrangement can acquire a lager MED than 8PSK in the condition of normalized average power, resulting inan improved BER under the high SNR condition.

The MEDs of the constellations are provided in Table 1. As shown, the MED of R-FLC constellation is improved by 20% more than 8PSK.

Similar to R-QPSK, R-FLC employs a pair of FLC constellations Q₀ and Q₁ that have a phase difference of 45 degreesbetween each other; the MEDs of the two constellations are same. The transmitter sends 3Nbits information that were modulated by the same type of R-FLC constellationQ_k, where $k\in \left\{ 0,\text{ }1 \right\}$. Therefore, the transmitter can send (3N+1) bits only occupying N symbol periods. The extraction of the additional bits is also decided by comparing the accumulated distance between constellation Q_k and the received symbols.

In this section, the rotated constellation is applied into the traditional OFDM transmission system. The transmitter of this new OFDM system is shown in Figure 3. Set the subcarrier number of this system as N. After serials/parallel (S/P) conversion, the data sequence is transformed into N roads original data that will be sent to the rotated constellation mapper module. The input data sequence X forming an OFDM symbol can be represented as

Where ${{x}_{b,m}}=({{b}_{m{{N}_{b}}}},\cdots ,{{b}_{(m+1){{N}_{b}}-1}})$, $m\in \{0,1,\cdots ,N-1\}$, N_b is the modulation order of the constellation.

As shown in Figure 3, in this system, each OFDM symbol can carry additional bits information. That is because N sub-channels are equally divided into N' groups. The sub-channel number of each group is N_d=N/N', where ${{N}_{d}}\in {{Z}^{+}}$. The sub-channels of the same group employ the same mapping constellation Q_k so that an OFDM symbol can carry N' bits without occupying time slot. The additional bits stream carried by an OFDM symbol can be represented as

Where N' represents the length of the additional bits.

After S/P conversion of A, the single bit of A can determine which constellation the N_d sub-channels of the i^th group utilize. After $X=\left( {{x}_{b,0}},{{x}_{b,1}},\cdots ,{{x}_{b,}}_{N-1} \right)$ is mapped by rotated constellation, N complex signal $S=\left( {{S}_{0}},{{S}_{1}},\cdots ,{{S}_{N-1}} \right)$ can be obtained. Then, S is converted into time-domain signal $S=\left( {{S}_{0}},{{S}_{1}},\cdots ,{{S}_{N-1}} \right)$ by N points inverse discrete Fourier transform (IDFT). Finally, a parallel/serials (P/S) conversion is employed to form an OFDM symbol. The OFDM symbol will be transmitted into the wireless channel after adding some cyclic redundancy prefix (CP) which can effectively reduce the effect of inter-symbol interference (ISI).

In the receiver, by discrete Fourier transformation (DFT), an OFDM symbol is generated into N complex signal $Y=\left( {{y}_{0}},{{y}_{1}},\cdots ,{{y}_{N-1}} \right)$.Y is equally divided into N' groups and re-written as a matrix Y_N'×Nd,which can be expressed as

Wherethe matrix element y_i,j represents the received j^th symbol of the i^th data group, $i\in [0,N'-1]$ and $j\in [0,{{N}_{d}}-1]$.

According to the system model, each row and/or group of the matrix can carry 1-bit additional information. If we can distinguish which constellation used by the group, the corresponding additional information of each group can be decoded correctly. Determining constellation type also utilizes comparing the accumulated distance of the two types of constellations and the N_d symbols of the same group. The accumulated distance between the i^th data group and constellation Q_k can be expressed as in

The estimation and decision of the additional information ${{\hat{a}}_{i}}$ of the i^th data group is given by

The demodulation of the symbol y_i,j is as follows. The corresponding constellation type is firstly determined by the row number i of the y_i,j. Then, we adopt maximum-likelihood criterion to demodulate the original data $\gamma $.$\gamma$ can be expressed as

Where $S_{{{Q}_{k}}}^{n}$ represents the n^th constellation point of the corresponding constellation type Q_k of the i^th row symbol.

SE is an important technical indicator of OFDM system. Assuming the sampling time is T_S seconds, we have the duration time and the bandwidth of an OFDM symbol as NT_S seconds and 1/T_S Hz respectively; the transmission rate R_S of the OFDM symbol of this system is 1/NT_Ssymbols per second. In our system, we know that the data rate R of an OFDM symbol is $N{{N}_{b}}+N'$ bits per symbol; thus, the Spectrum efficiency $\eta $ of this system can be expressed as

From (7), we can see that the larger the ratio of N' to N, the larger SE will be.

In this section, performances of this proposed rotated constellation aided OFDM system under AWGN are evaluated and simulated, and the BER performances of R-QPSK and R-FLC under different numbers of additional bits N' are compared. The number of subcarriers N is 120.

