Trellis-coded differential unitary space-time modulation over flat fading channels

Coding and modulation for multiple-antenna systems have gained much attention in wireless communications. This paper investigates a noncoherent trellis-coded scheme based on differential unitary space-time modulation when neither the transmitter nor the receiver know the channel. In a time-varying flat Rayleigh fading environment, we derive differentially noncoherent decision metrics and obtain performance measures for systems with either an ideal interleaver or no interleaver. We demonstrate that with an ideal interleaver, the system performance is dominated by the minimum Hamming distance of the trellis code, while without an interleaver, the performance is dominated by the minimum free squared determinant distance (a novel generalization of the Euclidean distance) of the code. For both cases, code construction is described for Ungerboeck-type codes. Several examples that are based on diagonal cyclic group constellations and offer a good tradeoff between the coding advantage and trellis complexity are provided. Simulation results show that, by applying the soft-decision Viterbi decoder, the proposed scheme can achieve very good performance even with few receive antennas. Extensions to trellis-coded differential space-time block codes are also discussed.     

Antenna selection for unitary space-time modulation

This correspondence studies receive antenna selection (AS) for multiple-antenna systems that employ unitary space-time (ST) signals, where the channel state information (CSI) is known neither at the transmitter nor at the receiver. Without CSI at the receiver, we perform AS only at the receiver and the selection is based on a maximum-norm criterion, i.e., a subset of receive antennas that have the largest received signal power is chosen. Using a Chernoff bound approach, we present theoretical performance analysis based on the pairwise error probability (PEP) and quantify the asymptotic performance at high signal-to-noise ratio (SNR) by giving the diversity and coding gain expressions. We prove that with no CSI at the receiver, the diversity gain with AS is preserved for unitary ST codes with full spatial diversity, the same as the case with known CSI. As a concrete example, for differential unitary ST modulation with M=2 transmit antennas and N=2 receive antennas, we have devised new excellent-performing parametric codes based on the derived PEP bound. The new codes, which are specifically designed for differential AS systems, outperform known differential codes when AS is employed. Corroborating simulations validate our analysis and code design.     

Receive antenna selection for MIMO systems over correlated fading channels

In this letter, we propose a novel receive antenna selection algorithm based on cross entropy optimization to maximize the capacity over spatially correlated channels in multiple-input multiple-output (MIMO) wireless systems. The performance of the proposed algorithm is investigated and compared with the existing schemes. Simulation results show that our low complexity algorithm can achieve near-optimal results that converge to within 99% of the optimal results obtained by exhaustive search. In addition, the proposed algorithm achieves near-optimal results irrespective of the mutual relationship between the number of transmit and receive antennas, the statistical properties of the channel and the operating signal-to-noise ratio.     

Differential space-time modulation over frequency-selective channels

We present herein a new differential space-time-frequency (DSTF) modulation scheme for systems that are equipped with an arbitrary number of transmit antennas and operate in frequency-selective channels. The proposed DSTF modulator consists of a concatenating spectral encoder and differential encoder that offer full spatio-spectral diversity and significant coding gain. A unitary structure is imposed on the differential encoder to admit linear, decoupled maximum likelihood (ML) detection in space and time. Optimum criteria based on pairwise error probability analysis are developed for spectral encoder design. We introduce a class of spectral codes, namely, linear constellation decimation (LCD) codes, which are nonbinary block codes obtained by decimating a phase-shift-keying (PSK) constellation with a group of decimation factors that are co-prime with the constellation size. Since LCD codes encode across a minimally necessary set of subchannels for full diversity, they incur modest decoding complexity among all full-diversity codes. Numerical results are presented to illustrate the performance of the proposed DSTF modulation and coding scheme, which compares favorably with several existing differential space-time schemes in frequency-selective channels.     

