INTRODUCTION

To combat ISI caused by multipath reception and avoid complex adaptive equalization, mobile engineers and researchers explored the use of Orthogonal Frequency Division Multiplexing (OFDM). OFDM divides the entire data stream into small number of low data-rate subcarriers, thus reducing the effect of frequency selective fading and Doppler spread. OFDM became popular because of its easy implementation as it makes an efficient use of Discrete Fourier Transforms (Weinstein and Ebert, 1971).

OFDM, due to the presence of Cyclic Prefix (CP), maintains the receiver carrier synchronization, therefore, does not need complex equalizers, making the receiver simple and efficient (Prasad, 2004). Although, highly spectrally efficient and robust against ISI, OFDM technique faces certain problems such as (Prasad, 2004).

In this study, an OFDM transceiver is proposed (Latif and Gohar, 2006) which make use of hybrid modulation scheme instead of conventional Modulator like QAM or PSK. In spite of improved BER performance, it exhibits low PAPR. The modified OFDM Transceiver makes use of multilevel QAM constellations, where the level of QAM is decided by specific number of bits chosen from a group of bits to be encoded in the QAM symbol. The simulated results show that PAPR is considerably reduced at the cost of sight increase in detection complexity. Like PTS or SLM (Müller Weinfurtner et al., 1997; Muller and Huber, 1997; Latif and Gohar, 2002, 2003), it works with arbitrary number of subcarriers but needs no side information to be transmitted. It is also shown that PAPR reduction capability of the proposed system is comparable to PTS. To further reduce the PAPR, one has to alter the Hybrid MQAM/LFSK (HQFM) signal sets like in PTS. At the receiver, these deformation can be recovered (needs not to be transmitted) in one or two iteration. Thus, increasing the detection complexity.

PROPOSED HYBRID MQAM/LFSK (HQFM) OFDM TRANSCEIVER

In a typical OFDM system, the bit rate per carrier (not the total bit rate) is reduced by converting binary serial bit stream into N_used parallel streams, with n bits in each stream. Then a suitable modulation technique, MQAM/MPSK (M = 2ⁿ), is applied to map these bits to N_used active carriers.

Here a novel modulator is proposed, which replace QAM signals with hybrid LFSK modulated MQAM (HQFM) signals. In HQFM, instead of modulating n = log₂ML information bits using a single frequency f_c, n-k = log₂L bits, the choice being arbitrary, are used to select the modulating frequency f_c + f_c`, f<sub>c</sub>`« f_c from a LFSK according to f_c` = lf_Δ, l = 0, 1, 2,..., L (Proakis, 1989; Rappaport, 2002). The minimum frequency separation for LFSK to meet the condition for orthogonality is f_Δ = 1/T_s. The remaining k = log₂M bits are modulated using ordinary MQAM.

The complex form of HQFM signal can be expressed as:

(1)

where, u_l(t) = exp(2πlf_Δt), m {0, 1, 2, ..., M-1} (from QAM), lε {0, 1, 2, ..., L-1} (from FSK), 0≤t≤T_s, T_s = T_blog₂ML, T_b being bit duration in seconds. C_mc`s and C<sub>ms</sub>`s can takes up to values from (2m-1-√M), defining the I- and Q-axis of the signal space diagram.

From (1) it can be observed that L/M HQFM constitute of L sets, each with MQAM modulated symbols, where in each set, the cross correlation coefficient |ρ| = 0 implies that the frequency difference, f_Δ, is an integral multiple of 1/T_s (non-coherent detection), or in other words, the modulation index h = f_ΔT_s is a positive integer.

It is worth mentioning that, QAM uses 2D, while, HQFM uses 2^L+1 dimensional signaling. Also, for ordinary MQAM, L = 1. For L = 2, M = 4, HQFM reduces to special modulation format known as Q2KSK (Saha and Birdshall, 1989) which is a member of general class of modulation format known as JPFM (Ghareeb, 1995). However, JPFM generally phase shifts the carriers, while HQFM utilizes amplitude/phase shift (QAM). One advantage of QAM over PSK is that QAM is more power efficient and supports high data rates for the same required SNR (Proakis, 1989; Rappaport, 2002).

As all the FSK frequencies are orthogonal to each other, the points lying in the HQFM signal space can be viewed as points lying in a smaller QAM with different orthogonal planes, where each plane is distinguished by its corresponding FSK frequency (Fig. 1). In this way ML-QAM signal can be split into smaller ML/2, ML/4, ML/8... MQAMs with carrier frequencies taken from 2, 4, 8, ... LFSK, respectively.

For transformation of these HQFM signals to an OFDM symbol, usually Nedused inactive carriers (set to zero) are added appropriately and then N-point IFFT is applied. The zero padded signals are used to shape the power spectral density of the transmitted signal. In order to avoid ISI and ICI, the transmitted signal is made periodic by cyclically appending CP (N_CP≤25%) of the OFDM symbol. This CP also plays a decisive role in synchronizing the OFDM frames properly. The signal is then D/A converted to produce the analog baseband signal, up-converted to RF and then transmitted. This whole process is shown in Fig. 2.

