Capacity Analysis for Transmit Antenna Selection Using Orthogonal Space-Time Block Codes

Antenna selection for multiple-input multiple-output (MIMO) where only a subset of antennas at the transmitter and/or receiver are activated for signal transmission is a practical technique for the realization of full diversity. Despite extensive research, closed-form capacity expressions for MIMO systems employing transmit antenna selection (TAS) and orthogonal space-time block codes (OSTBCs) are not available. We thus derive the exact closed-form capacity expressions when an OSTBC is employed and N transmit antennas out of total L_t antennas are selected for transmission. The expressions are valid for a frequency-flat Rayleigh fading MIMO channel and avoid numerical integration methods     

Limited feedback unitary precoding for spatial multiplexing systems

Multiple-input multiple-output (MIMO) wireless systems use antenna arrays at both the transmitter and receiver to provide communication links with substantial diversity and capacity. Spatial multiplexing is a common space-time modulation technique for MIMO communication systems where independent information streams are sent over different transmit antennas. Unfortunately, spatial multiplexing is sensitive to ill-conditioning of the channel matrix. Precoding can improve the resilience of spatial multiplexing at the expense of full channel knowledge at the transmitter-which is often not realistic. This correspondence proposes a quantized precoding system where the optimal precoder is chosen from a finite codebook known to both receiver and transmitter. The index of the optimal precoder is conveyed from the receiver to the transmitter over a low-delay feedback link. Criteria are presented for selecting the optimal precoding matrix based on the error rate and mutual information for different receiver designs. Codebook design criteria are proposed for each selection criterion by minimizing a bound on the average distortion assuming a Rayleigh-fading matrix channel. The design criteria are shown to be equivalent to packing subspaces in the Grassmann manifold using the projection two-norm and Fubini-Study distances. Simulation results show that the proposed system outperforms antenna subset selection and performs close to optimal unitary precoding with a minimal amount of feedback.     

Diversity performance of precoded orthogonal space-time block codes using limited feedback

Orthogonal space-time block codes (OSTBCs) are simple space-time codes that can be used for open-loop transmit diversity systems. OSTBCs, however, can only be designed for certain numbers of transmit antennas. Channel-dependent linear precoders have been proposed to overcome this deficiency, but it is not clear what conditions the precoder design must satisfy to guarantee full diversity order. In this letter, we show necessary and sufficient conditions for linear precoded OSTBCs to provide full diversity order. We show that limited feedback precoding can achieve full diversity order using fewer bits than limited feedback beamforming. We also present a simplified version of antenna subset selection for OSTBCs that can provide full diversity order with low complexity and only a small amount of feedback.     

Adaptive transmit antenna selection with pragmatic space-time trellis codes

We consider the problem of selecting a subset of transmit antennas in MIMO systems to minimize error probability when only partial channel information is available at the transmitter. An upper bound for error probability of space-time coded transmit antenna selection scheme conditioned on the channel state information is presented. Based on the performance analysis, a criterion of selecting a subset of available transmit antennas to minimize the upper bound on the PEP is proposed. In contrast to other transmit antenna selection schemes for uncoded transmission or with a fixed number of antennas within the selection subset in the literature, the proposed scheme can adaptively select both a variable number of transmit antennas and their corresponding space-time codes for transmission. Furthermore, we present pragmatic space-time trellis coding schemes for slow Rayleigh fading channels. The principal advantage of the schemes is that a single encoder and decoder can be used for systems with a variable number of transmit antennas. The performance of the pragmatic space-time codes with adaptive antenna selection and the effect of the imperfect channel estimation on performance are evaluated by simulations. It is shown that the adaptive selection offers considerable antenna selection gain relative to the antenna selection system with a fixed number of antennas within the selection subset     