Differential unitary space-time modulation

We present a framework for differential modulation with multiple antennas across a continuously fading channel, where neither the transmitter nor the receiver knows the fading coefficients. The framework can be seen as a natural extension of standard differential phase-shift keying commonly used in single-antenna unknown-channel systems. We show how our differential framework links the unknown-channel system with a known-channel system, and we develop performance design criteria. As a special ease, we introduce a class of diagonal signals where only one antenna is active at any time, and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error     

Blind equalization for an application of unitary space-time modulation in ISI channels

Transmit diversity schemes have gained attention due to the promise of increased capacity and improved performance. Among these schemes, unitary space-time modulation and differentially encoded unitary space-time modulation allow for simple noncoherent decoding for flat-fading channels. In this paper, a new blind equalization algorithm for these transmission schemes in intersymbol interference (ISI) channels is proposed. A matrix-type constant modulus algorithm that exploits the unitary structure of the space-time codes is developed. The equalizer is paired with a noncoherent decoder, resulting in a completely blind, low-complexity method for decoding in the presence of ISI. A noiseless convergence analysis is conducted and verified via simulation in both noiseless and noisy cases. The performance of the overall system is evaluated via simulation and semi-analytically, and the achieved performance is between that of the ideal zero-forcing and the minimum-mean squared-error equalizers.     

Receive antenna selection for MIMO flat-fading channels: theory and algorithms

This correspondence discusses the problem of the receive antenna subset selection in multiple-element antenna (MEA) transmission systems. The antennas are selected so as to maximize the channel capacity. A set of near-optimal selection algorithms is presented. The first algorithm in particular allows statistical analysis of selection gains. We present tight analytic lower bounds on the outage capacity achievable through antenna selection. Extensive simulations validating analysis and illustrating performance of the selection algorithms are also presented.     

Cross-layer based transmit antenna selection for decision-feedback detection in correlated Ricean MIMO channels

In this paper, we investigate a cross-layer transmit antenna selection (AS) approach for the decision-feedback detector (DFD) over spatially correlated flat Ricean fading multiple-input multiple-output (MIMO) channels. Closed-form expressions for the system throughput with both perfect and imperfect channel estimation are derived. Considering a training-based channel estimation technique, we show that the capacity-based AS is more robust to imperfect channel estimation. However, in all cases, the cross-layer AS delivers higher throughput gains than the capacity-based AS.     

Rotation constellation for differential unitary space-time modulation

I. Introduction Recently, Unitary Space-Time Modulation (USTM)[1] has attracted the significant attentions for its potentiality in realizing high data rate transmis- sion over the Rayleigh fading channels where the Channel State Information(CSI) is unknown both at the transmitter and the receiver. And the CSI is no longer necessary in USTM scheme if it is constant for consecutive T symbol periods[1]. For continu- ously changing slow fading channels, Differential USTM (DUSTM) was …     

Structures and performance of noncoherent receivers for unitary space-time modulation on correlated fast-fading channels

Fast fading used in this paper refers to multiple-input-multiple-output (MIMO) channels with channel gains changing from sample to sample, even within a block symbol. The impact of spatially correlated and sample-to-sample variant (SCSSV) fading channels on the design and error performance of noncoherent receivers is not yet clear in the literature. In this paper, we derive optimal and suboptimal noncoherent receivers for operating on SCSSV MIMO fading channels. The joint effect of spatial correlation and sample-to-sample variation of channel gains on various receivers in Rayleigh and Rician fading is investigated by the derivation of their pairwise error performance. Numerical and simulation results are also presented to illustrate the theory and to compare the performance of the optimal and suboptimal receivers.     

