Differential spatial modulation (DSM) is a noncoherent multi-antenna technique that conveys additional information by selecting transmit antennas. Space-time block coded DSM (STBC-DSM) combines DSM with STBC to achieve a transmit diversity order of two. Recently, we proposed a new STBC-DSM scheme that improves spectral efficiency through temporal permutations, termed bandwidth-efficient generalized DSM (BE-GDSM). This paper enhances BE-GDSM in two key aspects: either reducing detection complexity or increasing spectral efficiency. We propose a maximum-likelihood (ML) detector with significantly lower computational complexity for BE-GDSM. Besides, we introduce spatial permutations for STBC-DSM and demonstrate that such permutations require differential encoding. Building on this observation, we propose STBC-DSM with joint spatial and temporal permutations (STBC-DSM-JSTP), which achieves the maximal number of antenna bits among all STBC-DSM schemes. Numerical results show that STBC-DSM-JSTP improves error performance compared with BE-GDSM at the same data rate.

We present a correction to the above-named work. In Table III,$d_{free}^{2}$for new codes with$L=32$should be 3.561 (instead of 3.667) and 3.233 (instead of 3.385) for TCM-DE and DTCM, respectively. The corresponding paragraph on the same page, “For$L=32$, the best$d'^{2}_{free}$is …… in simulations.” should be modified as “For$L=32$, the best$d'^{2}_{free}$is$5\Delta _{1}^{2}+2\Delta _{0}^{2}$(for instance, two paths (0,0,0,0,0,0) and (0,2,0,1,2,2), so the resulting minimum squared distance is$\min [\Delta _{2}^{2},d'^{2}_{free}=3.233]=3.233$for 8PSK. There are some codes that have the best$d'^{2}_{free}$and we choose (C0,C2),(C3,C1),(C3,C1),(C2,C0),(C2,C0),(C1,C3) and (C1,C3) for$\sigma ^{(1)},\cdots ,\sigma ^{(7)}$in simulations.”. In addition, the trellis diagram in Fig. 12(b) should be corrected to Fig. 1.

Bit-interleaved coded modulation with iterative decoding (BICM-ID) are suitable for continuous fading channels. In addition, BICM-ID using differential encoding can avoid the rate loss due to pilot symbols. Conventional differential encoding for uncoded modulation was used for BICM-ID. In this paper, we propose new differential encoding of 16APSK (amplitude and phase-shift keying) signals for BICM-ID. We first derive the probability of receiving signals conditioned on the transmission of input bits of general differential encoding. After that, we propose a new algorithm to optimize differential encoding for BICM-ID, and use it to find the differential encoding of 16APSK. Besides, code searches for the proposed differential encoding are performed. Simulation results show that the proposed differential encoding has better error performance than conventional differential encoding, and the searched new codes can further improve error performance.

Differential encoding (DE) is a classical technique at the transmitter that allows simple noncoherent detection at the receiver. On the other hand, trellis-coded modulation (TCM) is a bandwidth efficient technique which offers reliable data transmission. In this paper, we aim to find the best concatenation order of TCM and DE for channel phase coherence over N=2 symbols. Besides the well-known TCM followed by DE (called TCM-DE) , we propose a new trellis coding extension of DE which extends our earlier work, called differential trellis coded modulation (DTCM) . DTCM is TCM with DE defined in states where distinct states may have distinct DE functions. We propose design methods of DE functions for noncoherently non-catastrophic DTCM. For both TCM-DE and DTCM, we propose additive distance measures and set partitioning. Based on the proposed set partitioning, trellis codes are designed or searched for both TCM-DE and DTCM. Both minimum distances and simulation results show that TCM-DE outperforms DTCM and the obtained new codes are better than the original codes.

Recently we proposed a novel differential encoder by a look-up table. In this paper, we present further research results on this subject. We first propose a bit-assigning algorithm and construct some new tables for various constellations that maximize the minimum noncoherent distance. Then differential encoding for multiple-symbol differential detection is proposed. After that, we indicate that differential encoding by a table is equivalent to differential encoding by a trellis, so we propose a novel differential detector which uses the Viterbi algorithm on the trellis. A theorem about the sufficient number of states for various modulations is proposed. In addition, we further enhance the error performance of the proposed differential encoder by concatenating it with trellis coding. For this noncoherent trellis coding scheme, we propose augmented-state Viterbi decoding. Finally, we extend the proposed differential encoding and detection to differential space-time modulation (DSTM). We propose a new definition of DSTM by which the set of transmitted blocks is determined first. The differential encoding is implemented by a look-up table which can be optimized. The proposed DSTM has satisfactory error performance without constellation expansion.

