Space-time block code designs based on algebraic field extension for full rate, large diversity product, and nonvanishing minimum determinant of codewords have received great attention. There are many different types of codes available for two-transmitter antennas, such as cyclotomic space-time block codes, the golden space-time block code, and rotation-based space-time block codes. In this paper, a more general space-time block code design scheme, which is called quadratic space-time block coding, is proposed for the two-transmitter antennas using quadratic field extension. The optimal design of the quadratic space-time block codes in terms of a diversity product criterion is also presented. It is shown that the optimal quadratic space-time block codes designed in this paper do not belong to the existing space-time block code family such as the cyclotomic, golden, and rotation-based space-time block codes. The simulation results demonstrate that the average codeword error rate of the optimal quadratic space-time block code attains about 0.5 dB signal to noise ratio gain over those of the optimal cyclotomic and golden space-time block codes.

The Alamouti orthogonal space-time block code for two transmit antennas was designed primarily for QAM and PSK modulations, and we have previously generalized it for the continuous phase modulation (CPM), denoted as OST-CPM, by maintaining the orthogonality (for the fast ML decoding/demodulation) and the phase continuity of two signals from two transmit antennas. In this paper, we design orthogonal-like space-time coded CPM systems for three and four transmit antennas based on orthogonal and quasi-orthogonal space-time codes. Although the signals from transmit antennas in the proposed orthogonal-like space-time coded CPM systems are not orthogonal, the fast decoding/demodulation is maintained like the two transmit antenna case. Simulation results show that the performance of the proposed orthogonal-like space-time coded CPM systems for four transmit antennas is much better than that of the OST-CPM systems for two transmit antennas.

For rapidly spinning targets, such as the rotating ground radar antenna, helicopter blades, spinning space debris, etc., the scatterers on the target may rotate for several periods in the observation time. Since the range and Doppler information of these scatterers are no longer constant, the conventional range-Doppler-based imaging algorithms are invalid. Meanwhile, 3-D imaging is necessary to obtain additional information for the spinning target. However, the available interferometric inverse synthetic radar (ISAR) and snapshot 3-D imaging algorithms do not work well since they require low target spinning speed. In this paper, a matched-filter-bank-based 3-D imaging algorithm for rapidly spinning targets is proposed, based on target motion features. This algorithm utilizes the rapidly rotating turntable model of the ISAR target instead of the slow rotating one. First, 2-D image slices of the target are obtained from the output of the matched filter bank by changing matching parameters. Then, a series of 2-D image slices are combined to form the 3-D target image. Since this algorithm applies to the monostatic radar system, it is easy to implement in practical applications. Both the theoretical derivation and the simulation results have proved the validity of the proposed algorithm.

Recently, distributed space-time code designs with high cooperative diversity for wireless communication networks, such as ad hoc and sensor networks, have received much attention. Amplify forward and decoding forward are widely used protocols for the cooperative diversity in the wireless communication networks. In both protocols, the information received by relay terminals are "forwarded" to destination or next relay terminals. Since the signals transmitted by relay terminals and those transmitted from the source terminal are correlated, there is information redundancy. To improve the energy efficiency of cooperative networks, we propose an encoding protocol, which is referred to as a nested cooperative encoding protocol. In our proposed protocol, the received signal at each relay terminal is divided into several sub-signals with the nest lattice structure of source information. Each of the sub-signals contains only a partial information with a smaller size of constellation compared to the original information sent by the source terminal. Do a new encoding or modulation by using these sub-signals before transmitting at relay terminals. It is shown that the proposed new protocols can achieve both high cooperative diversity and high energy efficiency.

In the conventional Chinese remainder theorem (CRT), a small error in a remainder may cause a large error in the solution of an integer, i.e., CRT is not robust. In this letter, we first propose a robust phase unwrapping algorithm with applications in radar signal processing. Motivated from the phase unwrapping algorithm, we then derive a type of robust CRT

It is well known that a multiple-input-multiple-output (MIMO) system can provide spatial diversity gain as well as spatial multiplexing capability. The MIMO concent has been extended to cooperative wireless networks to form distributed MIMO systems using virtual antennas located at cooperating terminals. The primary interest of cooperative MIMO networks, however, has been focused on the cooperative diversity (C-DIV) approaches to achieve spatial diversity gain. Recent work proposed cooperative spatial multiplexing (C-SM) to simplify the transmit and receive processing requirement on the relay nodes while providing significant energy savings. So far C-SM has been only considered for single-hop relaying. In this paper, we propose the use of multi-hop relaying C-SM systems for transmit energy reduction and performance improvement.

