A low-complexity noncoherent iterative space-time demodulator

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 symbol-assisted 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.     

MULTIPLE TRELLIS CODED ORTHOGONAL TRANSMIT SCHEME FOR MULTIPLE ANTENNA SYSTEMS

In this paper, a novel multiple trellis coded orthogonal transmit scheme is proposed to exploit transmit diversity in fading channels. In this scheme, a unique vector from a set of orthogonal vectors is assigned to each transmit antenna. Each of the output symbols from the multiple trellis encoder is multiplied with one of these orthogonal vectors and transmitted from corresponding transmit antennas. By correlating with corresponding orthogonal vectors, the receiver separates symbols transmitted from different transmit antennas. This scheme can be adopted in coherent/differential systems with any number of transmit antennas. It is shown that the proposed scheme encompasses the conventional trellis coded unitary space-time modulation based on the optimal cyclic group codes as a special case. We also propose two better designs over the conventional trellis coded unitary space-time modulation. The first design uses 8 Phase Shift Keying （8-PSK） constellations instead of 16 Phase Shift Keying （16-PSK） constellations in the conventional trellis coded unitary space-time modulation. As a result, the product distance of this new design is much larger than that of the conventional trellis coded unitary space-time modulation. The second design introduces constellations with multiple levels of amplitudes into the design of the multiple trellis coded orthogonal transmit scheme. For both designs, simulations show that multiple trellis coded orthogonal transmit schemes can achieve better performance than the conventional trellis coded unitarv space-time schemes.     

A Systematic Set Partitioning for Unitary Space-Time Signal Sets

Proper partitioning of a unitary space-time (UST) signal set is essential for the optimal design of trellis coded unitary space-time modulation (TC-USTM). The unique properties of these UST signals have necessitated a different partitioning methodology from that of the conventional two dimensional constellations. In this letter, we propose a systematic set partitioning through a novel subset-pairing strategy, for an arbitrary UST signal set. This approach leads to a geometrically congruent partitioning, i.e., subsets of the same size (order) have identical intra-distance profiles. Based on this partitioning, the resulting TC-USTM can achieve a minimum bit error probability.     

Space-Time Trellis Code Design Based on Super Quasi-Orthogonal Block Codes With Minimum Decoding Complexity

In this letter, we propose a new family of space-time trellis codes, which are constructed by combining a super set of quasi-orthogonal space-time block codes with minimum decoding complexity with an outer multiple trellis coded modulation encoder. A systematic set-partitioning method for quadratic amplitude modulation constellations is given. The proposed scheme can be used for systems with four or more than four transmit antennas. Furthermore, its decoding complexity is low because its branch metric calculation can be implemented in a symbolwise way. Simulation results demonstrate that the proposed scheme has a comparable performance as super quasi-orthogonal space-time trellis codes proposed by Jafarkhani and Hassanpour while providing a lower decoding complexity.     

Novel full diversity space time codes

A novel full diversity space-time trellis code, referred to as an assembled space-time trellis code (ASTTC), is presented in this letter. For this scheme, space-time trellis coded signals are first linearly transformed, and then the transformed signals are coded by using the Alamouti space-time block code. A new design criterion is proposed. It is shown that the ASTTCs can achieve not only the full diversity order but also a significant coding gain determined by the minimum weighted code distance (MWCD). Based on this design criterion, a new 4-state code is derived by a systematic code search. Simulation results show that the new ASTTC is superior by about 1.7 dB to the TSC (TarokhSeshadri-Calderbank) code at the frame error rate (FER) of 1.0e-2 over quasi-static fading channels.     