Layered space-time codes over Ricean fading channels by reducing the correlation of spatial shaping pulses

In this paper, an asynchronous layered space-time architecture is proposed to realize the spatial multiplexing over the Ricean multiple-input multiple-output (MIMO) channels. Based on reducing the correlation of spatial shaping pulses between the multiplexed streams, this approach can be used to solve the problem of detection in the ill-conditioned channel matrix. It is shown that at the receiver, the reduction of the correlation enables the requirement on the number of the receive antennas to be removed by the zero forcing (ZF) detector compared with the conventional synchronous layered space-time architecture. First, this paper presents how to exploit the correlation of spatial shaping pulses between the multiplexed streams. Then deriving the exact closed-form expression of error rate for the proposed scheme, this paper finds that the maximum possible diversity gain can be achieved based on the independent layered architecture by the ZF detector at the cost of limited multiplexing gain.     

Bound-intersection detection for multiple-symbol differential unitary space-time modulation

This paper considers multiple-symbol differential detection (MSD) of differential unitary space-time modulation (DUSTM) over multiple-antenna systems. We derive a novel exact maximum-likelihood (ML) detector, called the bound-intersection detector (BID), using the extended Euclidean algorithm for single-symbol detection of diagonal constellations. While the ML search complexity is exponential in the number of transmit antennas and the data rate, our algorithm, particularly in high signal-to-noise ratio, achieves significant computational savings over the naive ML algorithm and the previous detector based on lattice reduction. We also develop four BID variants for MSD. The first two are ML and use branch-and-bound, the third one is suboptimal, which first uses BID to generate a candidate subset and then exhaustively searches over the reduced space, and the last one generalizes decision-feedback differential detection. Simulation results show that the BID and its MSD variants perform nearly ML, but do so with significantly reduced complexity.     

Signal constellations design for differential unitary space-time in MIMO-OFDM system over frequency-selective fading channels

In this paper, the design of signal constellations parameters is studied for Differential Unitary Space-Time Modulation （DUSTM） based on the design criterion of maximizing the diversity product. Further, noninteger searching method for the signal constellation parameters design is proposed in order to get better codes. Experimental results show that under the different Doppler spread and data transmission rate, the proposed design performs better than the previous design using integer parameters in Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing （MIMO-OFDM） system over frequency-selective fading channels.     

On the diversity order of space-time trellis codes with receive antenna selection over fast fading channels

In this paper, we study the performance of space-time trellis codes (STTCs) with receive antenna selection over fast fading channels. Specifically, we derive upper bounds on the pairwise-error probability (PEP) with antenna selection. In performing the selection, we adopt a criterion that is based on using L out of the available M receive antennas that result in maximizing the instantaneous signal-to-noise ratio (SNR) at the receiver, where L les M. We show that the diversity order resulting from antenna selection deteriorates significantly and is actually dictated by the number of selected antennas. The implication of this result is that adding more receive antennas, while maintaining the same number of selected ones, will have no impact on the diversity order, but it does, however, provide some additional coding gain. This is unlike the case for quasi-static fading channels in which the diversity order is always preserved with antenna selection when the underlying STTC is full-rank. We present numerical examples that support our analysis     

Combined turbo coding and unitary space-time modulation

Space-time coding is well understood for high data rate communications over wireless channels with perfect channel state information. On the other hand, channel coding for multiple transmit antennas when channel state information is unknown has only received limited attention. A new signaling scheme, named unitary space-time modulation, has been proposed for the latter case. In this paper, we consider the use of turbo coding together with unitary space-time modulation. We demonstrate that turbo coded space-time modulation systems are well suited to wireless communication systems when there is no channel state information, in the sense that the turbo coding improves the bit error rate (BER) performance of the system considerably. In particular, we observe that the turbo-coded system provides 10-15 dB coding gain at a BER of 10/sup -5/ compared to the unitary space-time modulation for various transmit and receive antenna diversity cases.     

