This paper develops a method for constructing an OFDM signal from a pair of complementary sequences so that the resulting signal is constant-modulus. A recursive method of constructing complementary sequences is developed such that the length of the signal grows linearly with the number of information symbols encoded. The constant-modulus property is exploited at each stage of the backwards symbol-decoding iteration through simple means to progressively reduce noise. For diversity comparing purposes, the new scheme is compared in symbol and frame error rates to m-PSK transmission with time-diversity in AWGN. The constant-modulus signal construction is then extended to two dimensions for the motivating application where we expect this work to have the greatest impact: massive MIMO at mmWave frequencies.

Millimeter wave (mm-wave) communication is expected to be widely deployed in fifth generation (5G) wireless networks due to the substantial bandwidth available for licensed and unlicensed use at mm-wave frequencies. To overcome the higher path loss observed at mm-wave bands, most prior work focused on the design of directional beamforming using analog and/or hybrid beamforming techniques in large-scale multiple-input multiple-output systems. Obtaining potential gains from highly directional beamforming in practical systems hinges on sufficient levels of channel estimation accuracy, where the problem of channel estimation becomes more challenging due to the substantial training overhead needed to sound all directions using a high-resolution narrow beam. In this paper, we consider the design of multi-resolution beamforming sequences to enable the system to quickly search out the dominant channel direction for single-path channels. The resulting design generates a multilevel beamforming sequence that strikes a balance between minimizing the training overhead and maximizing beamforming gain, where a subset of multilevel beamforming vectors is chosen adaptively to maximize the average data rate within a constrained time. We propose an efficient method to design a hierarchical multi-resolution codebook utilizing a Butler matrix, i.e., a generalized discrete Fourier transform matrix. Numerical results show the effectiveness of the proposed algorithm.

Massive multiple-input multiple-output (MIMO) communication is an emerging technology that uses an excess of transmit antennas to realize high spectral efficiency. Achieving potential gains with large-scale antenna arrays hinges on sufficient channel estimation accuracy. Much prior work focuses on time-division duplex (TDD)-based networks, relying on reciprocity between the uplink and downlink channels. However, most currently deployed commercial wireless systems are frequency-division duplex (FDD)-based, making it difficult to exploit channel reciprocity. In massive MIMO FDD systems, the problem of channel estimation becomes even more challenging due to the substantial training resources and feedback requirements which scale with the number of antennas. In this paper, we consider the problem of training sequence design and the mapping of training signals to training periods. We focus on reduced-dimension training sequence designs, along with transmit precoder designs, aimed at reducing both hardware complexity and power consumption. The resulting designs are extended to hybrid analog-digital beamforming systems, which employ a limited number of active RF chains for transmit precoding, by applying the Toeplitz distribution theorem to large-scale linear antenna systems. A practical guideline for training sequence parameter selection is presented along with performance analysis.

In this contribution, we present low-complexity detection algorithms in large-scale MIMO systems where they achieve significantly better bit error rate (BER) performance than known heuristic algorithms in large-scale MIMO literature, such as local ascent search (LAS) and reactive tabu search (RTS) algorithms, especially at higher-order modulations. The proposed techniques are developed from the conventional quadratic programming (QP) detector. The first one is based on performing two stages of a QP detector with a novel combination of both interference cancellation and shadow area constraints of the constellation. The second one is based on the branch and bound search tree algorithm. The efficacy of the proposed algorithms is investigated at various QAM modulations. Computer simulations show that the proposed algorithms outperform LAS and RTS algorithms in both uncoded and turbo coded BER performance, especially at higher QAM levels, with no significant change in complexity as the modulation level increases. Also, an extension of the QP detector for iterative detection and decoding is developed for the case of QPSK using a low complexity approach.

There is growing interest in using millimeter wave (mmWave) communication for fifth generation (5G) wireless systems because of the large bandwidth available in these frequencies. To overcome the higher path loss at mmWave bands, highly directional beamforming using large-scale, or massive, multiple-input multiple-output (MIMO) systems is critical. In this scenario, the problem of channel estimation becomes challenging due to the substantial training overhead needed to sound all possible beam directions using a high-resolution narrow beam. To tackle the issue of beam search in a mmWave system, we consider the use and design of multi-resolution beamforming sequences, which can quickly search out the dominant channel direction in a bisection manner. Given the multi-resolution codebook, the proposed multi-resolution beamforming sequence is designed to strike a balance between minimizing the training overhead and maximizing beamforming gain. We discuss how the multi-resolution codebook can be designed using a phase-shifted version of a {\em discrete Fourier transform} (DFT) matrix. Numerical results show the effectiveness of the proposed algorithm.

In this contribution, we present a low complexity detection algorithm that is based on a quadratic programming (QP) formulation. It provides better trade-offs between complexity and performance, especially in large-scale MIMO systems. It also achieves better bit error rate (BER) performance than known heuristic algorithms in large-scale MIMO literature, such as Local Ascent Search and Reactive Tabu Search algorithms, especially at higher-order modulations. This algorithm improves the performance of the conventional QP detectors using two stages of QP with the concept of interference cancellation and also with the concept of shadow area constraints as a measure of symbols reliability. Thus, we call it a Two-stage quadratic programming detector. Computer simulations demonstrate the efficacy of the proposed algorithm in large-scale MIMO systems for both uncoded and turbo coded cases.

Interest in massive multiple-input multiple-output (MIMO) systems is growing because of their potential ability to improve spectral and energy efficiency. Most prior work on massive MIMO considers TDD operation that relies on channel reciprocity between uplink and downlink channels, whereas most current cellular systems adopt FDD without channel reciprocity. In an FDD mode, downlink channel estimation becomes a challenging issue due to the substantial training overhead that scales with the number of antennas, which can limit the potential gain of massive MIMO systems. To tackle the issue of channel estimation, we consider the design of a training codebook that has a suitable mapping for the training signal patterns in block transmissions under the assumption of a Kaiman filtering framework. We focus on a reduced dimensionality training codebook and transmit precoding design to enable low-complexity system configuration. We discuss how this framework can extend to hybrid analog-digital precoding using a limited number of active RF chains for transmit beamforming by applying the Toeplitz distribution theorem to large-scale linear antenna arrays. A practical guideline for training codebook parameters is presented, and numerical results show the effectiveness of the proposed algorithm.

In this paper, the design of training signals for channel estimation in massive multiple-input multiple-output (MIMO) systems is considered. Under a stationary, block Gauss-Markov channel model, a method for optimal pilot beam pattern design for enhanced channel estimation is proposed, exploiting both the properties of Kalman filtering and the spatio-temporal channel correlation. First, pilot beam pattern design is considered under the assumption of orthogonal beam patterns within a block. The orthogonality assumption is subsequently relaxed and the design problem is solved via a greedy approach. Numerical results show the efficacy of the proposed algorithm.

A new precoder for precoding-based blind channel estimation for MIMO-OFDM systems is proposed. In the proposed scheme, only a small number of data symbols, commensurate with the channel length, are linearly precoded prior to transmission to induce the signal correlation needed for the scheme to blindly estimate the channels. Similar to how pilot symbols are transmitted, the subcarriers carrying these linearly precoded data symbols are equi-spaced across the frequency band. The other subcarriers carry data symbols in the standard way, enabling MLD per subcarrier and also allowing for MIMO linear precoding across antennas at each subcarrier. This is in contrast to previous precoding-based blind channel estimation schemes which precode all of the data symbols so that every subcarrier carries a linear combination of symbols, aking the resulting joint MLD problem infeasible. In addition, this also makes it infeasible to employ MIMO precoding per subcarrier across the transmit antennas. The proposed precoder is designed via a multi-stage optimization process that seeks to minimize both channel estimation error and symbol estimation error. For channel estimation purposes, the resulting optimal design offers low-cost features such as sign change and FFT while providing reasonable channel estimation performance for low mobility applications.

Semi-Blind/Blind channel estimation for multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems has received a lot of attention in recent years. A new linear precoder for blind channel estimation is proposed in which only a small number of subcarriers carry symbols that are linearly precoded to effect the inter-symbol correlation needed for the blind channel estimation scheme to function properly. The proposed precoding scheme leaves most of the subcarriers intact, thereby minimizing the number of symbols that have to be jointly estimated via either Maximum Likelihood (ML) or MMSE. An optimal precoder under the sparse structure is developed, which insures that the precoder matrix is well-conditioned to minimize any noise enhancement that may occur in the process of MMSE based joint symbol estimation.

