- Research Article
- Open Access
Joint Multilevel Turbo Equalization and Continuous Phase Frequency Shift Keying
© Oguz Bayat et al. 2008
- Received: 2 May 2008
- Accepted: 31 December 2008
- Published: 21 January 2009
A novel type of turbo coded modulation scheme, called multilevel turbo coded-continuous phase frequency shift keying (MLTC-CPFSK), is designed to improve the overall bit error rate (BER) and bandwidth efficiency. Then, this scheme is combined with a new double decision feedback equalizer (DDFE) to remove the interference and to enhance BER performance for the intersymbol interference (ISI) channels. The entire communication scheme is called multilevel turbo equalization-continuous phase frequency shift keying (MLTEQ-CPFSK). In these schemes, parallel input data sequences are encoded using the multilevel scheme and mapped to CPFSK signals to obtain a powerful code with phase continuity over the air. The performances of both MLTC-CPFSK and MLTEQ-CPFSK systems were simulated over nonfrequency and frequency-selective channels, respectively. The superiority of the two level turbo codes with 4CPFSK modulation is shown against the trellis-coded 4CPFSK, multilevel convolutional coded 4CPFSK, and TTCM schemes. Finally, the bit error rate curve of MLTEQ-CPFSK system over Proakis B channel is depicted and ISI cancellation performance of DDFE equalizer is shown against linear and decision feedback equalizers
- Turbo Code
- Continuous Phase Modulation
- Decision Feedback Equalizer
- Turbo Encoder
- Feed Forward
With the development of the wireless communication industry, wireless data communications have become a very important research area for many scientists. As a result, tremendous improvements have occurred in coding, modulation, and signal processing subsystems to provide burst rates along with power efficiency at low bit error rates. First, conventional turbo code was found to be very attractive in the last decade , since turbo code reached theoretical limits in an iterative fashion at low signal-to-noise ratio with a cost of a low code rate and bandwidth expansion. Several years later, the compensation for bandwidth expansion and the low code rate was realized by applying multilevel and trellis-coded modulation to turbo code, known as multilevel turbo codes (MLTCs) [2, 3] and turbo trellis-coded modulation (TTCM) [4, 5], respectively, in the literature. These techniques increase the spectral efficiency of the coding via concatenating higher-order modulation using PSK or QAM modulations ; however, these communication models have phase jumps in their modulated signals. Continuous phase modulation (CPM) has explicit advantages in deep space and satellite communications, such as having low spectral occupancy property. Thus, to improve the bandwith usage further, MLTC design is concatenated and investigated with CPM modulation in this research.
MLTC is modeled by applying separate turbo encoders at each level. Each turbo encoder processes the information sequence simultaneously. For each level of the mutilevel encoder, there exists a corresponding decoder defined as a stage. The output of one stage is utilized at the decoder of the following stage in the decoding flow, known as multistage decoding .
The CPM model that is used with the MLTC is composed of a continuous-phase encoder (CPE) and a memoryless mapper (MM). The CPE is a convolutional encoder producing codeword sequences that are mapped onto waveforms by the MM, creating a continuous-phase signal. CPE-related schemes have better BER performance than systems using the traditional approach for a given number of trellis states due to larger Euclidean distances. When the decomposed structure of CPM is considered, joint trellis coded and CPM, and joint multilevel convolutional code and CPM systems can be designed as in [8, 9].
For achieving a low bit error rate (BER) over a severe ISI channel, the double decision feedback equalization is designed for MLTC-CPFSK system [10–12]. It is well know that maximum a posteriori probability (MAP) and soft output Viterbi algorithm-based equalizers are very effective, but having very high complexity, which is not applicable to our design since our transmission scheme has high complexity. Performances of traditional low-complexity equalizers such as linear equalizer (LE) and decision feedback equalizers (DFE) are not effective under severe channel conditions. To close the performance gap between high- and low-complexity equalizers, DDFE is proposed and implemented into the MLTC-CPFSK system. Thus, the effect of a severe ISI channel is mitigated by the equalization process and then the equalized information passes through the MAP algorithm-based decoders which decode the two encoded streams by exchanging the soft decisions.