The design of a linear space-time code with full rate, large diversity product, and non-vanishing minimum determinant of codewords continues to attract great attention. However, in most available no-vanishing determinant space-time codes for three, four, and six transmitter antennas, the average power at each layer is different, which results in a high peak to average power ratio. In this paper, a new cyclic algebraic space-time design scheme is proposed and the optimal codes in this class are provided by using some specific cyclic field extensions. Our proposed codes not only include the available non-vanishing determinant cyclotomic space-time codes for three, four, and six transmitter antennas, but also have the desirable property that the optimal codes can be achieved with the same average power at each layer.

In this paper, we introduce the definitions of a full diversity integer generating matrix and the corresponding norm form space-time code for MIMO systems. Subject to a power constraint, we characterize all full diversity integer generating matrices with the first three largest gains in the Gaussian integer ring and the Eisenstein integer ring for two transmitter antennas. Using this generating matrix family to separately design space-time codes layer by layer for two transmitter antenna and two receiver antenna MIMO systems, we obtain the optimal norm form integer space-time codes both in the Gaussian integer ring and the Eisenstein integer ring in the sense of maximizing the minimum determinant of codeword matrices. As a consequence, we prove that the golden code constructed by Dayal and Varanasi, Belfiore, Rekaya and Viterbo is optimal in the Gaussian integer ring. Also, we find the optimal code in the Eisentein integer ring, the coding gain of which is greater than that of the golden code.

Signal-space diversity is a power- and bandwidth-efficient diversity technique. To exploit the signal-space diversity, joint maximum-likelihood (ML) detection at the receiver is usually needed, where the complexity grows exponentially with the dimension of the lattice. In this letter, we propose a serial concatenated scheme and two simple iterative methods to exploit the signal-space diversity. The simple iterative methods are based on the idea of soft interference cancellation. The first iterative method is based on a vector Gaussian approximation, while the second one is based on a scalar Gaussian approximation. The complexity of the first iterative method grows cubically with the dimension of the lattice, and the simulations show that its performance approaches that of the optimal maximum a posteriori detection method. The complexity of the second iterative method grows linearly with the dimension of the lattice, and the simulations show that when the dimension of the lattice N=32, at bit-error rate =10/sup -5/, the performance gap between the Rayleigh fading channel and the Gaussian channel is only 0.3 dB.

High rate and large diversity product (or coding advantage, or coding gain, or determinant distance, or minimum product distance) are two of the most important criteria often used for good space-time code designs. In recent (linear) lattice-based space-time code designs, more attention is paid to the high rate criterion but less to the large diversity product criterion. In this paper, we consider these two criteria together for multilayer cyclotomic space-time code designs. In a previous paper, we recently proposed a systematic cyclotomic diagonal space-time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas, where diagonal codes correspond to single-layer codes in this paper. In this paper, we first propose a general multilayer cyclotomic space-time codes. We present a general optimality theorem for these infinitely many cyclotomic diagonal (or single-layer) space-time codes over general cyclotomic number rings for a general number of transmit antennas. We then present optimal multilayer (full-rate) cyclotomic space-time code designs for two and three transmit antennas. We also present an optimal two-layer cyclotomic space-time code design for three and four transmit antennas. The optimality here is in the sense that, for a fixed mean transmission signal power, its diversity product is maximized, or equivalently, for a fixed diversity product, its mean transmission signal power is minimized. It should be emphasized that all the optimal multilayer cyclotomic space-time codes presented in this paper have the nonvanishing determinant property.

In the above titled paper (ibid., vol. 51, no. 3, pp. 1102-1135, Mar 05), corrections were made to several equations.