In this paper, a novel hybrid OFDM receiver based on sparse variational Bayesian (VB) learning and soft-input soft-output decoding is proposed. By noticing that a key part of the inference problem approximated by VB (message-passing) methods may be inferred exactly, an genetic interfacing structure is proposed allowing the use of virtually all existing soft-input soft-output decoding schemes. Therefore the tasks of joint channel state estimation, demodulation and decoding are iteratively solved under the proposed hybrid variational Bayesian framework. The bit-interleaved coded modulation with Turbo coding is used to demonstrate the potential performance of the proposed structure. Very promising results in performance are observed in computer simulated experiments.

In this paper, we present a method of detecting the range and Doppler phase of a point target using multiple antennas. As a key illustrative example, we consider a 4 × 4 system employing a unitary matrix waveform set, e.g., formed from Golay complementary sequences. When a non-negligible Doppler shift is induced by the target motion, the waveform matrix formed from the complementary sequences is no longer unitary, resulting in significantly degraded target range estimates. To solve this problem, a novel Doppler estimation and compensation scheme based on a clever application of DFT is developed that provides notable improvements, both in detection performance, and processing times. Proof-of-concept simulations are presented verifying the efficacy of the proposed Doppler compensation and estimation technique for our unitary waveform matrix designs.

In this paper, we present a method of detecting the range and Doppler phase of a point target using multiple antennas. As a key illustrative example, we consider a 4 × 4 system employing a unitary matrix waveform set, e.g., formed from Golay complementary sequences. When a non-negligible Doppler shift is induced by the target motion, the waveform matrix formed from the complementary sequences is no longer unitary, resulting in significantly degraded target range estimates. To solve this problem, we adopt a subspace based approach exploiting the observation that the receive matrix formed from matched filtering of the reflected waveforms has a (non-trivial) null-space. Through processing of the waveforms with the appropriate vector from the null-space, we can significantly improve the range detection performance. Also, another very important target aspect is the velocity with which the target is moving, and to determine that, the exact Doppler phase shift induced by the target motion needs to be estimated with reasonable accuracy. To accomplish this task, we develop a strategy that uses the MUSIC algorithm to estimate the Doppler phase, and we use simulations to show that the phase estimates obtained are reasonably accurate even at low SNRs.

This paper proposes a space-time-frequency coding scheme for MIMO-OFDM that achieves full rate for an arbitrary number of antennas with complex-valued information symbols. In addition, the proposed scheme provides a very high level of diversity with relatively low complexity. In the new scheme, the spatial and frequency spreading is followed by a temporal spreading that facilitates simple separation of the respective signals sent by the various transmit antennas. This temporal spreading enables perfect separation of the superimposed transmit signals at the receiver prior to channel estimation. The Local Maximum Likelihood (LML) method of Rugini et al is employed to further reduce complexity. Simulations are presented demonstrating the efficacy of the new scheme. For example, for cases where an Orthogonal Space-Time Block (OSTBC) code exists, the new scheme is shown to provide the same full-diversity as the OSTBC. Again, though, the new scheme is applicable for an arbitrary number of transmit antennas and complex-symbol constellations.

In this paper, we present a method for detecting a point target using multiple antennas when the relative motion between the receivers and the target induces a non-negligible Doppler shift. As a key illustrative example, we consider a 4×4 system employing a unitary matrix waveform set, e.g., formed from Golay complementary sequences. When a non-negligible Doppler shift is induced by the target motion, the wave-form matrix formed from the complementary sequences is no longer unitary, resulting in significantly degraded target range estimates. To solve this problem, we adopt a subspace based approach exploiting the observation that the receive matrix formed from matched filtering of the reflected waveforms has a (non-trivial) null-space. Through processing of the waveforms with the appropriate vector from the null-space, we can significantly improve the detection performance. We provide simulation results to confirm the theoretical analysis.

Among existing classical cooperative localization techniques for wireless sensor networks, the maximum likelihood estimator (MLE) is theoretically the best in the sense that it asymptotically achieves the Cramér-Rao bound (CRB). However, the gradient based iterative algorithms that are commonly used to achieve ML estimated positions are quite sensitive to the initial values and cannot achieve the theoretic optimal performance. In this paper, we propose a complete MLE solution, named “MLE-MLE”, where a non-cooperative or single node MLE is first applied to generate the initial values for the iterative MLE cooperative localization algorithm. The inherent unimodal property of the single node log-likelihood guarantees that single node MLE method converges to the unique solution whatever the starting point is. As verified by numerical results, among existing practical classical cooperative location estimators, MLE-MLE is the best whose performance is closest to CRB.

In this paper, we present a hybrid automatic repeat request (ARQ) scheme for wireless multicast with incremental redundancy channel coding and packet retransmission. With this scheme, we can reliably deliver the same copy of information to different users with mild delay. In addition, the design of the feedback channel for this scheme can be greatly simplified as no effort must be expended to combat cross user interference. We assume that there is always a packet for the transmitter to send whenever the channel is available. The transmitter is assumed to have a buffer of infinite length so that there is no packet-dropping. Three specific schemes are studied, including generalized slotted ALOHA (GSA), repetition time diversity (RTD), and general incremental redundancy (IR). The scaling laws of the average delay and average throughput with respect of the number of users are derived. In addition, we also derive a condition to obtain a linear scaling for both the throughput and the delay with respect to the number of users. Since every user can achieve no more than the ergodic capacity, we actually achieve the optimal scaling law in this case. Simulation results confirm our findings.

We present a pilot-assisted method for estimating the frequency selective channel in a MIMO-OFDM system. The pilot sequence is designed using the DFT of the Golay complementary sequences. Novel exploitation of the perfect autocorrelation property of Golay complementary sequences, in conjunction with OSTBC based pilot waveform scheduling across multiple OFDM frames, facilitates simple separation of the channel mixtures at the receive antennas. The DFT length used to transform the complementary sequence into the frequency domain is shown to be a key critical parameter for correctly estimating the channel. This channel estimation scheme is then extended to antenna arrays of arbitrary sizes.

For multiuser multiple-input multiple-output (MIMO) uplink communications where the signal-to-interference-plus-noise ratio (SINR) of the k-th user, denoted as SINRk, is expected to achieve the target valueγk, we first consider the ideal scenario where multiuser channel matrices are perfectly known to every user and we solve the problem of maximizing mink(SINRk/γk) over all possible beamformers under individual transmit power constraints via alternating optimization strategies and the generalized eigenvalue problem (GEVP) programming. Then, we study a more realistic situation where only a few number of bits are allowed to feed back to users. We propose to integrate the genetic algorithm into the Lloyd's vector quantization method to design the optimum codebook in terms of maximizing E(mink(SINRk/γk)) with expectation taken with respect to fading channels.

In our previous works, we proposed an uplink transmit beamforming design algorithm for multiuser multiple-input multiple-output (MIMO) systems in frequency non-selective channels, under the assumption that cooperation exists among multiple users so that the full multiuser channel state information (FMCSI), i.e. the collection of the channel state information between each of the users and the base station, is available at each of the multiple users. The proposed algorithm, aiming to maximize the signal to multiuser interference plus noise ratio (SINR), is referred to as SINR-Max cooperative beamforming. In this paper, we extend the application of SINR-Max cooperative beamforming to frequency selective block invariant channels by combining orthogonal frequency division multiplexing technique into MIMO systems (MIMO-OFDM). We designed two alternative transmitter structures with pre-IDFT beamforming in the frequency domain and post-IDFT beamforming in the time domain respectively, and the receiver structure common to both types of transmitters. For post-IDFT transmitter, we investigated different implementation options. Performance of the designed systems with different schemes is evaluated and compared through simulations.

In this paper, we present a user selection scheme with a fairness constraint when zero-forcing beamforming (ZFBF) transmission is employed in a multiple-input multiple-output (MIMO) broadcast channel. This problem can be reduced to the maximization of a weighted sum rate with a power constraint. In this paper, we first derive a lower bound on the weighted sum rate. Roughly speaking, this bound is inversely proportional to the Frobenius norm of the inverse of the weighted composite channel matrix. We then present a greedy algorithm to select the users that maximize this lower bound, using the same technique in J. Wang et al. Finally, we show that this approach achieves the same scaling law as DPC does as presented in M. Sharif and B. Hassibi. Simulation suggests that this method achieves comparable or better performance than most existing schemes in the moderate to high SNR realm with comparable complexity.

