Frequency-domain Equalization Techniques for Multi-h Continuous Phase Modulation

A decomposition approach to continuous phase modulation (CPM), mostly due to the work of Rimoldi (1988), is significant in the design of combined coding and communication signaling scheme. In this paper the generalized decomposition model is developed and applies to the multi-h CPM. It is shown that any multi-h CPM can also be realized by a continuous phase encoder (CPE) concatenated with a memoryless modulator (MM). Moreover, depending on the manner that the modulation indexes are selected for each symbol interval, the CPE can be either a linear or nonlinear feedback convolutional encoder, in which both the CPE and MM are time-variant. Finally, some applications are employed to verify the advantage of the proposed decomposition model, namely, (1) natural trellis representation of the CPE for M-ary single-h CPM with different modulation indexes that have the same denominator P, (2) a reduction of the number of states of the MLSD receiver for conventional multi-h CPM, (3) asymmetrical multi-h CPM has no gain over conventional multi-h CPM, (4) nonlinear CPM has a CPE that is nonlinear.

Continuous phase modulation (CPM) is a widely used modulation scheme in communication systems. However, difficulties arise with the design of CPM receivers, due to the nonlinear nature of CPM. One popular solution to this problem is to linearize CPM with pulse amplitude modulation (PAM) representation. In this paper, a reduced-complexity superbaud timing recovery method is proposed for PAM-based multi-h CPM receivers. The proposed method is non-data-aided, feedforward, and suitable for M-ary, multi-h CPM in general. The novelties of the proposed method are twofold. On one hand, the proposed method is reduced-complexity for PAM-based receivers, because it shares the same match filters with the PAM-based detectors. On the other hand, it is shown that the proposed method is able to outperform the existing method with some modulation schemes. Therefore, the proposed method provides an important synchronization component for PAM-based multi-h CPM receivers.

Recently, single carrier block transmission (SCBT) has received much attention in high-rate phase-coherent underwater acoustic communication. However, minimum-mean-square-error (MMSE) linear FDE may suffer performance loss in the severely time dispersive underwater acoustic channel. To combat the channel distortion, a novel multi-channel receiver with maximum ratio combining and a low complex T/4 fractional iterative frequency domain equalization (FDE) is investigated to improve diversity gain and the bit error rate (BER) performance. The proposed method has been verified by the real data from a lake underwater acoustic communication test in November 2011. At 1.8 km, the useful data rates are around 1500 and 3000 bits/ s for BPSK and QPSK respectively. The results show the improvements of system performance. Compared with MMSE FDE system, the output SNR improvement is 6.9 dB, and the BER is from 10-3 to no error bits for BPSK. The output SNR improvement is 5.3 dB, and the BER is from 1.91×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2 to 2.2×10-4</sup> for QPSK.

The huge bandwidth available at 60 GHz will allow short range wireless communication to deliver bit rates over 1 Gbps. However the design of millimeter wave analog blocks is more critical than at lower frequencies, leading to a possible high non ideality of the radio front-end (FE). A suitable air interface for low cost, low power 60 GHz transceivers should thus use a modulation technique that has a high level of immunity to FE non-idealities. In this paper, we compare the sensitivity to FE non-idealities of two promising air interfaces namely offset quadrature phase shift keying (OQPSK) with frequency domain equalization (FDE) and continuous phase modulation (CPM) with time domain equalization (TDE). Our study focus on three main analog imperfections that are likely to have the biggest impact on the overall system performance: phase noise generated by the voltage control oscillator (VCO), clipping and quantization errors caused by the analog-to-digital converter (ADC) and non-linearity in the power amplifier (PA). Results show that CPM based air interface is more robust than OQPSK-based regarding the FE non-idealities. However the latter is less complex to design and offers much higher data rate than the former in the same bandwidth.

In this letter, an orthogonal space-time (ST) block coding (STBC) technique for continuous phase modulation (CPM) is proposed and combined with a frequency domain equalizer (FDE) to obtain high performance gains over frequency-selective channels. The new method maintains the constant envelope and phase continuity of the CPM waveforms perfectly by using appropriate tail symbols during the addition of cyclic prefix and interblock transitions and, therefore, has no negative impact on the spectral efficiency. Because the STcoded CPM blocks remain orthogonal, FDE is applied as in the case of single antenna transmissions without any increase in the computational load. Simulations corroborate the performance improvement offered by STBC while also preserving the desired bandwidth efficiency of CPM.