满速率串行级联空时分组MTCM编码方法研究

该文研究了级联空时编码系统在编码增益,分集增益和传输能量效率的限定下最大化传输速率的问题,提出了一种在保留TCM编码方法校验位冗余的同时,还可获得满速率串行级联空时分组TCM编码方法。新方法通过引入具有不同功率分集因子的正交发射码字矩阵,并给出新的译码算法,从而使得新的编码方法在获得满速率的同时还可以获得满分集增益。分析和MATLAB仿真结果表明,在相同的编码状态数下,新方法在编码增益上比现有的满速率超正交空时分组编码方法提高1dB左右。     

A comparison of two combining techniques for equal gain, trelliscoded diversity receivers

Trellis coded modulation is widely used for digital transmission over fading channels. Classical diversity techniques are also frequently employed to combat fading. In this paper two different strategies for equal gain combining are compared, One scheme is based on an interleaved code combining technique. The alternative scheme is based on averaged diversity combining. The well known transfer function bounding technique for trellis codes is used to obtain: expressions for the bit error rate performance of the two trellis coded diversity receivers over a slowly fading Rayleigh channel. The analysis of interleaved code combining is a straightforward modification of the analysis for multiple trellis coded modulation. The analysis of averaged diversity combining is accommodated through a more involved, novel modification of the branch labeling of the error state diagram. The analytic techniques presented in this paper are supported by simulation results using a TCM scheme based on QPSK modulation and a rate-l/2 linear convolution code     

An interleaved TCM scheme for single carrier multiple transmit antenna systems

Single carrier (SC) block transmission with frequency domain equalization (FDE) in multi-path fading channels is considered. It is shown that uncoded SC-FDE is resistant to fading even though the multi-path diversity cannot be harnessed. We propose simple schemes based on concatenations of trellis coded modulation (TCM) and interleaving for single and multiple transmit antennas to improve the coding gain, which also exploit spatial diversity in the multi antenna case.     

具有低复杂度的 LDPC 已编码非相干酉空时调制系统设计简

提出一种克服无线信道瑞利衰落和高斯白噪声干扰的非相干编码调制MIMO系统方案。纠错码采用IEEE 802.16e中的非规则QC-LDPC码,非相干调制采用基于三角函数的酉空时调制(SC-USTM)。在接收端,推导出SC-USTM的最大后验概率（MAP）解调算法;为了降低复杂度,构造了SC-USTM的双解调器方案;为了改善双解调的性能,在置信传播（BP）迭代解码器和MAP解调器之间引入了迭代反馈机制。仿真实验表明LDPC已编码SC-USTM的MIMO系统比未编码USTM的MIMO系统在 误码率时,性能改善15~17 dB,并且整个系统具有较低的计算复杂度。     

An efficient space-frequency coded OFDM system for broadband wireless communications

We propose an efficient space-frequency coded orthogonal frequency-division multiplexing (OFDM) system for high-speed transmission over wireless links. The analytical expression for the pairwise probability of the proposed space-frequency coded OFDM system is derived in slow, space- and frequency-selective fading channels. The design criteria of trellis codes used in the proposed system are then developed and discussed. It is shown that the proposed space-frequency coded OFDM can efficiently achieve the full diversity provided by the fading channel with low trellis complexity, while for traditional space-frequency coded OFDM systems, we need to design space-time trellis codes with high trellis complexity to exploit the maximum achievable diversity order. The capacity properties of space-frequency coded OFDM over multipath fading channels are also studied. Numerical results are provided to demonstrate the significant performance improvement obtained by the proposed space-frequency coded OFDM scheme, as well as the excellent outage capacity properties.     

Diagonal block space-time code design for diversity and coding advantage over flat fading channels