In this paper, we consider limited feedback for multiple antenna broadcast channels: each user quantizes its channel vector according to a rotated codebook which is optimal in the sense of mean square error and feeds back the codeword index. The paper is focused on characterizing the sum rate performance of zero-forcing dirty paper coding (ZFDPC) systems under limited feedback. We derive sum rate upper bound for systems employing Gaussian random codebooks and minimum distance decoding and link the throughput performance to some basic properties of the quantization codebook. Interestingly, we find that limited feedback employing a fixed codebook leads to a sum rate ceiling for asymptotically high SNR.

In this paper, we study the limited feedback model for partial CSI at the basestation (BS) for multiple antenna broadcast channels: the BS has the knowledge of quantized CSI of each user. We first give a practical limited feedback scheme designed for multiple antenna broadcast channels. Then, we study the sum rate performance of zero-forcing dirty paper coding under the proposed limited feedback scheme. An upper bound is also derived to get some insight about the impact of the use of limited feedback. Interestingly, we find that the systems experience a ceiling effect on the sum rate for a fixed feedback rate.

This paper investigates the performance of orthogonal frequency division multiplexing (OFDM) based asynchronous multiple access multiple input multiple output channels. In an asynchronous mode of data transmission, independent decoding without user cooperation is a more appropriate approach. Thus, various suboptimal transmitter diversity techniques such as space-time block coding and beamforming are employed, and their performances are evaluated. The average signal to interference and noise ratio (SINR) resulting from linear minimum mean squared error (MMSE) combining is exploited to compute symbol error rate. Simulation results demonstrate that space-time block coding hardly achieves substantial transmitter diversity gains in asynchronous channels. Moreover, receiver diversity is an important factor of the overall performance in a large system. However, beamforming, which uses only part of existing spatial dimensions, can improve the bit-and symbol-error rate performance in the low signal-to-noise ratio (SNR) region where practical communication systems are operated.

The output SINR achieved via indirect dominant mode rejection (IDMR) beamforming is substantially higher than the achieved with other beamforming algorithms. IDMR is based on a parametric estimate of the covariance matrix which is obtained using an estimate of the directions of the dominant sources and assuming that the array manifold is available. In most applications the array manifold is not known precisely and performance of IDMR can be deteriorated. The focus of this paper is to enable the IDMR beamformer to operate in a scenario of direction-independent steering vector mismatch. A modified version of an algorithm introduced by Friedlander is employed to estimate the direction-independent mismatch. Thereafter IDMR is implemented. Simulation analysis reveals that this technique enables IDMR to operate in a scenario of direction-independent manifold mismatch

In this paper, the effect of transmitter diversity on asynchronous co-channel interference suppression and equalization is studied in multi-user multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. Space division multiple access OFDM may be an appropriate solution to design spectrally efficient and high data-rate communication systems. Moreover, communication systems using transmitter diversity can provide additional spatial diversity gains. However, increasing the number of transmitting antennas may induce another source of co-channel interference in asynchronous multi-user channels. In order to observe the performance of various transmitter diversity techniques under the asynchronous mode of transmission, first, we develop space-time minimum mean squared error (MMSE) receivers for both space-time block coded OFDM and beamforming based MIMO OFDM. The average signal-to-interference and noise ratio (SINR) resulting from MMSE combining indicates that the bit-error rate (BER) performance of space-time block coded (STBC) multi-user OFDM is highly dependent on the amount of timing offset. Overall, simulation results demonstrate that closed-loop MIMO systems need to be employed to obtain substantial diversity gains in asynchronous multi-user OFDM channels with random timing offset

When a base-station with multiple antennas is transmitting to a single user with one antenna, feeding back the normalized channel vector (channel subsapce feedback) to the transmitter can achieve the same capacity as if the exact channel state information is available at the transmitter. For the multiuser scenario, however, perfect channel knowledge is usually required at the transmitter to obtain the sum rate advantage provided by the multiple transmit antennas. In this paper, we consider the sum rate of a multi-antenna broadcast channel when each user only feeds back the normalized channel vector. We show that in such situation the zero-forcing dirty paper (ZFDP) encoding scheme designed using channel subspace feedback achieves the throughput of full channel knowledge ZFDP encoding without optimal power allocation. It is shown to be asymptotically optimal for high signal-to-noise ratios. The closed-form expression of the ergodic sum rate for an independent Rayleigh fading channel is derived. The throughput performance of the regularized channel inversion technique under channel subspace feedback is also analyzed. We show that channel subspace feedback in the multi-antenna broadcast channel enables the system to achieve most of the sum rate advantage provided by the multiple antennas.

When the size of the training samples is limited the performance of the full rank minimum variance distortionless response (MVDR) beamformer is deteriorated; and a low rank solution of the MVDR problem can yield a better performance. A new adaptive approach, indirect dominant mode rejection (IDMR), was introduced in previous work to solve the MVDR optimization problem. In the previous work the IDMR beamformer was used to extract the desired signal, while in this work we use the IDMR beamformer to estimate the power spectrum. We also introduce several modifications, which bring more robustness to the basic IDMR. These include root-music, forward/backward averaging of the sample covariance matrix and power window

In this paper, a STBC/BF hybrid technique is proposed for outdoor multipath multi-input multi-output (MIMO) channel. Depending on the amount of partial channel state information (CSI), this system evolves from pure diversity waveform signalling to pure beamforming. The performance of this technique, in terms of signal vs noise ratio (SNR), is investigated in various multi-input single-output (MISO) scenarios. Though the method is evaluated in MISO, we give a simple way to extend it to MIMO case. In addition, a beamforming scheme based on sub-space approximation is also discussed which can reduce the amount of feedback from the receiver to transmitter. Simulation results are given at the end of this paper

We derive a hybrid of beam-forming (BF) and space-time block coding (STBC), where the space-time code is transmitted over the beams generated by the steering vectors corresponding to the channel path directions. This is for the practical case where the transmit array may have adequate information on the departure angles of the dominant paths between transmitter and receiver, but unreliable information on the associated complex path gains. We compute analytically the signal-to-noise ratio (SNR) of the proposed hybrid for the specific case of a two-path channel model and using the orthogonal Alamouti code, and compare the result to the SNR of optimal linear precoding (LP) and the theoretically possible SNR of orthogonal STBC (OSTBC). Simulation results show that the performance of the BF/STBC hybrid can be very close to LP /sup n/der certain conditions - or even better in the practical case where there are phase estimation errors in the path gain estimates employed at the transmitter.

Space-time transmit structures for multi-antenna systems have received considerable interest. Circulant structures were among the first space-time coding techniques ever used for multiple-input multiple-output (MIMO) systems due to their simplicity and full rate. The fact that a circulant matrix is diagonalized by the discrete Fourier transformation matrix suggests that the circulant structure can be combined with an inverse fast Fourier transform (IFFT) at the transmitter and a fast Fourier transform (FFT) at the receiver. Using this method, the spatial mixing effect of the MIMO channel is decoupled but the diversity gain is lost. To recover the diversity advantage, we propose to spread the transmitted symbols over the diagonalized channel using the constellation rotation matrix for signal diversity designs. After spreading, every symbol experiences all the components of the frequency counterpart of the channel vector which makes our scheme provide full diversity. The proposed scheme is full rate and can be easily applied to any number of transmit antennas. Our simulation results show that the performance of our scheme is close to the performance of the ideal orthogonal space-time code and much better than the conventional circulant space-time code.

This paper proposes a low complexity turbo multi-user receiver for the coded asynchronous multi-user orthogonal frequency division multiplexing (OFDM) signal over multipath fading channels. While asynchronous multi-user multiplexing with antenna diversity accommodates high speed applications and achieves the high spectral efficiency in communication systems, the multiple access interference deteriorates the quality of signal detection. In order to effectively suppress the interference and amplify a performance gain from channel coding, we employ a turbo equalization technique. Based on the asynchronous OFDM signal model and the corresponding linear minimum mean squared error (MMSE) estimator, an iterative space-time MMSE multi-user detector with a parallel soft interference canceller is developed. Simulation results demonstrate that iterative joint demodulation of the asynchronous multi-user OFDM signal achieves a significant performance gain even with a reduced complexity equalizer and a few iterations.

In the computation of the minimum variance distortionless response (MVDR) beamformer, scaling is necessary in order to satisfy the unity gain constraint. When estimating the power in the close vicinity of a source, the MVDR beamformer allocates a null at the direction of the source and the scaling factor becomes very large, and substantially increases the gain of the white noise. This situation can cause the non detection of a weaker source located in the vicinity of a higher power source. Comparing the equation of the MVDR beamformer to the Wiener-Hopf MMSE equation we observe that a initial estimate of the power can be used instead of scaling to satisfy the unity gain constraint. As an initial power estimate we propose to estimate the directions and powers of the dominant sources by applying the MUSIC algorithm; and to use this information to estimate the power spectrum using an artificially extended array. We also propose to use the dominant sources' powers and directions obtained with MUSIC to generate a spectrum composed of triangular windows.