We present an optimal maximum likelihood sequence estimating (MLSE) receiver which is based on the pulse amplitude modulation (PAM) representation of multilevel multi-h continuous phase modulation (CPM). We also give four different approaches to constructing suboptimal receivers which use a significantly reduced number of signal terms. We apply these techniques to two multi-h schemes in current use and evaluate receiver performance with computer simulations. In one instance we reduce the number of trellis states from 512 to 32, and the number of matched filters from 96 to 3, with a degradation of 0.7 dB. The simulations also show that the complexity reductions preserve the performance advantage multi-h CPM schemes have over single-index schemes.

The underwater acoustic (UWA) communication system is characterized by limited bandwidth, while continuous phase modulation (CPM) offers a constant envelope, improving power and spectrum utilization efficiency. However, severe inter-symbol interference (ISI) poses a significant challenge in CPM-based UWA communication. Traditional CPM frequency domain equalization (FDE) combined with simple phase detection neglects the inherent coding gain from CPM, leading to performance degradation. Although Viterbi detection provides high performance, its complexity makes it unsuitable for computationally constrained UWA systems. This paper proposes a symbol detection algorithm based on posterior probabilities combined with FDE (PS-FDE). PS-FDE improves CPM signal detection performance by effectively separating information, applying delay, and performing multiple rounds of information merging. Simulations using minimum shift keying (MSK) and Gaussian MSK signals demonstrate significant performance improvement in just a few iterations over UWA channels. A sea trial further validates the algorithm, showing a 15.83% reduction in bit error rate after three information mergings.

Spatial Modulation (SM), is a new multiple antennas transmission technique for broadband wireless communications. In this paper, SM is firstly combined with single-carrier (SC) transmission systems for the merit of low peak average power ratio (PAPR) over conventional SM-orthogonal frequency division multiplexing (OFDM). Furthermore, for SM-SC systems, different detection techniques such as linear frequency-domain equalization (FDE) detection, decision feedback equalizer (DFE) detection and maximum likelihood detection (MLD) employing QR decomposition and M algorithm (QRM-MLD) techniques are explored to investigate the system performance. Finally, a comparison of the bit error rate (BER) performance between SM-SC and clipped SC-OFDM systems is given to show the merits of SM-SC systems.

Single carrier (SC) modulations employing frequency domain equalization (FDE) have been shown to be appropriate for severe time-dispersive channels, having similar or better performances than OFDM modulations, while offering the same complexity and lower peak-to-average power ratio. In this paper we introduce a class of low complexity linear frequency domain precoders (multiple-beamformers) for spatially correlated frequency selective multiple-input-multiple-output MIMO systems employing SC modulations. The specific designs targets minimization of a lower bound on the mean-square-error (MSE) under the assumption that only second order statistics of channel (covariance matrix of channel and noise) is available at the transmitter. These precoders are designed for different wideband receivers such as BLAST, MIMO-DFE, linear FDE. The proposed designs are assessed and compared for relatively large correlations and severely frequency selective channels.

Frequency-domain equalization for continuous phase modulation (CPM) is investigated. A discrete representation of the CPM signal is obtained by using the Gram-Schmidt orthonormalization procedure. The CPM discrete signal representation admits frequency-domain equalization for the purpose of mitigating intersymbol interference. General full- and partial-response CPM waveforms, and specific examples of MSK and GMSK with BT=0.3 are considered. Frequency-domain equalization is shown to be effective for CPM on severe frequency-selective fading channels.

