Recursive Bit Metric Generation for PSK Signals with Gray Labeling

Experimental measurements have shown that the noise in many communication channels is non-Gaussian. Bit interleaved coded modulation (BICM) is very popular for spectrally efficient transmission. Recent results have shown that the performance of BICM using convolutional codes in non-fading channels can be significantly improved if the coded bits are not interleaved at all. This particular BICM design is called BICM trivial (BICM-T). In this paper, we analyze the performance of a generalized BICM-T design for communication over Gaussian mixture noise (GMN) channels. The results disclose that for an optimal bit error rate (BER) performance, the use of an interleaver in BICM for GMN channels depends upon the strength of the impulsive noise components in the Gaussian mixture. The results presented for 16-QAM show that the BICM-T can result in gains up to 1.5 dB for a target BER of 10 -6 if the impulsive noise in the Gaussian mixture is below a certain threshold level. The simulation results verify the tightness of developed union bound (UB) on BER performance.

In this paper, we propose a reduced complexity (RC) per-survivor-processing (RC-PSP) iterative timing recovery scheme. The objective is to lessen the computational burden while approaching the optimal system performance of the existing full-complexity (FC) log-MAP (FC-PSP) iterative recovery scheme. This is achieved by utilising the max-log-MAP framework, which converts the multiplications and additions to maximum operations. According to Spasov, Gushev and Ristov, such framework consumes less power, reduces space on a chip and increases decoding speed. Robertson et al. showed that max-log-MAP PSP requires only 5 × 2M − 2 max operations, 10 × 2M additions and 8 multiplications by ±1. Furthermore, it offers a direct mathematical framework for converting the log-MAP-based PSP to max-log-MAP-based PSP for timing recovery. The simulations show that the proposed method outperforms the previous methods. The computational complexity for the max-log-MAP PSP is significantly reduced at the cost of a small bit error rate (BER) performance loss.

Classical Turbo code suffers from high error floor due to its small minimum Hamming distance (MHD). Newly-proposed 3D-Turbo code can effectively increase the MHD and achieve a lower error floor by adding a rate-1 post encoder, through which part of the parity bits from the classical Turbo encoder are further encoded. In this paper, a novel bit-interleaved coded modulation (BICM) system is proposed by combining rotated mapping QAM and 3D-Turbo code to effectively improve the performance of 3D-Turbo code over Raleigh fading channels. A 2D iterative soft demodulating-decoding algorithm is developed for the proposed BICM system. Simulation results show that the proposed system can obtain about 0.8-1.0 dB gain at bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> , compared with the existing BICM system with Gray mapping QAM.

The generalized mutual information (GMI) of bit-interleaved coded modulation (BICM) systems, sometimes called the BICM capacity, is investigated at low signal-to-noise ratio (SNR). The combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${- 1.59}\;{\rm dB}$</tex></formula> are completely characterized. The main conclusion is that a BICM system with probabilistic shaping achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR BICM-GMI, in addition to what is provided by geometrical shaping. The analytical conclusions are confirmed by numerical results, which also show that for a fixed input alphabet, probabilistic shaping can improve the BICM-GMI in the low and medium SNR range.

Hierarchical constellations offer a different degree of protection to the transmitted messages according to their relative importance. As such they found interesting application in digital video broadcasting systems as well as wireless multimedia services. Although a great deal of attention has been devoted in the literature to the study of the bit error rate (BER) performance of uniform phase shift keyed (PSK) constellations, very few results were published on the BER performance of hierarchical PSK constellations. We obtain exact and generic expressions in M for the BER of the generalized hierarchical M-PSK constellations over additive white Gaussian noise (AWGN) and fading channels. For the AWGN case, these expressions are in the form of a weighted sum of Pawula (1982) F-functions and are solely dependent on the constellation size M, the carrier-to-noise ratio, and a constellation parameter which controls the relative message importance. Because of their generic nature, these new expressions readily allow numerical evaluation for various cases of practical interest.