Multisampling decision-feedback linear prediction receivers for differential space-time modulation over Rayleigh fast-fading channels

Novel decision-feedback (DF) linear prediction (LP) receivers, which process multiple samples per symbol interval in conjunction with optimal sample combining, are proposed for differential space-time modulation (DSTM) over Rayleigh fast-fading channels. Performance analysis demonstrates that multisampling DF-LP receivers outperform their symbol-rate sampling counterpart in fast fading substantially. In addition, an asymptotically tight upper bound on the pairwise error probability is derived. In view of this bound, the design criterion of DSTM for fast fading is the same as that for block-wise static fading. To avoid the estimation of the second-order statistics of the channel, a polynomial-model-based DF-LP receiver is proposed. It can approach the performance of the optimum DF-LP receiver at high signal-to noise ratios, provided fading is moderate.     

Space-time coding over correlated fading channels with antenna selection

In a previous paper by Bahceci et al., antenna selection ' for multiple-antenna transmission systems under the assumption that the subchannels between antenna pairs fade independently was studied. In this paper, the performance of such systems when the subchannels experience correlated fading is considered. It is assumed that the channel-state information (CSI) is available only at the receiver, the antenna selection is performed only at the receiver, and the selection is based on the instantaneous received signal power. The effects of channel correlations on the diversity and coding gain when the receiver system is a subset of the antennas are quantified. Theoretical results indicate that the correlations in the channel do not degrade the diversity order, provided that the channel is full rank. However, it does result in some performance loss in the coding gain.     

Receive antenna selection for closely-spaced antennas with mutual coupling

We investigate the achievable rate of receive antenna selection MIMO systems in the presence of mutual coupling and spatial correlation. For that, we assume the antenna array to consist of dipole antennas placed side-by-side in a linear pattern and in a very limited physical space. In a first step, we will assume perfect channel state information at the receiver side only and a negligible training overhead compared with the payload. We will demonstrate that in contrast to what might be expected based on results for cases without mutual coupling, MIMO receive antenna selection can achieve higher data rates than the system using all antennas provided that the total number of receive antennas is larger than a critical value that we will further discuss. We then propose an optimal antenna selection processing that ensures rate maximization regardless of the number of antennas used. In a later step, we will address the impact of training overhead on the system achievable rate when the training overhead is considerable. We will show that such a rate is reduced dramatically due to the large amount of training overhead arising from the presence of mutual coupling. To overcome this problem, we will thus propose a novel channel estimation method, which reduces the training overhead greatly and improves the system achievable rate performance.     

Iterative decoding of space-time differentially coded unitary matrix modulation

Noncoherent communication over the Rayleigh flat fading channel with multiple transmit and receive antennas is investigated. Codes achieving bit error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 0.8 to 2.8 dB from the capacity limit were found with coding rates of 0.5 to 2.25 bits per channel use. The codes are serial concatenation of a turbo code and a unitary matrix differential modulation code. The receiver is based on a high-performance joint iterative decoding of the turbo code and the modulation code. Information-theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.     

On the robustness of decision-feedback detection of DPSK and differential unitary space-time modulation in Rayleigh-fading channels

Decision-feedback differential detection (DFDD) of differential phase-shift keying (DPSK) and differential unitary space-time modulation (DUST) in Rayleigh-fading channels exhibits significant performance improvement over standard single-symbol maximum-likelihood detection. However, knowledge of channel fading correlation and signal-to-noise ratio (SNR) is required at the receiver to compute the feedback coefficients used in DFDD. In this letter, we investigate the robustness of the DFDD to imperfect knowledge of the feedback coefficients by modeling the mismatch between estimated feedback coefficients and ideal coefficients in terms of mismatch between the estimated values of fading correlation and SNR and the true values. Under the assumption of a block-fading channel when nondiagonal DUST constellations are used and a continuous fading channel otherwise, we derive exact and Chernoff bound expressions for pair-wise word-error probability and then use them to approximate the bit-error rate (BER), finding close agreement with simulation results. The relationships between BER performance and various system parameters, e.g., DFDD length and Doppler mismatch, are also explored. Furthermore, the existence of an error floor in the BER-vs-SNR curve is investigated for the infinite-length DFDD. For the special case of Jakes' fading model, it is shown that the error floor can be removed completely even when the Doppler spread is over-estimated.