On channel orthogonalization using space-time block coding with partial feedback

Orthogonal space-time block codes (OSTBCs) yield full diversity gain even while requiring only a linear receiver. Such full-rate (rate-one) orthogonal designs are available for complex symbol constellations only for N=2 transmit antennas. In this paper, we propose a new family of full-rate space-time block codes (STBCs) using a single parameter feedback for communication over Rayleigh fading channels for N=3,4 transmit antennas and M receive antennas. The proposed rate-one codes achieve full diversity, and the performance is similar to maximum receiver ratio combining. The decoding complexity of these codes are only linear even while performing maximum-likelihood decoding. The partial channel information is a real phase parameter that is a function of all the channel gains, and has a simple closed-form expression for N=3,4. This feedback information enables us to derive (channel) orthogonal designs starting from quasi-orthogonal STBCs. The feedback complexity is significantly lower than conventional closed-loop transmit beamforming. We compare the proposed codes with the open-loop OSTBCs and also with the closed-loop equal gain transmission (EGT) scheme which uses equal power loading on all antennas. Simulated error-rate performances indicate that the proposed channel orthogonalized STBCs significantly outperform the open-loop orthogonal designs, for the same spectral efficiency. Moreover, even with significantly lower feedback and computational complexity, the proposed scheme outperforms the EGT technique for M>N.     

On the probability of error of antenna-subset selection with space-time block codes

Orthogonal space-time block codes (OSTBCs) can obtain full diversity advantage with a simple, but optimal, receiver. Unfortunately, OSTBCs lack in array gain compared with beamforming techniques and suffer a rate loss for more than two transmit antennas. One simple method for improving the array gain and adapting OSTBCs to any number of transmit antennas is antenna-subset selection, where the OSTBC is transmitted on a subset of the transmit antennas. In this letter, we analyze the symbol-error rate performance of antenna-subset selection combined with OSTBCs.     

Antenna selection for multiple-antenna transmission systems: performance analysis and code construction

This correspondence studies antenna selection for wireless communications systems that employ multiple transmit and receive antennas. We assume that (1) the channel is characterized by quasi-static Rayleigh flat fading, and the subchannels fade independently, (2) the channel state information (CSI) is exactly known at the receiver, (3) the selection is available only at the receiver, and it is based on the instantaneous signal-to-noise ratio (SNR) at each receive antenna, and (4) space-time codes are used at the transmitter. We analyze the performance of such systems by deriving explicit upper bounds on the pairwise error probability (PEP). This performance analysis shows that (1) by selecting the set of antennas that observe the largest instantaneous SNR, one can achieve the same diversity gain as the one obtained by using all the receive antennas, provided that the underlying space-time code has full spatial diversity, and (2) in the case of rank-deficient space-time codes, the diversity gain may be dramatically reduced when antenna selection is used. However, we emphasize that in both cases the coding gain is reduced with antenna selection compared to the full complexity system. Based on the upper bounds derived, we describe code design principles suitable for antenna selection. Specifically, for systems with two transmit antennas, we design space-time codes that perform better than the known ones when antenna selection is employed. Finally, we present numerical examples and simulation results that validate our analysis and code design principles.     

Efficient signal processing techniques for exploiting transmitantenna diversity on fading channels

A class of powerful and computationally efficient strategies for exploiting transmit antenna diversity on fading channels is developed. These strategies, which require simple linear processing at the transmitter and receiver, have attractive asymptotic characteristics. In particular, given a sufficient number of transmit antennas, these techniques effectively transform a nonselective Rayleigh fading channel into a nonfading, simple white marginally Gaussian noise channel with no intersymbol interference. These strategies, which we refer to as linear antenna precoding, can be efficiently combined with trellis coding and other popular error-correcting codes for bandwidth-constrained Gaussian channels. Linear antenna precoding requires no additional power or bandwidth and is attractive in terms of robustness and delay considerations. The resulting schemes have powerful and convenient interpretations in terms of transforming nonselective fading channels into frequency- and time-selective ones     

Performance analysis of space-time transmitter diversity techniques for WCDMA using long range prediction

Transmitter diversity in the downlink of code-division multiple-access (CDMA) systems achieves similar performance gains to the mobile-station receiver diversity without the complexity of a mobile-station receiver antenna array. Pre-RAKE precoding at the transmitter can be employed to achieve the multipath diversity without the need of the RAKE receiver at the mobile station. We examine feasibility of several transmitter diversity techniques and precoding for the third-generation wideband CDMA (WCDMA) systems. In particular, selective transmit diversity, transmit adaptive array and space-time pre-RAKE (STPR) techniques are compared. It is demonstrated that the STPR method is the optimal method to combine antenna diversity and temporal precoding. This method achieves the gain of maximum ratio combining of all space and frequency diversity branches when perfect channel state information is available at the transmitter. We employ the long range fading prediction algorithm to enable transmitter diversity techniques for rapidly time varying multipath fading channels.     