In this paper, a pseudo minimum mean square error (P-MMSE) frequency domain equalizer (FDE) is proposed to combat deep fading channel for single carrier (SC) modulation under IEEE 802.11ad and IEEE 802.15.3c standard. This FDE has resistance like MMSE to deep fading channel and maintain low complexity like zero-forcing (ZF) equalizer. In order to calculate bit error rate (BER) performance, the proposed P-MMSE integrating with our previous dual-mode baseband receiver [1] to do simulation. P-MMSE FDE can provide about 1dB improvement for 16QAM and 5 dB improvement for QPSK and BPSK when BER at 10−-2 in serious deep fading channel. Besides, it enhances the BER floor from 4 × 10−-3 to 10−-3 in 16-QAM Moreover, P-MMSE FDE maintains the same complexity as ZF FDE.

Chapter 19 - Improving Receiver Performance in a High EMI Environment

Recent research has shown that single carrier frequency domain equalization (SC-FDE) is an attractive technology for broadband wireless communications for its advantages such as lower peak-to-average power ratio and reduced sensitivity to carrier frequency offset, when compared to orthogonal frequency-division multiplexing (OFDM) systems. In this paper, we propose a novel structure, FDE-NP, which consists of a linear frequency domain equalizer (FDE) and a time domain noise predictor (NP). It is shown that the proposed scheme has lower complexity and achieves better performance and complexity trade-off than the conventional FDE designs. In particular, by using a simple block interleaver/deinterleaver pair to rearrange the order of the received signals prior to decoding, delayed reliable decisions can be fed back to predict and cancel their post-cursor inter-symbol interference (ISI) effects to the following signals. Simulation results show that the proposed FDE-NP scheme achieves 1.5-2 dB performance improvement over the conventional FD-LE and FD-DFE schemes. Furthermore, we extend the design of unbiased and biased time domain equalizers (TDEs) into the frequency domain and propose the unbiased FDE. It is shown that although the unbiased FDE has a larger MSE than the biased one, it reduces the required SNR by about 0.3 dB in some cases

Continuous phase modulation (CPM) and trellis-coded modulation are well-understood schemes that layer trellis codes with multilevel modulation to produce efficient bandwidth waveforms. This paper describes a novel modulation scheme which takes advantage of existing trellis codes and adds parallel branches to create a new modulation with greater spectral efficiency and reduced receiver complexity. The first part of the paper discusses the trade-off between Euclidean distance and modulation bandwidth for the standard 1-REC CPM waveform. A set of orthogonal signals can be added to the CPM constellation which provides a series of parallel branches in the natural trellis structure of the CPM modulation. The corresponding bandwidth expansion and throughput improvement is analyzed and the advantages of this modulation technique are discussed. This new, non-constant envelope CPM waveform is compared to the multi-level, multi-amplitude CPM waveform (described in Proakis). In similar fashion, a trellis-coded, shaped PSK modulation is expanded to include orthogonal signal shaping and the power and spectral efficiencies are discussed.

Multicarrier transmission techniques like multicarrier code division multiple access (MC-CDMA) is the strongest contender for the future generation wireless networks which is supposed to cater to the need of very high data rate with mobility and at the same time combat multipath and intersymbol interference in a spectrally efficient manner. To enhance the spectral efficiency further, some form of adaptive modulation is being proposed (Wasantha et al. (2002)). In this paper, first of all, we simulate the performance of various single-h continuous phase modulation (CPM) schemes in an MC-CDMA system by varying the two CPM parameters - size of symbol alphabet (M) and modulation index (h). The parameter sets considered are {M=2, h=0.5}, {M=2, h=0.875}, {M=4, h=0.5} and {M=4, h=0.875}. Simulation results show that the higher order modulation schemes (M=4) need better channel conditions than the lower order schemes (M=2) for a given bit error rate (BER). Moreover, as expected (Xiong (2000)), h=0.875 (approximate optimum value) gives a better BER performance than h=0.5 for a given BER. Based on these simulation results, we then design two adaptive modulation based systems, one considering h=0.5 and the other with h=0.875, each with M=2 and 4. Results of the adaptive systems clearly indicate that the adaptive switching of the modulation formats in each of these two systems increases the system capacity per given bandwidth (spectrum efficiency) effectively without sacrificing the expected BER performance. Also, it is seen that the adaptive system with h=0.875 is superior to the h=0. 5 system, both in terms of BER performance and the number of simultaneous users, but obviously at the cost of reduced bandwidth efficiency as higher the value of h, the higher bandwidth it requires.