Super-orthogonal space-time trellis codes recently proposed in the literature are space-time trellis codes of full diversity and high rates systematically constructed by concatenating orthogonal space-time codes and multiple trellis coded modulation (MTCM). However, the existing MTCM only has designs for phase-shift keying (PSK) signals. In this paper, MTCM is extended from PSK signals to non-PSK signals in some special cases. With obtained constellations of MTCM, several super-orthogonal space-time trellis codes for two transmit antennas are presented. The 2- and 4-state codes have a simple mathematical expression for the coding gain distance (CGD), or diversity products. At rates 2.5, 3, 3.5, 4 bits/s/Hz, the newly proposed codes outperform the existing ones.

In this paper, an orthogonal space-time coded partial response continuous phase modulation (OST-PCPM) system with two transmit antennas is proposed. It can achieve full diversity with arbitrary inner memory length and phase smoothing functions of CPM schemes. Based on the orthogonality between signals from two transmit antennas and the proposed differential encoding scheme, a fast decoding algorithm is developed for some special cases. Simulation results show that this scheme can provide much better performance with a reasonable complexity, as compared to one transmit antenna CPM scheme. We also give a suboptimal decoding method that provides a tradeoff between complexity and performance.

An optimization of cyclotomic lattices based diagonal/single-layer space-time block codes is discussed. The concrete full diversity cyclotomic generating matrices are used to generalize the lattices and also studies the optimality in the sense that for a fixed diversity product and thus the transmission signal power is minimized.

In this correspondence, a new and systematic design of cyclotomic lattices with full diversity is proposed by using some algebraic number theory. This design provides infinitely many full diversity cyclotomic lattices for a given lattice size. Based on the packing theory and the concrete form of the design, optimal cyclotomic lattices are presented by minimizing the mean transmission signal power for a given minimum (diversity) product (or equivalently maximizing the minimum product for a given mean transmission signal power). The newly proposed cyclotomic lattices can be applied to both space-time code designs for multi-antenna systems and linear precode design for signal space diversity in single antenna systems over fast Rayleigh fading channels. Although there are some cyclotomic lattices/space-time codes existing in the literature, most of them are not optimal.

In this correspondence, we propose some new designs of 2/spl times/2 unitary space-time codes of sizes 6, 32, 48, 64 with best-known diversity products (or product distances) by partially using sphere packing theory. In particular, we present an optimal 2/spl times/2 unitary space-time code of size 6 in the sense that it reaches the maximal possible diversity product for 2/spl times/2 unitary space-time codes of size 6. The construction and the optimality of the code of size 6 provide the precise value of the maximal diversity product of a 2/spl times/2 unitary space-time code of size 6.

Trellis-coded space-time (TC-ST) coding for continuous-phase modulation (TC-ST-CPM) was recently proposed by Zhang and Fitz. In this paper, we propose an orthogonal space-time coding for CPM (OST-CPM) systems and two transmit antennas. In the proposed OST-CPM, signals from two transmit antennas at any time t are orthogonal while both of them have continuous phases. Similar to Alamouti's OST coding for phase-shift keying (PSK) and quadrature amplitude modulation (QAM) systems, the newly proposed OST-CPM has a fast decoding algorithm.

Unitary space-time codes have been used in differential space-time modulation, when neither the transmitter nor the receiver of a multiple antenna system knows the channel state information in Rayleigh fading channels. Among the codes in literature, unitary orthogonal space-time codes, constructed from Alamouti's scheme, have the advantage of fast maximum likelihood (ML) decoding but they require signal constellations to be phase-shift keying (PSK). In this paper, unitary space-time codes are constructed from Alamouti's scheme with amplitude/phase-shift keying (APSK) constellations. We show that the unitary space-time codes from Alamouti's scheme with APSK signals have larger diversity products than those with PSK signals while the complexity of their ML decoding algorithm is comparable. Our newly proposed 4 b/s/Hz code has about 2 dB gain over the same rate code with PSK signals at bit-error rate (BER) of 10/sup -3/ with one receive antenna. We also propose a noncoherent scheme of rate 5 b/s/Hz, which has the same BER performance as the 4 b/s/Hz unitary orthogonal space-time code in DSTM while having comparable decoding complexity.