Fig. 1:	Decomposition of 16-QAM into 4-QAM using 4-FSK for HQFM

Fig. 2:	Hybrid MQAM/LFSK (HQFM-OFDM) transmitter

(2)

where, Δf = 1/NT_s is the frequency separation between each subcarrier, N number of OFDM subcarriers, T_s is the data symbol period and c_p,q = (c_p,0, c_p,1,..., c_p,N-q) is a set of alphabet taken from HQFM.

At the receiver side, HQFM signals are recovered after removal of CP and application of FFT. As mentioned earlier, L/M HQFM signals consist of L set of M QAM modulated signal where members of each set are orthogonal to the members of other sets. So a two stage demodulation process is carried out to extract the information bits: Multiple representations of received signal are passed through L-sub-receivers, where unique frequencies, f_i, i = 0, 1, ..., L-1, orthogonal to each other are known to each sub-receiver. Meanwhile, each sub-receiver estimate QAM symbols by computing the minimum distance between the received signal and M possible transmitted signal. Among these sub-receivers, that receiver is chosen which give the maximum value for the assigned frequency matched to that particular signal and zero for all other frequencies.

Fig. 3:	Hybrid MQAM/LFSK Demodulator

Thus, a correct estimate of frequency is made (non-coherent part). Consequently, the estimated QAM symbol for the chosen sub-receiver is selected (coherent part). Figure 3 shows a complete picture of the proposed demodulator (After/IFFT).

CCDF of Peak-To-Average Power Ratio (PAPR): Peak-to-Average Power Ratio (PAPR) of the p^th OFDM symbol s_i,k is defined as:

(3)

where, s_p,q = (s_p,0, s_p,1,..., s_p,N-1) is the time domain representation of vectors associated with the p^th OFDM symbol and E{|s_i,k|²} denotes the expectation.

The distribution of PAPR of the OFDM signal can be well understood by famous “Waterfall Curves” for Pr{PAPR₀}. These curves describe the Complementary Cumulative Distribution Function (CCDF) of PAPR which is the most frequently used analysis tool described in literature.

Assuming symbol size N large (N≥64) and the transmitted signal nearly Complex Gaussian Distributed, the OFDM signal follows a Rayleigh distribution with zero mean and a variance σ²_OFDM If the OFDM symbols are assumed to be i.i.d., the probability that magnitude of the entire OFDM symbol that exceeds a certain threshold can be approximated as (Müller Weinfurtner et al., 1997; Muller and Huber, 1997):

(4)

Equation 4 shows that large PAPR occurs against a certain threshold infrequently. Also, PAPR is highly dependent on the IFFT length N of the OFDM transmitter, i.e., PAPR increases with the increase in subcarriers for a single OFDM symbol.

Relationship between OFDM subcarrier separation, Δf and FSK tone separation, f _Δ, is f_Δ = NΔf⇔N = f_Δ/Δf. Also, PAPR is direct function of N or f_Δ/Δf. As mentioned earlier, for fixed N, PAPR can be reduced by decreasing f_Δ. Bringing FSK tones closer to each other while maintaining their orthogonality, means that more frequencies can be adjusted in a given frequency band. Therefore PAPR decreases by decreasing f_Δ or increasing L. This is justified for HQFM-OFDM, for which PAPR decreases by increasing the number of FSK tones as compared to 2ⁿQAM-OFDM (L = 1).

MODIFIED HQFM-OFDM

The PAPR reduction capabilities of HQFM-OFDM are not as good as reduction algorithms applied to conventional 256QAM-OFDM e.g., PTS-OFDM. Therefore, a modification is proposed, termed as HQFM-I. It will be shown in the next section that HQFM-OFDM shows a strong dependence of decrease in PAPR on number of keying frequencies (L). In HQFM-I, a multi-stage modulator is designed which uses variable FSK modulator to generate frequencies. In first stage, n-k = log₂L bits are used to generate L frequencies and remaining k = log₂M bits are used for QAM Modulation. Other stages generate 2L, 4L, ..., frequencies which are used for M/2, M/4,..., QAM Modulation, respectively. The overall number of bits, n, for HQFM signal remains constant. After applying IFFT, HQFM signal with least PAPR is chosen. The receiver first demodulates the OFDM symbols using FFT, then determine the number of bits used by QAM by observing the maximum amplitude C_max. The demodulation process is carried out to detect the correct HQFM symbol as per Fig. 3. Only two-stage HQFM modulator is sufficient to achieve the desirable results. Monte Carlo simulations show that PAPR reduction capability is comparable to PTS-OFDM.

To further reduce the PAPR, PTS algorithm is used. The whole HQFM signal set is divided into V subblocks, V = p; P = 0, 1, 2, ... with number of carriers N_v≥32 in each subblock. Phase vector of {0} is sufficient to obtain the results, which can be detected, in one or two iterations, without transmitting it, hence increasing the detection complexity.