Recently, we proposed a novel differential encoder for non-constant energy signals, by a look-up table instead of a rule. In this paper, we present further research results on this subject. We first propose a new bit-assigning algorithm and some constellations maximizing minimum noncoherent distance. Then we show that differential encoding by a table is equivalent to differential encoding by a trellis, so we use the Viterbi algorithm at the differential detector to improve the error performance. A theorem about the sufficient number of states for various modulations is proposed. Finally, we extend the proposed differential encoding and detection to differential space-time modulation (DSTM). We propose a new definition of DSTM, by which the transmitted block is determined according to the previously transmitted block and current data bits. The encoding table that determines the transmitted block can be optimized. We also propose a theorem to reduce the number of states of the decoding trellis. The proposed DSTM has satisfactory error performance without constellation expansion.

In this paper, we propose a novel differential encoder for QAM (quadrature-amplitude modulation), by a look-up table instead of a rule. Using a table for differential encoding has the advantages of both low complexity and good error performance. We propose algorithms to construct the table for maximizing the minimum noncoherent distance and minimizing the number of different data bits between two codewords with small noncoherent distance. For 16QAM and 32QAM, we show that the differential encoders obtained by the proposed algorithms are optimal in terms of minimum noncoherent distance. Differential detectors for QAM, including a reduced-complexity two-symbol detector and multiple-symbol detectors, are proposed as well. Simulation results of 16QAM show that the proposed differential encoder provides significant gain over existent differential encoders as expected by distance analysis, and the proposed low-complexity multiple-symbol differential detector can further improve the error performance.

In this paper, we propose a noncoherently non-catastrophic trellis-coded modulation scheme, in which the transmitter includes a differential encoder, a rotator, an inverse signal mapper, a convolutional encoder and a signal mapper. We present examples of the proposed scheme including MPSK (M-ary phase shift keying), QAM (quadrature-amplitude modulation), and TAPSK (twisted amplitude and phase shift keying). For trellis-coded QAM, a differential encoder with which the complexity of the proposed scheme can be reduced is proposed. Simulation results demonstrate that for noncoherent decoding, the proposed trellis-coded QAM has much better error performance than conventional trellis-coded QAM, and the proposed trellis-coded 16APSK outperforms trellis-coded 16QAM for short observation length.

In this paper, we propose a novel differential encoder for QAM (quadrature-amplitude modulation), by a look-up table instead of a rule. Using a table for differential encoding has the advantages of both low complexity and good error performance. We propose algorithms to construct the table for maximizing the minimum noncoherent distance and minimizing the number of different data bits between two near codewords. For 16QAM, we show that the differential encoder obtained by the proposed algorithms is optimal in terms of minimum noncoherent distance.

In this paper, we propose a new noncoherent trellis-coded QAM (quadrature-amplitude modulation) scheme, in which a differential encoder, a rotator and an inverse signal mapper are added in front of the convolutional encoder. Trellis codes of the proposed scheme are shown to be noncoherently non-catastrophic and have better error performances than conventional trellis-coded QAM. %for short observation length. New trellis codes which, for the proposed cheme, have better bit error rates than Ungerboeck's codes are found by computer searches.

In this paper, we derive the minimum noncoherent distance of block-coded 16QAM, and propose noncoherent block-coded 16QAM (NBC-16QAM) accordingly. Various noncoherent block coding schemes are compared via computer simulations. We find that for both NBC-16QAM and the noncoherent 16QAM scheme proposed in 2002, the curves of bit error rates do not decade exponentially. When the block length is very small, NBC-16QAM performs worse due to its small minimum noncoherent distance. However, if the block is not short, NBC-16QAM has the best error performance because the codewords with small noncoherent distances are rare.

In this paper, we derive minimum noncoherent distances of block-coded TAPSK (twisted amplitude and phase shift keying) and 16QAM (quadrature-amplitude modulation), both using linear component codes. According to the derived distances, noncoherent block-coded TAPSK (NBC-TAPSK) and noncoherent block-coded 16QAM (NBC-16QAM) are proposed. If the block length is very small, NBC-16TAPSK performs best among all noncoherent schemes and NBC-16QAM performs worse due to its small minimum noncoherent distance. However, if the block is not short, NBC-16QAM has the best error performance because the codewords with small noncoherent distances are rare.

In this letter, we propose three noncoherent block coded twisted amplitude and phase shift keying (NBC-TAPSK) schemes which are derived from noncoherent block-coded MPSK. We also propose a new noncoherent detector and a corresponding noncoherent distance for nonconstant-energy signals over the additive white Gaussian noise (AWGN) channel. At high data rates, NBC-8TAPSK has the best bit error performance among all noncoherent schemes.