The potential promised by multiple transmit antennas has raised considerable interest in space-time coding for wireless communications. In this paper, we propose a systematic approach for designing space-time trellis codes over flat fading channels with full antenna diversity and good coding advantage. It is suitable for an arbitrary number of transmit antennas with arbitrary signal constellations. The key to this approach is to separate the traditional space-time trellis code design into two parts. It first encodes the information symbols using a one-dimensional (M,1) nonbinary block code, with M being the number of transmit antennas, and then transmits the coded symbols diagonally across the space-time grid. We show that regardless of channel time-selectivity, this new class of space-time codes always achieves a transmit diversity of order M with a minimum number of trellis states and a coding advantage equal to the minimum product distance of the employed block code. Traditional delay diversity codes can be viewed as a special case of this coding scheme in which the repetition block code is employed. To maximize the coding advantage, we introduce an optimal construction of the nonbinary block code for a given modulation scheme. In particular, an efficient suboptimal solution for multilevel phase-shift-keying (PSK) modulation is proposed. Some code examples with 2-6 bits/s/Hz and two to six transmit antennas are provided, and they demonstrate excellent performance via computer simulations. Although it is proposed for flat fading channels, this coding scheme can be easily extended to frequency-selective fading channels.     

Coded Phase/Frequency Modulation

Channel coding combined with expanded signal sets has been shown [1] to improve error performance over uncoded modulation without expanding the bandwidth of the transmitted signals. In this paper, new coded modulation formats defined over an expanded set of signals varying both in phase and frequency are presented. The new schemes combine FSK and PSK modulation and make use of trellis coding and Viterbi decoding to improve error performance over uncoded modulation. The free Euclidean distance is calculated for several classes of codes, and upper bounds and simulation results are also presented for some simple codes. The spectral characteristics of the proposed coded modulation formats are evaluated and compared to conventional two-dimensional modulation formats. Differential encoding and various extensions of the basic scheme are also discussed.     

Space-time code design for CPFSK modulation over frequency-nonselective fading channels

We derive a novel space-time code (STC) design criterion for continuous-phase frequency-shift keying (CPFSK) over frequency-nonselective fading channels. Our derivation is based on a specific matrix that is related to the input symbols of the CPFSK modulators. With this code-design criterion, we propose a simple interleaved space-time encoding scheme for CPFSK modulation over frequency-nonselective correlated fading channels to exploit potential temporal and spatial diversity advantages. Such an encoding scheme consists of a ring convolutional encoder and a spatial encoder, between which a convolutional interleaver is placed. A decoding algorithm that generates symbol metrics for the Viterbi decoder of convolutional codes from the spatial modulation trellis is examined. Simulation results confirm that the advantages of the combination of the interleaved convolutional encoding (for temporal diversity) and the spatial encoding (for spatial diversity) are promising for various system parameters.     

A simple and general parameterization quantifying performance in fading channels

We quantify the performance of wireless transmissions over random fading channels at high signal-to-noise ratio (SNR). The performance criteria we consider are average probability of:error and outage probability. We show that as functions of the average SNR, they can both be characterized by two parameters: the diversity and coding gains. They both exhibit identical diversity orders, but their coding gains in decibels differ by a constant. The diversity and coding gains are found to depend on the behavior of-the random SNR's probability density function only at the origin, or equivalently, on the decaying order of the corresponding moment generating function (i.e., how fast the moment generating function goes to zero as its argument goes to infinity). Diversity and coding gains for diversity combining systems are expressed in terms of the diversity branches' individual diversity and coding gains, where the branches can come from any diversity technique such as space, time, frequency, or, multipath. The proposed analysis offers a simple and unifying approach to evaluating the performance of uncoded and (possibly space-time) coded transmissions over fading channels, and the method applies to almost all digital modulation schemes, including M-ary phaseshift keying, quadrature amplitude modulation, and frequency-shift keying with coherent or noncoherent detection.     

Multiple trellis coded modulation (MTCM)

The authors demonstrate a trellis coded modulation technique referred to as multiple trellis coded modulation (MTCM) wherein more than one channel symbol per trellis branch is transmitted. They have found simple two-state trellis codes for symmetric MPSK multiple phase-shift keying and AM modulations that can achieve 3-dB gain over uncoded modulation at very high signal-to-noise ratios without bandwidth expansion or reduction in information bit rate. The gain of these codes with respect to previously reported two-state trellis codes is between 1 and 2 dB at very high signal-to-noise ratios, depending on the number of bits per Hertz transmitted. These gains are achieved for those of the equivalent conventional trellis codes with the same number of states in the trellis diagram. The authors note that additional computations per branch are needed for the multiple trellis coding scheme. The concept can be extended to a higher number of states and other types of modulations     