We consider point-to-point wireless links with multiple antennas in the presence of interference, and exploit channel's spatial correlation and the temporal covariance of the interference to design multiantenna transmitters. We develop a space-time spreading scheme that maximizes average signal-to-interference-and-noise ratio, and an optimally power-loaded space-time beamforming (STBF) scheme which improves error-probability performance. In order to increase transmission rates, we combine orthogonal space-time block coding with STBF, optimize power loading across beams, and develop low-complexity receivers. Optimal training for least-squares error channel estimation, and STBF for minimum mean-square error channel estimation, are also studied. Our analytical and simulated results corroborate that STBF with optimal power loading can considerably reduce error probability and channel-estimation errors.

Under the condition of low sample support, there is deviation between the estimated and true correlation matrices. In this case, the full-rank sample matrix inversion (SMI) beamformer is no longer optimal. Instead, a low-rank adaptive beamformer could yield better performance. When extending from a couple of signal directions to the entire spatial spectrum, the output power is a more applicable touchstone than SINR, which is only defined for signal directions. Adaptive algorithms (CG/DMR), if operating at the best rank for each direction, could effectively reveal the spatial spectrum. The best rank is obtained by investigating an ideal evaluation from the true correlation matrix and adaptive beamformer.

We use the preconditioned conjugate gradient (PCG) method to compute rapidly the tap weights of a minimum mean-square error (MMSE) decision feedback equalizer (DFE). The equalizer setting is computed indirectly after channel estimation. According to the Toeplitz block structure of the MMSE DFE equation, Rw=r (R is the system matrix), the preconditioner, P, is chosen to be a block diagonal matrix with circulant blocks along its diagonal. The spectral clustering property of the preconditioner matrix is analyzed. It is shown that the eigenvalues of P/sup -1/R are clustered around unity, except for a small number of outliers when the number of the equalizer taps becomes large. The preconditioner can be inverted via a fast Fourier transform (FFT) with complexity O(N log N). Since the PCG method converges in a small number of steps, the total complexity for computing the DFE setting is proportional to O(N log N). The proposed scheme is also suitable for smart initialization which can further reduce the computational burden by decreasing the number of iteration steps. Simulations of a DFE for digital TV channels demonstrates the superior performance of the scheme.

We study asynchronous multiuser orthogonal frequency division multiplexing (OFDM) systems over fading channels. Multiuser multiplexing is essential to the design of a spectrally efficient communication system. On the other hand, a synchronous mode of communication may not be a practically realizable solution considering the demand for high-speed services with portability. Therefore, we develop the model of asynchronous multiuser OFDM signals, and propose several minimum mean squared error (MMSE) based equalization methods to suppress the asynchronous interference effectively. The proposed space-time domain MMSE filter mitigates the inter-carrier interference (ICI) and the inter-block interference (IBI) induced by the interfering user's relative delay. Furthermore, additional performance gains can be achieved via a two-step procedure, which applies the space-time MMSE filter twice, first to estimate the interference and secondly to equalize the signal after interference cancellation.

In array applications an important task is adaptive beamforming. The minimum variance distortionless response (MVDR) beamformer can only be computed if the true spatial correlation matrix is available. In practice, the correlation matrix has to be estimated from the arriving signals, and in some cases there are only a small number of samples (snapshots) available. When the number of snapshots is small, the MVDR beamformer is no longer optimal, and a low rank MVDR solution can provide a higher SINR. In this work we analyze two methods of finding low rank solutions: steering independent conjugate gradient (SI-CG) and steering dependent conjugate gradient (SD-CG). We also propose a simplified expression to compute the arriving power from any given direction.

It has been previously shown that the effects of error propagation in a decision feedback equalizer may be reduced by constraining the 2-norm of the feedback filter. This paper describes three algorithms for calculating the constrained equalizer based on a channel estimate. An iteration function is derived for the Karush-Kuhn-Tucker multiplier and the algorithms are designed to quickly find a fixed point of this function. The algorithms include a modified regula falsi algorithm known as the Pegasus iteration, a modified secant algorithm, and a nonlinear fit to the iteration function. At each iteration, the conjugate gradient algorithm is used to solve the resulting linear equations. The algorithms are demonstrated on the 8-VSB terrestrial broadcast digital TV system. While all three algorithms exhibit good convergence characteristics, the nonlinear fit converges the fastest.

A two-dimensional space-time pilot-symbol assisted demodulation system is proposed in this paper. Since complex scattering environments can produce nontrivial space-time correlation characteristics, this paper proposes coherent demodulation by estimating the fading channel distortion using pilot observations across both space and time. The optimum interpolation filter takes in multiple signals from receiving antennas and exploiting the space-time channel correlation to produce multiple channel-estimate outputs corresponding to every antenna. The optimal channel-estimation filter, its mean-square error performance, and the pairwise symbol-error probability are derived for realistic scattering models to characterize the system performance. A design criterion is proposed for the pilot-symbol spacing and the filter length. Since the filter is a function of the statistical description of the channel, we investigate if this statistical description and the resulting optimal filters can be estimated simply from the pilot observations.

Abstract Future broadband cellular wireless communication systems will be characterized by high delay spread and the need to maximize the system capacity. One method of increasing capacity, aggressive frequency reuse, subjects mobiles to high levels of interference from neighboring basestations. Receiver interference suppression algorithms that work well for conventional MIMO systems may not be appropriate for suppressing interference in multiple‐input‐multiple‐output (MIMO) orthogonal frequency division multiplexing (OFDM) cellular systems, since differing propagation delays and channel lengths can destroy the alignment of the cyclic prefixes, making the interference asynchronous. This work presents MIMO algorithms for cyclic prefix based systems that are suitable for scenarios where the interferer's cyclic prefix is not time‐aligned with the desired signal's cyclic prefix. Specifically, we present several space‐time partial equalization techniques for the alignment of cyclic prefixes for aiding in interference suppression. We use a two‐stage architecture with partial equalization for cyclic‐prefix alignment in the time domain followed by simple channel equalization in the frequency domain. We consider interference suppression in both domains and demonstrate the efficacy of the two‐stage architecture over both zero‐forcing (ZF) and per frequency bin minimum mean squared error (MMSE) equalization. Copyright © 2004 John Wiley & Sons, Ltd.

Future broadband cellular wireless communication systems will be characterized by high delay spread and the need to maximize the system capacity. Aggressive frequency reuse, one technique of maximizing capacity, subjects the mobile to high levels of interference when the mobile is near the cell edge. Traditional interference suppression techniques designed for synchronized OFDM systems do not perform optimally when the desired and interfering signals are asynchronous at the receiver. Methods of time aligning asynchronous signals (i.e., signals whose channel plus delay is longer than the cyclic prefix length) were recently presented (Breinholt, M. et al., Allerton, 2002). This paper presents results of the synchronization algorithms for coded systems. The results show that the algorithms give significantly different results when coding is applied.

Compared to wired channels, time dispersive radio channels possess more frequent nulls in their spectral characteristics. Thus, the performance of linear filters to compensate intersymbol interference degrades dramatically. The well-known nonlinear decision feedback equalizer (DFE) is one approach to improve this behavior. However, in systems with observations of high dimensionality, the optimum DFE structure is computational intensive. In this paper, we apply the method of the multi-stage Wiener filter (MSWF) to a conventional minimum mean square error (MMSE) DFE in order to reduce computational complexity. The application of the new algorithm to an Enhanced Data rates for GSM Evolution (EDGE) system demonstrates the ability to outperform the even more computational intensive linear Wiener filter (WF).

In this paper, we use an alternative approach to derive the minimum mean-square error decision feedback equalizer. This derivation yields insight which allows the equalizer to be designed so that its SINR performance is relatively insensitive to variations in the decision delay (also known as the cursor). The design, while generally applicable to the DFE, is illustrated using 8-level vestigial sideband modulation as used in the ATSC digital television standard. We simulate several channels and show that the SINR varies little across a relatively wide band of decision delays.

We introduce a new structured channel impulse response (CIR) estimation method for sparse multipath channels where we demonstrate a robust way of restoring the pulse shape into the composite CIR. We call this novel CIR estimation method time-of-arrival based blended least squares (TOA-BLS) which uses symbol rate sampled signals, and it is based on blending correlation processing followed by TOA estimation in the frequency domain by the least squares based channel estimation. TOA estimation in the frequency domain is accomplished by estimating the AR model parameters by solving the forward and forward-backward linear prediction equations in the least squares sense. Simulation examples are drawn from the ATSC digital TV 8-VSB system (ATSC Digital Television Standard, A/53, 1995). The delay spread for digital TV systems can be as long as several hundred times the symbol duration; however, digital TV channels are sparse where there are only a few dominant multipaths.