In this letter, we propose a novel bandwidth-efficient noncoherent trellis-coded MPSK scheme, in which a particularly designed differential encoder is added in front of the trellis encoder. With this differential encoder, trellis-coded MPSK proposed by Ungerboeck is no longer noncoherently catastrophic and thus achieves better error performance. Moreover, new trellis codes which, for the proposed scheme, have better bit error rates than Ungerboeck's codes are found by computer searches.

Turbo coded unitary space-time modulation (USTM) can provide large coding gain as compared to uncoded USTM. Because the noncoherent space-time maximum a posteriori demodulator is very complicated, in this letter, we propose a new low-complexity noncoherent iterative space-time demodulator for the USTM constructed from pilot symbolassisted modulation. The proposed demodulator utilizes both hard and soft decisions from the turbo decoder to simplify the computational task as well as produce reliable soft outputs. Several examples demonstrate that this demodulator has both low complexity and good error performance.

A novel noncoherent block coding scheme, called noncoherent block-coded MPSK (NBC-MPSK), was proposed recently. In this paper, we present further research results on NBC-MPSK. We first focus on the rotational invariance (RI) of NBC-MPSK. Based on the RI property of NBC-MPSK with multistage decoding, a noncoherent near-optimal linear complexity multistage decoder for NBC-MPSK is proposed. Then we investigate a tree-search ML decoding algorithm for NBCMPSK. The derived algorithm is shown to have low complexity and excellent error performance. In this paper, we also utilize the idea of the NBC-MPSK to design noncoherent space-time block codes, called noncoherent space-time block-coded MPSK (NSTBC-MPSK). For two transmit antennas, we propose a signal set with set partitioning and derive the minimum noncohent distance of NSTBC-MPSK with this signal set. For the decoding of NSTBC-MPSK, we modify the ML decoding algorithm of NBC-MPSK and propose an iterative hard-decision decoding algorithm. Compared with training codes and unitary space-time modulation, NBC-MPSK and NSTBC-MPSK have larger minimum noncoherent distance and thus better error performance for the noncoherent ML decoder.

We investigate block-coded QAM constructed by multilevel coding for the noncoherent generalized likelihood ratio test (GLRT) detector. For the AWGN channel, we derive a new GLRT detector and the corresponding distance. The minimum noncoherent distance of block-coded QAM is derived and two construction of noncoherent block-coded QAM (NBC-QAM) are proposed accordingly. In the NBC-QAM scheme, the error performance can be optimized by adjusting the constellation. The superior error performances of NBC-QAM are verified by simulation results.

It is known that tail-biting codes T' constructed from trellis coded modulation (TCM) with a delay processor can achieve large minimum Euclidean distances. In this paper, concatenated space-time block coding (STBC) with T' for multiple-input multiple-output (MIMO) and MIMO-OFDM (orthogonal frequency-division multiplexing) systems is investigated. We propose an improved system which is implemented by inserting a specific block interleaver between the encoders of coded modulation and STBC. We also propose sliding-window-type iterative decoding using partial hard-decision feedback (SW-IDPHF) with low complexity to decode T', which provides better error performance as compared to sliding-window-type iterative decoding using full hard-decision feedback (SW-IDFHF). In addition, we apply sliding-window-type iterative decoding using soft-decision feedback (SW-IDSF) to T' for improved error performance. The decoder of concatenated system based on T' can converge faster and provide better ultimate error performance as compared to the case of BICM under various channel conditions for either MIMO or MIMO-OFDM systems.

Unitary space-time modulation (USTM) is well-tailored for noncoherent space-time modulation. Trellis coded USTM (TC-USTM) can obtain significant coding gains over uncoded USTM for the noncoherent block fading channel. Conventional TC-USTM schemes expand the signal set of uncoded USTM by a factor of two. In this letter, we propose a new TC-USTM scheme in which the size of USTM set is not limited to be just double for uncoded USTM. However, in TC-USTM schemes, because signals of the same trellis branch are transmitted over the same fading coefficients, one trellis branch can only obtain one temporal diversity. In this letter, we also propose a new trellis coded noncoherent space-time modulation scheme by interleaving space-time signals. The proposed scheme can enlarge temporal diversity at the price of increased complexity and delay. Simulation results demonstrate the excellent error performances of codes found by computer searches for both schemes.