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.     

Performance Analysis of OSTBC Transmission in Amplify-and-Forward Cooperative Relay Networks

A performance analysis is presented for amplify-and-forward (AF) cooperative relay networks employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where multiple antennas are equipped at the transmitter. We develop a symbol-error-rate (SER) and outage performance analysis for OSTBC transmissions with and without cooperative diversity over flat Rayleigh fading channels. We first derive exact probability density functions (pdf's) and cumulative distribution functions (cdf's) for the system SNR without direct transmission with an arbitrary number of transmit antennas and then present the exact closed-form SER and outage probability expressions. Next, we derive the moment-generating function (MGF) for the overall system SNR with direct transmission and present the exact SER and outage probability with joint transmit antenna diversity and cooperative diversity. The theoretical analysis is validated by simulations, which indicate an exact match between them. The results also show how the transmit antenna diversity and the cooperative diversity affect the overall system performance.      

Transmit antennae space-time block coding for generalized OFDM inthe presence of unknown multipath

Transmit antenna diversity has been exploited to develop high-performance space-time coders and simple maximum-likelihood decoders for transmissions over flat fading channels. Relying on block precoding, this paper develops generalized space-time coded multicarrier transceivers appropriate for wireless propagation over frequency-selective multipath channels. Multicarrier precoding maps the frequency-selective channel into a set of flat fading subchannels, whereas space-time encoding/decoding facilitates equalization and achieves performance gains by exploiting the diversity available with multiple transmit antennas. When channel state information is unknown at the receiver, it is acquired blindly based on a deterministic variant of the constant-modulus algorithm that exploits the structure of space-time block codes. To benchmark performance, the Cramer-Rao bound of the channel estimates is also derived. System performance is evaluated both analytically and with simulations     

Antenna selection for spatial multiplexing systems with linearreceivers

Future cellular systems will employ spatial multiplexing with multiple antennas at both the transmitter and receiver to take advantage of large capacity gains. In such systems it will be desirable to select a subset of available transmit antennas for link initialization, maintenance or handoff. We present a criterion for selecting the optimal antenna subset when linear, coherent receivers are used over a slowly varying channel. We propose use of the post-processing SNRs (signal to noise ratios) of the multiplexed streams whereby the antenna subset that induces the largest minimum SNR is chosen. Simulations demonstrate that our selection algorithm also provides diversity advantage thus making linear receivers useful over fading channels     

Analysis of Differential Orthogonal Space–Time Block Codes Over Semi-Identical MIMO Fading Channels

We study the performance of differential orthogonal space-time block codes (OSTBC) over independent and semi-identically distributed block Rayleigh fading channels. In this semiidentical fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are nonidentically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another are considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit-error probabilities (BEPs) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas, and any number of transmit antennas for which OSTBCs exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. For an arbitrary number of transmit antennas, a Chernoff bound on the BEP for the optimal detector is also derived. Our results show that the semi-identical channel statistics degrade the error performance of differential OSTBC, compared with the identical case. Also, the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly. But in near-static fading channels, the two detectors have similar performances     

Double differential space-time block coding for time-selectivefading channels

Most existing space-time coding schemes assume time-invariant fading channels and offer antenna diversity gains relying on accurate channel estimates at the receiver. Other single differential space-time block coding schemes forego channel estimation but are less effective in rapidly fading environments. Based on a diagonal unitary matrix group, a novel double differential space-time block coding approach is derived in this paper for time-selective fading channels. Without estimating the channels at the receiver, information symbols are recovered with antenna diversity gains regardless of frequency offsets. The resulting transceiver has very low complexity and is applicable to an arbitrary number of transmit and receive antennas. Approximately optimal space-time codes are also designed to minimize bit error rate. System performance is evaluated both analytically and with simulations     

Peroformance analysis of decode-and-forward MIMO relay channels with OSTBCs

Performance analysis is presented for multiple-input multiple-output(MIMO) relay channels employing transmit antenna diversity with orthogonal space-time block codes(OSTBCs),where the source and the destination are equipped with Ns and Nd antennas,and communicate with each other with the help of a multiple-antenna relay operating in decode-and-forward(DF) mode.Over independent,not necessarily identical Rayleigh fading channels,exact closed-form symbol error rate(SER) expressions are derived for various digi...     