The multi-code CDMA problem, and the corresponding data and noise model is discussed. The problem of "crosstalk", which occurs when using an MMSE receiver in colored noise, is addressed. A method to avoid "crosstalk", by choosing the eigenvectors of the interference plus noise matrix as codes, is introduced. This approach is shown to produce codes that are orthogonal not only in the conventional sense, but also with respect to the interference plus noise matrix. The gain on the codes is shown to be inversely proportional to the corresponding eigenvalue. Simulation results demonstrate that the codes corresponding to the smallest eigenvalues dramatically outperform the MMSE receiver for Walsh-Hadamard codes in terms of mean-square error (MSE).

We discuss the interrelationship between the spatial and the temporal correlation of the frequency-flat Rayleigh fading channels, and propose a joint design of the mobile station (MS) antenna separation (AS), base station (BS) antenna separation, and the channel interleaving depth (ID) for achieving the spatial, temporal, and space-time channel independence. The proposed design is based on a model generalized from the Jakes/Clarke (1968, 1974) ring-of-scatterer fading model. A space-time channel correlation function of two BS and two MS antennas is derived and examined to produce the AS and ID design rule. Analytical binary phase shift keying (BPSK) bit error probability with perfect channel state information is used to compare the performance.

We propose an open-loop symbol period estimation algorithm that can be used alone or to speed up symbol timing recovery loops. The proposed algorithm is effective in frequency selective channels, does not require the resampling of the digital received signal while estimating the symbol period, and does not require estimation of the transmitted symbols. The algorithm is performed in a computationally efficient manner. Included is a simple method of finding a DFT value for subsequent overlapping blocks of data using only one complex multiply. Simulations of the proposed algorithm show significant improvements in estimation time and reduction of jitter when compared to a Gardner timing recovery loop.

In recent years, receivers based on channel equalization on the chip-level prior to despreading have been proposed for the 3G wideband CDMA forward link. Of these the chip-level MMSE equalizer has attracted much interest. In this paper, we investigate the performance of training-based MMSE equalizers in moderate to rapid time-varying Rayleigh faded channels. We show that the standard MMSE equalizers fail to adequately track the time-variations as large Doppler shifts. We also demonstrate that chip-level MMSE equalizers that exploit the underlying channel structure, specifically the fact that the channel impulse response is sparse, are much more robust against time-selective fading. This equalizer is obtained by projecting the full-rank data vectors onto a much lower dimensional subspace spanned by a few columns of the pulse shaping filter convolution matrix, as determined by the multipath delays. Simulations results show that this low-rank MMSE equalizer performs significantly better than both standard MMSE equalizers and the RAKE receiver in time-varying situations.

A generalized statistical signal processing framework developed in [2] is utilized for interference suppression for Joint Multiuser Detection (MUD). Previous work on the efficient correlations subtractive architecture form of the reduced rank multistage Wiener filter (CSA-MWF) is extended by considering the multiple signal constraint case. The reduced rank algorithm is not based on an eigen-decomposition, which requires the signal subspace rank to be greater than or equal to the number of signals present in the system. The solution meets or exceeds full rank MMSE at a significantly reduced rank. System performance is characterized for a highly loaded synchronous DS-CDMA system in the presence of multi path. The bit error rate (BER) performance of the Joint CSA-MWF (JCSA-MWF) is compared to MMSE and RAKE receivers.

This paper presents two new algorithms that operate in beamspace and provide closed-form arrival angle estimates in conjunction with uniform linear arrays. The algorithms window the array data using either a cosine shaped window or a Hanning window prior to beamforming. The resulting array patterns have low sidelobe levels (peak sidelobe leve ≈ −23.5dB for cosine window, peak sidelobe level ≈ −32.3dB for Hanning window) and provide enhanced out-of-band source suppression. In contrast, the existing DFT Beamspace ESPRIT algorithm employs a rectangular window; the resulting array pattern has a peak sidelobe level of ≈ −13.5dB. The new algorithms clearly provide better out-of-band source suppression than DFT Beamspace ESPRIT. They can provide arrival angle estimates of sources in a given spatial sector without being swamped by powerful sources lying outside the sector of interest.

In this paper we introduce a novel channel estimation method which uses symbol rate sampled signals, based on blending the least squares based channel estimation and the correlation based channel estimation methods. We first overview the shortcomings of the least squares and the correlation based channel estimation algorithm, where a training sequence is utilized in both cases. The performance of the new channel estimation method will be demonstrated, such that the channel estimation will be more robust, and the overall quality of the estimate will be improved by recovering the pulse shape which is naturally embedded in the overall channel impulse response. We will demonstrate how both methods can be combined effectively to minimize the problems associated with the effective channel delay spread being longer than the known training sequence can support.

A new reduced rank multiuser detector (MUD) for DS-CDMA is presented. The algorithm is derived for the general case of an asynchronous DS-CDMA system in frequency selective multipath. The MUD solution is shown to be equivalent to a bank of parallel, single user detectors. The algorithm is implemented in reduced rank form using the correlations subtractive algorithm of the multistage Wiener filter (CSA-MWF). It is shown that the CSA-MWF implementation performs identically to the full rank solutions of MMSE MUD and meets single user, full rank performance at a substantially reduced rank for all levels of system load.

We present chip-level MMSE equalizers for the forward link in CDMA that exploit the underlying channel structure, specifically the fact that the channel impulse response is sparse. The assumption we make is that the channel vector lies in the subspace associated with the pulse shaping filter convolution matrix. We can then project the chip-level MMSE equalizers onto a much lower dimensional subspace due to the sparseness of the channel. The simulations demonstrate that this low-rank MMSE equalizer converges very quickly to the asymptotic SINR, even where the underlying assumption is not valid.

This paper investigates the performance of reduced rank spacetime processors in the context of anti-jam mitigation for an M-code based GPS receiver utilizing a circular array. Several adaptive processing algorithms are discussed utilizing power minimization techniques. It is assumed an INS (inertial navigation system) or direction finding algorithm is incorporated into the receiver for satellite look direction based algorithms. Reduced rank space-time processing is accomplished via the innovative multistage Wiener filter (MSWF). It is demonstrated that the MSWF does not require matrix inversion, thereby reducing computational complexity. The processing algorithms are compared in terms of available degrees of freedom and distortion of the GPS cross correlation function (CCF).

A novel "self-decorrelating" technique is proposed to enhance the multipath constructive summation capability and the interference rejection capability of a class of maximum-SINR blind space-time CDMA RAKE receivers designed to tackle the near-far problem. This proposed "self-decorrelating" technique appears to have effectively removed the near-far problem's error floor at high SNR; and the proposed technique can also significant decrease the error rate. Moreover, this "blind" space-time processing receiver architecture needs no prior knowledge nor explicit estimation of (1) the channel's multipath arrival angle or arrival delay or power profile, (2) the receiver's nominal or actual antenna array manifold, and (3) the other CDMA users' signature spreading codes. Preliminary simulations suggest very significant performance improvement realizable from the proposed technique. Though developed for direct-sequence CDMA, the proposed technique might be adopted for frequency-hopping CDMA.

The chip-level MMSE estimate of the (multiuser) synchronous sum signal transmitted by the base-station, followed by a correlate and sum, has been shown to perform very well in the CDMA forward link using orthogonal channel codes. In this paper, adaptive chip-level MMSE estimation based on the conjugate gradient (CG) algorithm is presented. Our simulations show that, adaptive CG using the pilot channel for training can achieve excellent convergence at a moderate computational cost.

The Wiener filter solves the Wiener-Hopf equation and may be approximated by the multi-stage nested Wiener filter (MSNWF) which lies in the Krylov subspace of the covariance matrix of the observation and the cross-correlation vector between the observation and the desired signal. Moreover, since the covariance matrix is Hermitian, the Lanczos algorithm can be used to compute the Krylov subspace basis. The conjugate gradient (CG) method is another approach to solving a system of linear equations. We derive the relationship between the CG method and the Lanczos based MSNWF and finally transform the formulas of the MSNWF into those of the CG algorithm. Consequently, we present a CG based MSNWF where the filter weights and the mean square error (MSE) are updated at each iteration step. The resulting algorithm is used for linear equalization of the received signal in an enhanced data rates for GSM evolution (EDGE) system. Simulation results demonstrate the ability of the MSNWF to reduce receiver complexity while maintaining the same level of system performance.