A novel noncoherent block coding scheme, called noncoherent block-coded MPSK (NBC-MPSK), was proposed in [1] recently. This NBC-MPSK scheme was generalized to multiple-antenna systems in [2] as well. In this paper, we present further research results on NBC-MPSK and its generalization. We first focus on the rotational invariance (RI) of NBC-MPSK. Based on the RI property of NBC-MPSK with multistage decoding, a noncoherent near-optimal linear-complexity multistage decoder for NBC-MPSK is proposed. Then we propose a tree-search ML decoding algorithm for NBC-MPSK. The proposed algorithm is shown to have low complexity and excellent error performance. This ML decoding algorithm can also be applied to the generalized NBC-MPSK for multiple antennas. In addition, we propose a new signal set with partitioning for the generalized NBC-MPSK. Error performance and complexity of decoding algorithms is verified by simulations.

For original paper, see Fan and Xia (IEEE Trans. Commun., vol.49, no.4, p.585-8, 2001 April).

For coherent detection, block-coded modulation is a bandwidth efficient scheme. In this paper, we propose theorems about the error performance of block-coded modulation using M-ary phase-shift keying (MPSK) for noncoherent detection. Based on these theorems, we propose a novel block-coded modulation scheme for noncoherent detection called noncoherent block-coded MPSK. The proposed scheme provides flexible designs of noncoherent block codes with different code rate, block length and error performance. Good noncoherent block codes can be easily obtained by properly choosing binary linear block codes as the component codes. Moreover, noncoherent block codes of this new scheme can be decoded by multistage decoding, which has the advantage of low complexity and satisfactory error performance. In this paper, two algorithms of multistage decoding for noncoherent detection are proposed as well. The error performance of some designed codes and decoding algorithms is verified by computer simulation.

Unitary space-time modulation is well tailored for flat fading channels where the noncoherent receiver is used. In this paper, we propose a novel scheme of unitary space-time modulation, called noncoherent space-time block coded modulation, by using the set partitioning of signal sets and multilevel coding. Signal sets for two and four transmitter antennas are proposed, and the factor which dominates the error performance is derived as well. Unitary space-time modulations of the proposed scheme are designed by selecting appropriate component codes. The advantage of the proposed scheme can be demonstrated by the distance analysis and computer simulations.

In this paper, a new noncoherent space-time coding scheme for the quasistatic flat fading channel is proposed. The proposed codes, called unitary space-time trellis codes, can be decoded by using the Viterbi algorithm without the knowledge of fading coefficients. The Viterbi decoder uses a sliding window for the observations where each observation covers several branches of the trellis. Appropriate decoding metrics for the observations are proposed also. We propose a systematic method for searching good unitary space-time trellis codes by computers. Simulation results indicate that the unitary space-time trellis codes are suitable for both the quasistatic and slow continuous flat fading channels.

For coherent detection, block coded modulation with multistage decoding is a bandwidth efficient coded modulation system. In this paper, a novel block coded modulation system for noncoherent detection called noncoherent block coded modulation (NBCM) is proposed. We present a theorem for the distance property of the NBCM. This theorem provides a guideline of constructing good codes of NBCM. Specific designs of NBCM are given also. In addition, to simplify the decoding of NBCM, two algorithms for multistage decoding are proposed. The advantage of NBCM is demonstrated by comparing examples with respect to code rate, block length, error performance and decoding complexity.

This letter shows several methods for improving the decoding of noncoherent trellis-coded M-ary phase-shift keying. We propose two new metrics for the basic decision-feedback algorithm. These metrics are derived based on the idea of reducing the effect of incorrect amplitude of the reference signal. We also propose a new decoding algorithm that uses a simple way to estimate the metric of the future sequence.

We show that decision-feedback differential phase detection (DFDPD) is equivalent to a technique which generates a phase reference by averaging several primitive phase references. We then modify the DFDPD into a differential phase detection (DPD) technique which generates the phase reference using a simple recursive form. The proposed technique can be easily implemented and has satisfactory error performance.

We derive a new upper bound on the pairwise error probability for MPSK sequences over the Rayleigh fading channel when channel state information (CSI) is not available. This is obtained by adding weight factors in calculating the symbol metrics. Simulation shows that the weight factors which optimize the upper bound are likely to optimize the error rate too. We also design multilevel coded MPSK schemes which are suitable for the Rayleigh fading channel. These schemes are basically in the form of block coded modulation with interblock memory (BCMIM), which was originally designed for an additive white Gaussian noise (AWGN) channel. The added weight factors are found to be effective in improving the error performance of these BCMIM schemes in case that CSI is not available.

A conventional decision feedback differential detection technique can be regarded as a technique using L previously received signal samples and L-1 previously decided data phases to generate a phase reference for the phase detection operation of a currently received MPSK signal sample. With this observation, we propose a differential detection technique which uses a new way to generate the phase reference. In the proposed technique, the phase reference called weighted phase reference is the weighted sum of primitive phase references derived from previously received signal samples. The weighted phase reference can be generated using a simple recursive form. The proposed detection technique can be easily implemented and has satisfactory error performance.