Adaptively Grouped Multilevel Space-Time Trellis Codes

Grouped multilevel space-time trellis codes (GMLSTTCs) utilize multilevel coding (MLC), antenna grouping and space time trellis codes (STTCs) for simultaneously providing coding gain, diversity improvement and increased spectral efficiency. The performance of GMLSTTCs is limited due to predefining of the antenna groups. It has been shown that when perfect or partial channel state information is available at the transmitter, the performance and capacity of space-time coded system can be further improved. In this paper, we present a new code designed by combining MLC, STTCs, antenna grouping and channel state information at transmitter, henceforth referred to as adaptively grouped multilevel space time trellis codes (AGMLSTTCs). AGMLSTTCs use a single full-diversity STTC at initial some levels and multiple STTCs at some later levels. The single full diversity STTC at each initial level spans all transmit antennas and the STTC at each later level spans a group of transmit antennas. The channel state information at the transmitter is used to adaptively group the transmit antennas for the later levels. Instantaneous channel power gain is calculated between each transmit antenna and all the receive antennas. A subset of transmit antennas having maximum channel power gain is selected to form a group. The simulation results show that AGMLSTTCs enable to transmit more than one data symbol per time slot with improved error performance over GMLSTTCs with predefined transmit antenna grouping.     

Adaptive precoding and power allocation in distributed antenna systems with limited feedback

This paper introduces the limited feedback precoding into the distributed antenna system and proposes to adapt the predetermined orthogonal space time block codes to the available channel state information at the transmitter. The optimal representation of precoding information, namely the precoder, with least bits therefore becomes the key problem. Inspired by the characteristics of the distributed antenna system, we focus our work on the precoder construction, adaptable in response to the large and small scale fading, such that the symbol error probability is significantly reduced over that of a fixed, non‐adaptive, independent and identically distributed precoder codebook design. Furthermore, a suboptimal power‐loading strategy is presented by minimizing the derived tight upper bound on the average pairwise error probability of the precoded orthogonal space time block codes, which approaches the optimal performance asymptotically without additional channel knowledge other than the available feedback information. We prove that the proposed precoded orthogonal space time transmission scheme can achieve full diversity order. In particular, the robustness of our proposed transmission scheme to channel estimation error and feedback delay is respectively investigated in some detail, and numerical results show that it obviously improves the link reliability and obtains substantial gains even with few bits of feedback in comparison with conventional antenna selection scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal space-time constellations from groups

We consider the design of space-time constellations based on group codes for fading channels with multiple transmit and receive antennas. These codes can be viewed as multiantenna extensions of phase-shift keying (PSK), in the sense that all codewords have equal energy, all are rotations of a fixed codeword, and there is a simple differential transmission rule that allows data to be sent without channel estimates at the transmitter or receiver. For coherent detection, we show that all optimal full-rank space-time group codes are unitary (each code matrix has equal-energy, orthogonal rows). This leads to a simpler code design criterion and suggests that unitary codes may play an important role in coherent as well as noncoherent communication. For any number of transmit antennas t, we then use the design criterion to characterize all full-rank unitary space-time group codes of minimum block length (also t) which have 2/sup p/ codewords. These results allow us to characterize all optimal 2/sup p/-ary unitary group codes with square code matrices. This restricted class of block codes matches the class proposed for differential modulation by Hughes (see IEEE Trans. Inform. Theory, vol.46, p.2567-78, Nov. 2000), and by Hochwald and Sweldens (see IEEE Trans. Commun., vol.48, p.2041-2052, Dec. 2000).     

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.