Concatenated space-time block coding with trellis coded modulation in fading channels

Trellis coded modulation (TCM) is a bandwidth efficient transmission scheme that can achieve high coding gain by integrating coding and modulation. This paper presents an analytical expression for the error event probability of concatenated space-time block coding with TCM which reveals some dominant factors affecting the system performance over slow fading channels when perfect interleavers are used. This leads to establishing the design criteria for constructing the optimal trellis codes of such a concatenated system over slow flat fading channels. Through simulation, significant performance improvement is shown to be obtained by concatenating the interleaved streams of these codes with space-time block codes over fading channels. Simulation results also demonstrate that these trellis codes have better error performance than traditional codes designed for single-antenna Gaussian or fading channels. Performance results over quasi-static fading channels without interleaving are also compared in this paper. Furthermore, it is shown that concatenated space-time block coding with TCM (with/without interleaving) outperforms space-time trellis codes under the same spectral efficiency, trellis complexity, and signal constellation.     

Golden Space–Time Trellis Coded Modulation

In this paper, we present a multidimensional trellis coded modulation scheme for a high rate 2times2 multiple-input multiple-output (MIMO) system over slow fading channels. Set partitioning of the Golden code is designed specifically to increase the minimum determinant. The branches of the outer trellis code are labeled with these partitions and Viterbi algorithm is applied for trellis decoding. In order to compute the branch metrics, a sphere decoder is used. The general framework for code design and optimization is given. Performance of the proposed scheme is evaluated by simulation and it is shown that it achieves significant performance gains over the uncoded Golden code     

交织的空时分组码级联不对称网格编码调制方法

根据交织的空时分组码级联TCM编码设计标准,提出了一种空时分组码级联不对称网格编码调制(A-TCM)的优化设计方案,并得到了在空时分组码级联不对称8PSK调制的TCM情况下最优的星座图旋转角度.仿真和分析结果表明,在相同的频谱效益和译码复杂度的情况下,相比传统空时分组码级联TCM的方法,新方法可进一步提高系统性能.     

On the Performance of Golden Space-Time Trellis Coded Modulation over MIMO Block Fading Channels

The Golden space-time trellis coded modulation (GST-TCM) scheme was proposed in [1] for a high rate 2 × 2 multiple-input multiple-output (MIMO) system over slow fading channels. In this letter, we present the performance analysis of GST-TCM over block fading channels, where the channel matrix is constant over a fraction of the codeword length and varies from one fraction to another, independently. In practice, it is not useful to design such codes for specific block fading channel parameters and a robust solution is preferable. We then show both analytically and by simulation that the GST-TCM designed for slow fading channels are indeed robust to all block fading channel conditions.     

Multiple-symbol trellis-coded modulation applied to noncoherentcontinuous-phase frequency shift keying

This paper considers a maximum-likelihood (ML) noncoherent detection scheme for multiple full response continuous-phase frequency shift keying (CPFSK) waveforms and introduces a trellis-coded modulation (TCM) scheme for this noncoherent modulation. By utilizing a Gaussian approximation for Rician random variables, we express the pairwise error probability as a function of the equivalent normalized squared distance (ENSD). ENSD plays the same role as normalized squared Euclidean distance when evaluating error probability performance for coherent detection. We derive an analytical approximation on the bit-error probability by employing ENSD for both the coded system and the uncoded system. For the uncoded system we show that the bit-error probability of noncoherent detection approaches that of coherent symbol-by-symbol detection in the limit as the multiplicity of the symbol goes to infinity for large signal-to-noise ratio (SNR), We determine specific optimal trellis encoders for binary and 4-ary CPFSK with modulation index 1/2 and 1/4, respectively, by application of Ungerboeck's (1982) set partitioning approach