Cooperative transmission is an efficient way to combat fading for wireless communication. In this paper, a bandwidth-efficient multi-user cooperation scheme is proposed, that is based on TPC(Turbo Product Codes)-BICM(Bit-Interleaved Coded Modulation). In the multi-user cooperation, we use distributed transmission to achieve diversity gain. The bit error rate(BER) performance is discussed and BER upper bound is deduced. Modulation order M, component codes and cooperation level α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> are the main parameters that influence system performance. Assumed that the first two parameters are fixed, we discussed the optimal α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> value on principle of minimum BER. An optimal transmission rule is presented. When all the uplink channels are same, uniformity distribution is optimal. Simulation results in slow fading show that the BER performance curve approach the upper bound at high SNR. In a general way, the optimal transmission outperforms uniformly transmission.

Band-limited single-carrier signals, even with a phase-shift keying (PSK) constellation, suffer from relatively high peak-to-average power ratio (PAPR) when a narrow pulse-shaping filter is used at the transmitter. In our recent work, an application of trellis shaping (TS) has been studied extensively for the purpose of reducing PAPR of band-limited single-carrier PSK signals, and it has been shown that a nearly constant envelope signal can be generated even with the use of nearly rectangular pulse-shaping filter. In this paper, we first demonstrate that the uncoded bit error rate (BER) and PAPR reduction capability of the TS considerably depend on the bit labeling. We then propose a new bit labeling for high-order PSK constellation that can efficiently reduce PAPR while achieving BER performance comparable to that of Gray labeling. Finally, the BER of each constellation is theoretically analyzed and compared with the simulation results.

The bit error rate (BER) performance of orthogonal space-time block codes (STBC) in correlated multiple input multiple output (MIMO) channels is studied. We derive closed-form exact BER equations for pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM), and phase shift keying (PSK) constellations in a correlated Rayleigh MIMO channel. The BER expressions can be easily evaluated without any numerical methods.

Adaptive modulation techniques combat fading by employing a suitable modulation mode depending on the instantaneous channel conditions for improving the Bit Error Rate (BER) performance or the average throughput. Based on a generic model of constant-power adaptive modulation, exact closed form expressions of the average BER and the average throughput are derived, when employing square Quadrature Amplitude Modulation (QAM) or Phase Shift Keying (PSK) as the constituent modulation modes, operating over a Nakagami fading channel. The optimum modulation-mode switching levels, achieving the highest possible throughput under the constraint of the average BER, are obtained using the Lagrangian optimisation method. Adaptive modulation employing the optimum switching levels shows a superior performance, while maintaining a constant average BER.

Time division duplex (TDD) pre-equalized orthogonal frequency division multiplexing (OFDM) systems can save system resources by omitting pilot symbols. Meanwhile, a new problem arises that the timing error would degrade system performance, because this error cannot be revised in the absence of pilot symbols. The paper investigates the impact of timing error on the receiver's bit error rate (BER) performance for TDD pre-equalized OFDM systems using phase-shift keying (PSK) modulation. The analytic binary PSK (BPSK) and quadrature PSK (QPSK) BER expressions of ideally and nonideally pre-equalized OFDM systems are obtained, in multipath Rayleigh fading environment. The corresponding simulations verify the analytic expressions. Compared with the theoretical system performance bound, the performance of ideal and nonideal pre-equalized BPSK systems entail loss of 1 dB and 3 dB respectively when the normalized timing error is 1/8. When it is 1/4, the performances of both systems degrade severely. At the same time, the gap between them diminishes. In that case, timing error becomes dominant among those elements which would affect systems performance. The higher the modulation order adopted, the more sensitive to timing error the system performance becomes.