Since the design by S.M. Alamouti (see IEEE Journal on Selected Areas in Communications, vol.16, no.8, p.1451-8, October 1998) of a simple orthogonal space-time block code that achieves the same diversity order as maximal-ratio receiver combining, there has been a flurry of work to produce similar codes. While Alamouti's scheme cannot be extended to more than two antennas for complex modulation, other non-orthogonal codes have been developed. In this paper we analyze a space-time block code formed using Hankel data blocks that is good for any number of antennas. Through analysis and computer simulation we show that this scheme provides the same signal-to-noise ratio for each recovered symbol but fails to reach, on average, the gain reached by Alamouti's scheme. The methods used in this paper serve as an instructive example of how to look at similar coding schemes to see their utility in the area of space-time coding.

This work focuses on the forward link in a CDMA based multiuser communication system experiencing frequency dependent multipath fading. The mobile handset is assumed to have two antennas, either spatially separated or having diverse polarizations. Previous work on linear equalizers to restore orthogonality of the Walsh-Hadamard channel codes in this scenario led to a comparison of zero-forcing (ZF) equalizers and the RAKE receiver. A chip-rate MMSE equalizer is derived that minimizes the MSE between the synchronous "sum signal" of all the users from a given base station and the equalized chip sequence; this equalizer is followed by correlation with the desired user's spreading code times the base-station's long code. In this MMSE derivation, the sum of chip sequences of all the users is modeled as an i.i.d. random sequence. This leads to a "simple" MMSE equalizer that does not depend on the Walsh-Hadamard spreading codes, or the long code, currently employed at the base station. For further improvement, the "best" equalizer delay is chosen to minimize the MSE. Theoretically, the MMSE equalizer approaches the RAKE receiver at low SNR and the ZF equalizer at high SNR. Simulation results show that the ZF equalizer's average performance is dominated by a very small percentage of "bad channels" with close to common zeroes, while the MMSE equalizer is resistant to this pathological noise gain problem. The end result is that the MMSE's average BER performance is dramatically better than that of both ZF and RAKE (even though only moderately better than ZF for most well behaved channels).

A novel semi-blind channel identification scheme is proposed for 3G W-CDMA communication systems by using orthogonal transmit diversity where two transmit antennas and one receive antenna are employed. After decomposing the de-spread signals into two independent signals, an equivalent SIMO channel model is obtained. Semi-blind channel identification is then achieved by applying both the cross-relation method and pilot symbols to the derived channel model. This scheme allows one to perform semi-blind channel identification without increasing both the cost and complexity of mobile stations. Simulation results are presented to evaluate the proposed semi-blind channel identification method.

Space-time power minimization pre-processing can exhibit a significant improvement in GPS receiver performance by exploiting spatial and temporal processing techniques. This type of preprocessing however, will require significant computations due to the large dimensionality of the complex valued space-time correlation matrix and will cause some distortion of the PN codes due to temporal processing. To reduce the computational complexity and distortion effects simultaneously, a conjugate symmetry space-time pre-processor has been proposed. It is demonstrated that this pre-processor enhances smoothness across angle and frequency and facilitates the use of real valued space-time correlation matrices in a reduced dimension utilizing the multi-stage nested Wiener filter (MSNWF).

We examine the performance of two linear equalizers for a CDMA downlink over a frequency-selective multipath channel: the traditional RAKE receiver, and a chip-level MMSE (minimum mean square error) equalizer. The mobile-station assumed to be midway between two base-stations. We examine the system performance for one versus two receive antennas, and normal operation versus soft-hand-off mode. MMSE is confirmed to outperform RAKE. Also, having two receive antennas is superior to having a single antenna. Simulation results are presented for uncoded BPSK and 16-QAM, and BPSK with convolutional coding.

In this paper, a novel semi-blind channel identification scheme is proposed for 3G W-CDMA communication systems by using orthogonal transmit diversity where two transmit antennas and one receive antenna are employed. After decomposing the de-spread signals into two independent signals, an equivalent single input multiple output (SIMO) channel model is obtained. Semi-blind channel identification is then achieved by applying both the cross-relation method and pilot symbols to the derived channel model. This scheme allows one to perform semi-blind channel identification without increasing both the cost and complexity of mobile stations. Simulation results are presented to evaluate the proposed semi-blind channel identification method.

This paper extends the traditional Clarke/Jakes (1968, 1974) model for a frequency flat fading process in a land mobile radio system to facilitate the examination of coherent space-time demodulation systems. The work develops a space-time correlation function using a ring of scatterers model around the mobile unit. The resulting correlation function permits the investigation of a variety of issues concerning base station configurations in space-time systems. The interrelationship of the fading process between the space and the time domain is explored. A detailed example regarding the effects of antenna separation in a receiver diversity system is considered. A set of design rules for interleaving depth and antenna separation in a space-time modem is presented and quantified.

In orthogonal frequency-division multiplex (OFDM) communications, the loss of orthogonality due to the carrier-frequency offset must be compensated before discrete Fourier transform-based demodulation can be performed. This paper proposes a new carrier offset estimation technique for OFDM communications over a frequency-selective fading channel. We exploit the intrinsic structure information of OFDM signals to derive a carrier offset estimator that offers the accuracy of a super resolution subspace method, ESPRIT.

In this paper, we propose an algorithm for joint estimation of the angle of arrival (AOA) and delay of each dominant multipath for the desired user for use in a reduced dimension space-time RAKE receiver for DS-CDMA communications that is "near-far" resistant. After we estimate the desired spatio-frequency signal vector, we propose the 2D unitary ESPRIT algorithm as our estimator which provides closed-form as well as automatically paired AOA-delay estimates. We effectively have a single snapshot of 2D data and thus require 2D smoothing for extracting multiple snapshots. The comparative performance of two 2D smoothing schemes, pre-eigenanalysis and post-eigenanalysis 2D smoothing, is discussed. The space-time data model for the IS-95 uplink is presented. The performance of a reduced dimension space-time RAKE receiver for the IS-95 uplink using the AOA-delay estimates is assessed through Monte-Carlo simulations.

We observe that the channel matrix in the standard multiuser, multichannel (MIMO) digital communications model is linear in the channel coefficients. Also, previous work incorporating "basis functions" suggests that the multipath channel itself is in a subspace formed by delayed versions of the transmission pulse. Hence the channel matrix is linear in the coefficients of this subspace. We propose two algorithms based on the sample covariance matrix of the received signal (i.e., second-order statistics) that take advantage of this linear parameterization: a new identification algorithm that estimates the outer product of the model coefficients via multiplication by a predetermined matrix, and a multiuser version of the previously presented "subspace method" that employs knowledge of the transmission pulse. While both methods are superior to the original non-parameterized subspace method in terms of computation and performance, the new method requires less computation and in some cases outperforms the other.

One of the most popular blind equalization techniques is the constant modulus algorithm (CMA), and it has gained popularity in the literature and in practice because of its LMS-like complexity and its robustness to non-ideal, but practical, conditions. Although the CMA has been well-studied in the literature, these analyses have typically implemented the algorithm using "infinite" precision arithmetic. The motivation for this paper is a VLSI implementation of a high data rate, fractionally spaced, linear forward equalizer whose taps are adjusted using the CMA. We examine how implementing the CMA using finite bit precision affects the algorithm's performance.

Pilot symbol assisted modulation (PSAM) is known to provide good performance in estimating the multiplicative distortion of fading channels. The 2-D space-time PSAM is derived and analyzed in this paper by applying the multiple-antenna reception at the base station. The interrelationship between temporal and spatial correlations is shown to provide better channel information than using the temporal correlation solely. The average mean square error (MSE) per antenna and the binary phase shift keying (BPSK) bit error probability (BEP) are used to characterize the performance analytically and draw comparisons with the traditional 1-D PSAM. When 5 antennas are used, the 2-D space-time PSAM has better average performance over the l-D PSAM for about 4 dB of MSE or 1 dB of BPSK BEP.

CDMA communication employing coherent detection with pilot symbol assisted channel estimation significantly outperforms non-coherent detection. In this paper, a semi-blind channel identification method is proposed for third-generation wideband CDMA communication systems, in order to reduce the need for pilot symbols in coherent detection. After an equivalent time-invariant single-input multi-output channel model is created for the de-spreaded signals through employing multiple antennas at the receiver site, both the cross-relation and the pilot symbols are applied to the equivalent linear time-invariant single-input multi-output channel model to derive a semi-blind channel identification solution. Simulations are performed to evaluate the semi-blind channel identification method's applicability to the 3G wideband CDMA communication systems.