In this paper, Section 2 explains the design of multilevel turbo encoder with CPFSK modulation. Section 3 describes the DDFE-based turbo equalization receiver scheme. In Section 4,the performances of the proposed MLTC-CPFSK and MLTEQ-CPFSK schemes are presented over AWGN, Rician, Rayleigh, and Proakis B channels, respectively, and the conclusion is stated at the last section.
where is the asymmetric carrier frequency as and is the carrier frequency. is the energy per channel symbol and is the initial carrier phase. We assume that is an integer; this condition leads to a simplification when using the equivalent representation of the CPM waveform.
where K is the Rician factor in terms of dB. We assume that the demodulator operates over one symbol interval, which yields a discrete memoryless channel. At the receiver, the corrupted MLTC-CPFSK signals are processed by the demodulator and MAP decoder to extract the information sequence.
where are the coefficients of the equivalent discrete channel.
After the M-CPFSK modulated signals are run through the channel, they are demodulated and then noisy demodulator outputs are evaluated for every equalization and decoding process. The following is the high-level summary of the equalization and decoding process. In the first step, the probabilities of received signal being zero and one is computed as in (7) and then, the probabilities are mapped to range via (8). In the second step, the computation of the equivalent discrete channel taps is explained when the channel conditions are known for the traditional decision feedback equalizer. In our application and real applications, the channel information is not known. Thus, the estimation process of the channel via LMS algorithm is performed and described. The coefficient vectors of the filters are defined from (14) and their adaptation is explained from (15). The DDFE equalization output is derived with (17). Finally, the equalized information is processed by the MAP decoder as in (18).
where and indicate zero and one probabilities of the received signal at time k and stage st. The partitioning stage is equal to . , are the selected signal sets at stage st.
In order to reduce the notation of the equations and figures, the notation is not changed when the information is processed by the interleavers. Only the channel output feeds the equalizer at the first iteration, therefore, the equalizer uses training sequence to operate for the initial process. For further iterations, the FF filter is fed by the channel output and the channel estimator output. The channel estimator uses both the hard decision of the first decoder and the channel output to estimate the channel information. The first FB filter uses the hard decision of the first decoder whereas the second FB filter uses the hard decision of the second decoder .
Since the equivalent discrete channel taps are unknown in most of the communication applications, the filter coefficient cannot be computed from the equation above.
During the initializing period, the coefficients of the FF filter at the first iteration are estimated from the training sequence by the LMS criterion due to the fact that the hard decision of the decoder does not exist at the first iteration. Therefore, the DDFE structure behaves as a linear equalizer fed by the training sequence at the first iteration.
Coding gains (in dB) over reference systems for .
Coding gains for 2LTC-4CPFSK over ref-1
( K = 10 dB)
Coding gains for 2LTC-4CPFSK over system (S-5) in ref-2
We have presented multilevel turbo codes scheme with CPFSK modulation, and joint multilevel turbo equalization scheme with CPFSK modulation in this paper. MLTC-CPFSK design compensates the requirement of large frame size and high iteration number to obtain low BER at low SNR for turbo codes by adding complexity and slight latency due to the multistage structure. As shown in Figure 7, MLTC-CPFSK model achieves BER performance at the third iteration when SNR equals to 3 dB and 3.7 dB for AWGN and Rician channels, respectively. When we compared our model with the well-known multilevel coded CPFSK and TTCM schemes in the literature, we observed important coding gains with the simulation results. Furthermore, low-complexity DDFE equalizer was designed and its good interference cancellation performance was presented against LE and DFE equalizers. Eventually, satisfactory performance results for MLTEQ-CPFSK scheme is demonstrated for severe ISI channels.
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