Performance of both orthogonal frequency division multiplexing (OFDM) and single carrier (SC) systems suffers from a carrier frequency offset (CFO) due to Doppler effect and the carrier instability between the transmitter and the receiver. We investigate the bit error rate (BER) performance degradation of OFDM and SC systems due to the frequency offset in an additive white Gaussian noise (AWGN) channel as well as multipath Rayleigh fading channels. We consider three effects to the BER degradation, i.e., phase shift, useful power decrease and intercarrier interference (ICI). We also derive the approximate expressions of BER under binary phase shift keying (BPSK) and quaternary phase shift keying (QPSK) for both OFDM and SC systems in the presence of CFO. In general, SC is more robust to CFO in the AVVGN channel than OFDM in terms of BER, while both of them suffer similarly from CFO in the multipath Rayleigh fading channels assuming the the same CFO.

In recent years, there has been enormous interest in millimeter (mm) wave communication systems such as IEEE 802.11ad and IEEE 802.15.3c operating in higher and unused frequency bands. To make system more resilient in time varying, multipath fading channels, a modulation scheme called π/2-quadrature phase shift keying (QPSK) along with a forward error control (FEC) scheme has been proposed in these systems. The performance of the FEC decoder is improved when soft information in the form of log likelihood ratio (LLR) is given to it In this paper, we propose a method for soft demapping of π/2-QPSK symbols. This method is also applicable to other schemes such as differential QPSK (DQPSK) and offset QPSK (OPSK). The complexity of the proposed method is very less and requires one adder and one multiplier. We demonstrate the bit error rate (BER) performance of the proposed method using simulations and compare it with that of other methods.

The application of bit-interleaved coded modulation (BICM) in combination with differential encoding and non-coherent reception over flat fading channels is assessed. Since the labeling plays a central role for BICM we propose a suitable definition of Gray labeling for differentially encoded transmission. We show that for multiple symbol detection such a Gray labeling does not exist. Finally, we illustrate the consequences on the capacity by comparing BICM and an optimum coded modulation scheme.

Orthogonal Frequency Division Multiplexing (OFDM) has been considered as a strong candidate for next generation wireless communication systems. Compared to traditional OFDM, Single Carrier OFDM (SC-OFDM) has demonstrated excellent bit error rate (BER) performance, as well as low peak to average power ratio (PAPR). Similar to other multi-carrier transmission technologies, SC-OFDM suffers significant performance degradation resulting from intercarrier interference (ICI) in high mobility environments. Existing techniques for OFDM can be directly adopted in SC-OFDM to improve performance, however, this improved performance comes at costs such as decreased throughput. In this paper, we analyze the effect of ICI on an SC-OFDM system and propose a novel modulation scheme. The proposed Magnitude-Keyed Modulation (MKM) modulation provides SC-OFDM system immunity to ICI and with an easy implementation it significantly outperforms OFDM, SC-OFDM and MC-CDMA systems with Phase Shift Keying (PSK) modulation and Quadrature Amplitude Modulation (QAM) in severe ICI environment. Analysis also illustrates the proposed SC-OFDM system with MKM modulation maintains low PAPR compared to traditional OFDM and SC-OFDM systems with PSK and QAM modulations. Simulation results for different modulation schemes in various ICI environments confirm the effectiveness of the proposed system.

In this paper, we propose a novel peak to average power ratio (PAPR) reduction scheme of orthogonal frequency division multiplexing (OFDM) signals. In our proposed scheme we exploit the repeated rotation and recombination of the in-phase and the quadrature components of an OFDM symbol in time domain. Our proposed scheme has two main advantages over the previously known scheme such as iterative partial transmit sequence (I-PTS), which are 1) remarkably lower computational complexity and 2) less required side information overhead than the I-PTS scheme. Based on our derived complementary cumulative distribution (CCDF) of PAPR, we show that our proposed scheme gives only 0.2 - 0.3 dB loss compared to the I-PTS scheme in terms of PAPR threshold while the complexity for the implementation is much reduced. Furthermore, the proposed scheme does not cause any loss of bit error rate performance over both the additive white Gaussian noise (AWGN) channel and the frequency selective channel even though the simulation results regarding the bit error rate (BER) performance is not shown in this paper due to the limited space of the pages.