A common technique in a blind equalization communication system is to use the constant modulus algorithm (CMA) to open the channel eye and then to switch to decision-directed LMS once the error rate has dropped to a sufficiently low level. The propose a new algorithm, blended CMA, which dynamically selects to use either the CMA or DD-LMS update term when adapting the equalizer taps. The decision rule governing this selection is also adaptive. Simulation results presented in this paper demonstrate how the algorithm performs when equalizing 64-QAM over real-world channels and highlights the performance gain over using traditional transfer methods.

We previously presented a blind 2-D RAKE receiver for CDMA that cancels strong multi-user access interference and optimally combines multipath. The weight vector yielding the optimum signal to interference plus noise ratio for bit decisions is the "largest" generalized eigenvector of the spatio-frequency (spatio-temporal) correlation matrix pencil. However, the eigen-analysis based algorithm is on the order of O(N/sup 3/) computational complexity and the resulting spatio-frequency (spatio-temporal) correlation matrix pencil is of a large dimension. This detracts from the real-time applicability of that scheme. A blind 2-D RAKE receiver is thus presented based on an RLS-type space-time adaptive filtering scheme which offers O(N/sup 2/) computational complexity and competitive performance. The applicability of the scheme to the IS-95 uplink is also addressed as in a decision directed fashion.

This paper introduces a novel closed-form ESPRIT-based algorithm for multi-source direction finding using arbitrarily spaced electromagnetic vector-sensors whose locations need not be known. The electromagnetic vector-sensor, already commercially available, consists of six co-located but diversely polarized antennas separately measuring all six electromagnetic-field components of an incident wavefield. In this novel algorithm, ESPRIT exploits the non-spatial inter-relations among the six unknown electromagnetic-field components of each source and produces from the measured data a set of eigenvalues, from which the source's electromagnetic-field vector may be estimated to within a complex scalar. Application of a vector cross-product operation to this ambiguous electromagnetic-held vector estimate: produces an unambiguous estimate of that source's normalized Poynting-vector, which contains as its components the source's Cartesian direction-cosines. Monte Carlo simulation results verify the efficacy and versatility of this innovative scheme.

A linear receiver for direct-sequence spread-spectrum multiple-access communication systems under the aperiodic random sequence model is considered. The receiver consists of the conventional matched filter followed by a tapped delay line with the provision of incorporating the use of antenna arrays. It has the ability of suppressing multiple-access interference (MAI) and narrowband interference in some weighted proportions, as well as combining multipath components without explicit estimation of any channel conditions. Under some specific simplified channel models, the receiver reduces to the minimum variance distortionless response beamformer, the RAKE receiver, a notch filter, or an MAI suppressor. The interference rejection capability is made possible through a suitable choice of weights in the tapped delay line. The optimal weights can be obtained by straightforward but computationally complex eigenanalysis. In order to reduce the computational complexity, a simple blind adaptive algorithm is also developed.

Provides an abstract for each of the exprt presentations and a brief professional biography of each presenter. The complete presentations were not made available for publication as part of the conference proceedings.

A novel wideband beamforming technique for cellular CDMA systems is presented. The proposed algorithm asymptotically provides the optimum combination of space-time samples to maximize the SINR for the signal with the desired code (SDC) by optimally combining its multipath and canceling strong multiuser access interference (MUAI). In contrast to previously proposed techniques, code synchronization for the SDC is not required. The algorithm presented asymptotically provides the exact time of arrivals of the multipaths within a bit period, and subsequently the optimum space-time weights for combining the fingers across both space and time. The instrumental property exploited in this technique is the fact that although the respective spectra of the SDC and MUAI components at the output of the matched filter are statistically equal, the respective spectra of their squared values differ.

A space-time processing scheme is proposed for TDMA based cellular/PCS communications that cancels co-channel interference while simultaneously equalizing the desired signal. This is achieved through processing of a training signal designed from a PN code. At the receiver, the symbol waveform is built up above the noise and interference through correlation with a sampled waveform designed to exploit the PN code. From this built up signal, interference canceling beams are formed along with estimates of the initial equalizer coefficients. Then a decision directed algorithm is applied to track variations in the multipath channel. Simulations involving three-ray multipath are presented demonstrating the efficacy of the method.

A closed-form multi-dimensional multi-invariance generalization of the ESPRIT algorithm is introduced to exploit the entire invariance structure underlying a (possibly) multiparametric data model, thereby greatly improving estimation performance. The multiple-invariance data structure that this proposed method can handle includes: (1) multiple occurrence of one size of invariance along one or multiple parametric dimensions, (2) multiple sizes of invariances along one or multiple parametric dimensions, and (3) invariances that cross over two or more parametric dimensions. The basic (uni-dimensional uni-invariance) ESPRIT algorithm is applied in parallel to each multiple pair of matrix-pencils characterizing the multiple invariance relationships in the data model, producing multiple sets of cyclically ambiguous estimates over the multi-dimensional parameter space. A weighted least-squares hyper-plane is then fitted to these set of estimates to yield very accurate and unambiguous estimates of the signal parameters.

A novel sparse array geometry embedding two sizes of spatial invariances is proposed for extended-aperture spatial diversity using a new ESPRIT-based algorithm. This novel direction-finding method extends the array aperture without additional antennas, irregular inter-element spacings, nor any cyclic ambiguity in the final arrival angle estimates. The half-wavelength invariance yields unambiguous but high-variance DOA estimates to disambiguate low-variance but cyclically ambiguous estimates obtained using the larger invariance. This novel approach facilitates (1) multipath de-correlation (independent fading), (2) coherent summation of multipaths from the same source, and (3) down-link beamforming from the base-station to the mobile. Under one simulation scenario involving two closely spaced time-delayed multipaths in frequency-selective slow-fading, the proposed algorithm offers an impressive 80% reduction in the standard deviation and bias. Any additional computation needed by this method may be performed in parallel, thereby requiring no serious increase in the overall computational time.

An algorithm is presented for estimating the quantities needed by a space-time RAKE receiver for DS-CDMA to achieve maximum SINR for the desired user. The proposed algorithm, which is applicable in the case of either periodic or aperiodic spreading codes, asymptotically provides the exact time of arrival of each dominant multipath within a bit period, and the optimum beamformer for extracting each multipath. This is achieved by using cyclostationarity to exploit the difference between the respective spectra of the desired user and each multiuser access interferer at the output of the correlator based on the desired user's code. Estimates of the relative time delay and optimal beamformer for each RAKE finger are used by the space-time RAKE receiver to optimally combine the desired user's multipath while simultaneously canceling strong multiuser access interference. Simulations of a near-far scenario are presented demonstrating the efficacy of the proposed algorithm.

We discuss a new approach to self-organization that leads to novel adaptive algorithms for generalized eigen-decomposition and its variance for a single-layer linear feedforward neural network. First, we derive two novel iterative algorithms for linear discriminant analysis (LDA) and generalized eigen-decomposition by utilizing a constrained least-mean-squared classification error cost function, and the framework of a two-layer linear heteroassociative network performing a one-of-m classification. By using the concept of deflation, we are able to find sequential versions of these algorithms which extract the LDA components and generalized eigenvectors in a decreasing order of significance. Next, two new adaptive algorithms are described to compute the principal generalized eigenvectors of two matrices (as well as LDA) from two sequences of random matrices. We give a rigorous convergence analysis of our adaptive algorithms by using stochastic approximation theory, and prove that our algorithms converge with probability one.

Simultaneous estimation of the azimuth and elevation arrival angle of each of a number of co-channel signals incident upon an array of antennas is addressed. A new closed-form algorithm that works for filled circular arrays (FCAs) with any sampling lattice is developed. Although based on TLS-ESPRIT, the algorithm does not require arrays exhibiting translational symmetry. The only constraint imposed on the array for the algorithm to perform properly is that the spacing between adjacent sensors across the aperture be roughly a half-wavelength or less on average. A set of ESPRIT-like equations with unknowns are of the form sin(/spl theta//sub i/)e/sup j/spl phi/i/, where /spl theta//sub i/ and /spl phi//sub i/ are the elevation and azimuth of the i-th source, respectively, is constructed by means of linear combinations of the received signals exploiting a recurrence property satisfied by Bessel functions. Simulations verifying the efficacy of the algorithm in conjunction with rectangular, hexagonal, polar raster, and random sampling lattices have been performed. An illustrative simulation is presented and compared with performance predicted by theoretical analysis.