Figure 4 is BER performances of the R-QPSK aided OFDM system under AWGN where N' is the number of additional bits carried by an OFDM symbol. From Figure 4, it can be seen that when $N'\le 12$, the BER performance of R-QPSK is close to the conventional QPSK and the SE has a slightly increase than QPSK. When N'=20 and N'=30, the BER performance of R-QPSK is slightly worse than QPSK in small E_b/N_o and is slightly better than QPSK in large E_b/N_o. When N'=40 and N'=60, the R-QPSK lose 0.7dB and 1.7dB E_b/N_o gain than QPSK respectively at the BER of ${{10}^{-3}}$. In conclusion, R-QPSK can obtain at most 12.5% SE gain than QPSK without sacrificing E_b/N_o.

Figure 5 is the BER performances of the R-FLC aided OFDM system under AWGN where N' is also the number of additional bits carried by an OFDM symbol. From Figure 5, it can be seen that when $N'\le 40$, the BER performances of R-FLC are better than 8PSK. The new system can obtain at least 1dB E_b/N_o gain at the BER of ${{10}^{-3}}$ and the SEs of R-FLC also spontaneously improved. When N'=60, the BER performance of R-FLC is slightly worse than 8PSK in small E_b/N_o; however, it is close to the 8PSK in large E_b/N_o. Simulation results indicate that spectrum efficiency can be improved by 16.7% than 8PSK without sacrificing E_b/N_o gain when using the R-FLC scheme.

To directly and comprehensively evaluate the rotated aided OFDM system, a comprehensive metric known as effective spectral efficiency (ESE)is proposed; it can be expressed as

Where R_F is the information bits per frame, T_F is the time duration per frame, R_FER is the frame error rate.

Assuming a frame includes N_F OFDM symbols, according to (7), we can get ${{R}_{F}}=(N{{N}_{b}}+N'){{N}_{F}}$ bits per frame and ${{T}_{F}}={{N}_{F}}N{{T}_{s}}$; thus, (8) can be represented as

As seen from (9), we simulate ESEs of R-QPSK and R-FLC in our simulation. The frame size N_F is set as 1000, i.e. a frame contains 1000 OFDM symbols.

Figure 6 is the ESE curves of R-QPSK aided OFDM system under AWGN according to (9). It can be seen that when $N'\le 30$, the ascending curve of R-QPSK is close to the QPSK; this phenomenon demonstrates that the SE of R-QPSK architecture has an improvement of QPSK without the loss of SNR gain. It is further proved that the comprehensive performance of R-QPSK is better than QPSK. When N'=40, the R-QPSK loses about 1dB SNR gain than QPSK but acquires 16.7% SE gain. When N'=60, the R-QPSK loses about 2dB SNR gain than QPSK but acquires 25% SE gain.

Figure 7 is the ESE curves of R-FLC aided OFDM system under AWGN according to (9). From Figure 7, it can be seen that when $N'\le 40$, the ascending curve of R-FLC is at the left of the QPSK. It demonstrates that R-FLC not only obtains 1dB SNR gain than 8PSK, but also acquires the SE gain. When N'=60, the ascending curve of R-FLC coincides with the QPSK; this phenomenon shows that the SE has a 16.7% improvement without the loss of SNR gain.

In the following, the BER performance of the rotated constellations aided OFDM system under multipath Rayleigh channel is investigated and evaluated. The multipath Rayleigh channel may arouse Inter Symbol Interference (ISI); therefore, we need add cyclic prefix (CP) to prevent ISI. Assuming the length of CP is${{N}_{c}}$, the duration of an OFDM symbol is$({{N}_{c}}+N){{T}_{s}}$. According to (7), the SE of the new OFDM system adding CP can be represented as

In the simulations, the number of subcarriers used in the OFDM system is 120, while the number of the CP is set to 16.

Figure 8 is the BER performances of the R-QPSK aided OFDM system with different number of additional bits N' under multi-path Rayleigh fading channel. When N'=12, the R-QPSK obtains about 1dB E_b/N_o gain than QPSK at the BER of 10^-3; in additional, the R-QPSK acquires 5% SE gain. When N'=30, the R-QPSK is close to the conventional QPSK; however, the SE of R-QPSK has a 12.5% improvement than QPSK. In conclusion, R-QPSK can obtain at most 12.5% SE gain than QPSK without sacrificing the E_b/N_o gain under multi-path Rayleigh fading channel.

Figure 9 is BER performances of the R-FLC aided OFDM system under MULTI-PATH RAYLEIGH FADING CHANNEL. From the simulation results, it can be seen that when N'=30, R-FLC obtains about 0.2dB E_b/N_o gain than 8PSK at the BER of ${{10}^{-3}}$;in addition, the R-FLC also acquires8.33% SE gain. When N'=60, the R-FLC is close to the conventional 8PSK; however, the SE of R-FLC has 16.7% improvement than 8PSK. In conclusion, R-FLC can obtain at most 16.7% of SE gain than 8PSK without the loss of E_b/N_o gain under multi-path Rayleigh fading channel.

A rotated four leaves clover constellation and a general rotated constellation aided OFDM system are provided in this paper. We compare the comprehensive performance of this new system with the conventional QAM aided OFDM system at the same modulation level. Extensive simulation results demonstrate that the SE has an improvement without sacrificing the SNR gain. The system architecture has a certain reference and practical value for the development of OFDM modulation technology.

This work was supported by the Scientific Research Project of Education Department of Hubei Province, China (No. B2017160).