A systematic diagonal space-time block code (cyclotomic space-time code) design is proposed by using high dimensional cyclotomic lattices and some algebraic number theory. This design can be applied to any number of transmit antennas and for a fixed number of transmit antennas, there are infinitely many cyclotomic space-time codes. It is shown that all the cyclotomic space-time codes from the design have full diversity. Furthermore, optimal cyclotomic space-time codes from the design for different numbers of transmit antennas are obtained, where the optimality is in the sense that, for a fixed mean transmission signal power, its diversity product is maximized, or for a fixed diversity product, its mean transmission signal power is minimized. Although there are some cyclotomic space-time codes existed in the literature, most of them are not optimal.

The Alamouti's orthogonal space-time block codes are for QAM modulations and two transmit antennas. We have recently generalized it for the continuous phase modulation (CPM) by maintaining the orthogonality (for the fast ML decoding/demodulation) and the phase continuity of two signals from two transmit antennas denoted as OST-CPM. In this paper, we design orthogonal-like space-time coded CPM systems for three and four transmit antennas based on the existing orthogonal and quasi-orthogonal space-time codes in the literature. Although the signals from the transmit antennas in the proposed orthogonal-like space-time coded CPM systems are not orthogonal, the fast decoding/demodulation is maintained as in the two transmit antenna case. Simulation results show that the performance of the proposed orthogonal-like space-time coded CPM systems for four transmit antennas is much better than that of the OST-CPM systems for two transmit antennas.

In over-the-horizon radar (OTHR) target detection, the signal-to-clutter ratio (SCR) is very low, typically from -50 dB to -60 dB. Furthermore, for maneuvering targets, such as aircraft and missiles, Doppler frequencies of their radar return signals may be time-varying. In this case, the Fourier transform based techniques and super resolution spectrum estimation techniques may not work well since they use sinusoidal signal models. We propose a signal subspace clutter rejection algorithm combined with an adaptive chirplet transform technique for maneuvering target detection with OTHR. Simulation results of adding simulated maneuvering targets into raw OTHR clutter data are presented to illustrate the effectiveness of the proposed algorithm. The simulation results show that moving targets with -53.5 dB SCR can be detected.

Because of the low signal-to-clutter ratio, it is a difficult problem to detect and image moving targets in foliage. In this paper, a multifrequency multiaperture polarimetric synthetic aperture radar (MFMA POLSAR) system is proposed for imaging of moving targets in foliage. The MFMA POLSAR extends the multifrequency antenna array SAR (MF-SAR) system to multiple polarizations. Full polarization is used in MFMA POLSAR to achieve an optimal polarization adaptive to the environment such that the images obtained by different apertures are of the best coherence that is used to obtain the highest accuracy of the phase estimation. It is also shown that the MFMA POLSAR cannot only accurately locate both the slow and the fast moving targets but also reveal moving targets in foliage.

Trellis-coded space-time (TC-ST) coding for continuous phase modulation (TC-ST-CPM) was recently studied by X. Zhang and M.P. Fitz (see Proc. 38th Annual Allerton Conf. on Commun. Control and Computing, 2000). Similar to TC-ST for PSK and QAM systems, it has good performance but its decoding complexity may be high. We propose an orthogonal space-time coding for CPM (OST-CPM) systems. Similar to S. Alamouti's OST coding for PSK and QAM systems (see IEEE J. Select. Areas Commun., vol.16, no.8, p.1451-8, 1998), the newly proposed OST-CPM has a fast decoding algorithm.

We present a quantitative signal-to-noise ratio (SNR) analysis of linear chirps in the continuous-time short-time Fourier transform (STFT) domain using Gaussian windows; the 3 dB SNR definition is used. It is compared with the SNR in the time and the Fourier transform domains. Some numerical examples are shown to illustrate the theory.

The conventional ISAR image is a two-dimensional (2-D) projection of a three-dimensional (3-D) object surface. The image (projection) plane is related to the motion of a target with respect to the line of radar sight (LOS). In general, the image plane and the image scale in the cross range direction can not be determined by the traditional ISAR system with one receiver unless the target motion knowledge is known. In this paper, we propose a new ISAR system with three receivers. Using the three-receiver ISAR system, 3-D images of maneuvering targets can be generated, where the knowledge of the target motion is not required.