A novel ESPRIT-based 2D angle estimation scheme is proposed involving the use of a right-triangular array of three vector sensors spaced much farther apart than a half-wavelength. A vector sensor is composed of six co-located antennas distinctly measuring all six electromagnetic field components of a multi-component incident wavefield. Information on each source's respective electromagnetic field components is obtained by decoupling the signal eigenvectors via lower dimensional eigenvectors derived from TLS-ESPRIT. This facilitates estimation of each source's respective Poynting vector thereby enabling one to resolve the phase ambiguities in ESPRIT's eigenvalues when the intervector-sensor spacing is greater than a half-wavelength. Simulations are presented showing the sample variance of the direction cosine estimates decreasing linearly on a log-log scale as the intervector-sensor spacing is increased from a half-wavelength to 30 wavelengths, with a factor of 80 reduction in the latter case relative to the former case. The proposed scheme and attendant vector sensor array also outperform a uniformly-spaced array of scalar sensors with the same aperture and same number of component antennas whenever the intervector sensor spacing in the former case is greater than 3 half-wavelengths.

We previously presented a blind 2D RAKE receiver for CDMA that cancels strong multi-user access interference and optimally combines multipath. After passing the output of each antenna through a matched filter based on the spreading waveform of the desired user, one estimates the signal plus interference spatio-frequency correlation matrix during that portion of the bit interval where the fingers of the RAKE occur, and the interference alone spatio-frequency correlation matrix during that portion of the bit interval away from the fingers. The weight vector yielding the optimum signal to interference plus noise ratio for bit decisions is the "largest" generalized eigenvector of the resulting matrix pencil. However, even when the number of elements comprising the array is relatively small, this spatio-frequency correlation matrix pencil is of large dimension. In addition to detracting from the real-time applicability of the scheme, this slows up the time to convergence. A reduced complexity scheme is presented based on a data adaptive transformation to a beamspace of dimension equal to the effective number of spatial degrees of freedom taken up by the desired user's multipath.

We are developing a new graduate program at Purdue in Video and Image Systems Engineering (VISE). The project is comprised of three parts: a new curriculum centered around a degree option in VISE to be earned as part of the Masters or Ph.D. degrees; a state-of-the-art lecture/laboratory facility for instruction, laboratory experiments, and project and homework activities in VISE courses; and enhancement of existing courses and development of new courses in the VISE area.

The 2D DFT beamspace ESPRIT is an algorithm for use in conjunction with uniform rectangular arrays (URAs) that provides automatically paired azimuth and elevation angle estimates of incident signals via a closed-form procedure. We investigate the statistical performance of 2D DFT beamspace ESPRIT. Expressions for the 2D DFT beamspace ESPRIT estimator variances are obtained. Samples variances of the azimuth and elevation angle estimates obtained through Monte Carlo simulations are shown to be in close agreement with theoretically predicted variances.

Considers multiple narrowband signals that are incident upon a planar sensor array. 2D unitary ESPRIT is a new closed-form high resolution algorithm to provide automatically paired source azimuth and elevation angle estimates along with an efficient way to reconstruct the impinging signals. In the final stage of the algorithm, the real and imaginary parts of the ith eigenvalue of a matrix are one-to-one related to the respective direction cosines of the ith source relative to the two array axes. 2D unitary ESPRIT offers several advantages over other ESPRIT based closed-form 2D angle estimation techniques. First, except for the final eigenvalue decomposition of dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Second, it is amenable to an efficient DFT beamspace implementation. Third, it is also applicable to array configurations that do not exhibit three identical subarrays, as long as the array is centro-symmetric and possesses invariances in two distinct directions. Finally, 2D unitary ESPRIT easily handles sources having one member of the spatial frequency coordinate pair in common.

The problem addressed is that of narrowband digital cellular communications in the presence of multipath and co-channel interferers having the same symbol rate and same overall signal characteristics as the desired source. For a given signal source, an algorithm is presented for blindly estimating the weight vector yielding the optimum SINR at the beamformer output. The instrumental quantity, denoted S/sub xx/(f), is the Fourier transform of the expected value of the zero-lag autocorrelation matrix for one symbol period. The proposed scheme employs the PRO-ESPRIT algorithm to exploit the relationship between the timing offset and optimum beamforming weight vector for each source and the principal generalized eigenvalues and eigenvectors of the matrix pencil.

The new approach to undergraduate DSP education at Purdue is based on a simple idea: emphasize applications. Students are assumed to have a significant exposure to sampling and discrete-time signals, systems, and transforms at the junior level. In the senior course, the traditional DSP topics of digital filter design, the DFT, radix-2 FFT's, and quantization are covered in the first five weeks of the semester. Coverage of these topics is augmented by treatment in the laboratory component of the course using diverse software tools and by Matlab based homework assignments. The remainder of the course is devoted to treating the topics of speech processing and image processing in substantial depth and involves a design project. The course has been very successful in terms of increasing enrolment and outstanding student evaluations.>

A novel implementation of Root-MUSIC is introduced based on the observation that the MUSIC null spectrum created with a beamspace noise eigenvector is bandpass exhibiting nulls at the locations of in-band sources. Thus, after telescoping to element space and modulating to broad-side, the telescoped noise eigenvector may be decimated yielding a small order polynomial with the separation between signal roots increased by the decimation factor. Depending on the out-of-band response of the beamformers, the telescoped noise eigenvector may be passed through a lowpass filter prior to decimation to preserve in-band source nulls. A low cost algorithm is realized by invoking linearity and performing the modulation, filtering, and decimation operations a-priori on the beamformers yielding a transformation to be applied to the beamspace noise eigenvectors.>

A novel implementation of Root-MUSIC is introduced based on the observation that the MUSIC null spectrum created with a beamspace noise eigenvector is bandpass exhibiting nulls at the locations of in-band sources. Thus, after telescoping to element space and modulating to broadside, the telescoped noise eigenvector may be decimated yielding a small order polynominal with the separation between signal roots increased by the decimation factor. Depending on the out-of-band response of the beamformers, the telescoped noise eigenvector may be passed through a lowpass filter prior to decimation to preserve in-band source nulls. A low cost algorithm is realized by invoking linearity and performing the modulation, filtering, and decimation operations a priori on the beamformers yielding a simple transformation to be applied to the beamspace noise eigenvectors.>

Beamspace root-MUSIC is a computationally efficient, beamspace implementation of root-MUSIC developed recently for use in conjunction with a uniform linear array. Using B real-valued beams having all but B-1 nulls in common, the major computations in beamspace root-MUSIC are a B*B real-valued eigenvalue decomposition and the rooting of a polynomial of order B-1. Recently, beamspace root-MUSIC was adapted for use in conjunction with a uniform circular array (UCA) using the interpolated array concept of Friedlander. An alternative means of using beamspace root-MUSIC with a UCA based on the concept of phase mode excitation is developed.>

A computationally efficient beamspace implementation of Root-MUSIC is developed. The algorithm exploits the common out-of-band nulls property exhibited by discrete Fourier transform (DFT) beams. For each set of B successive DFT beams encompassing a given spatial sub-band, the major computations are an eigenvalue decomposition of the real part of the B*B beamspace sample correlation matrix and the rooting of a polynomial of order 2B-2. Virtual tapering is effected by summing weighted DFT beams to yield reduced out-of-band sidelobes while retaining the common out-of-band nulls property. Experimental results are presented involving data obtained from an N=32 element uniformly-spaced, linear array operating at X-band.>

Summations of cumulants (projections) along parallel lines in the cumulant domain are formed. The projection procedure first relies on a change of variables through rotation of the cumulant axes. The cumulants are effectively decoupled. Summing the cumulants reduced the dimensionality of the system from six cumulant terms to one term. An eigenstructure-based method for frequency and biphase estimation is offered as an alternative to Fourier schemes on the slice after biphases have been converted to estimable amplitudes by forming symmetric and skew-symmetric projections.>

A novel algorithm for sensor array signal processing and spatial source parameter estimation, referred to as the method of simultaneous rotations, is introduced. The algorithm is in the same genre as the recently proposed ESPRIT algorithm, which works with two identical arrays, an X array and a Y array. A major tenet of the originality of the new approach is that it treats the X and Y data matrices as a rectangular matrix pencil and uses the fact that they have the same row space, the source subspace, as well as the same column space, the signal subspace. A novel technique for reducing the problem to that of solving the eigensystem of a square matrix pencil of dimension equal to the number of sources is developed, based on the solution to the Procrustes problem for optimally performing an invariant subspace rotation. Refinements to the algorithm invoking the total-least-squares concept are also presented for the purpose of further exploiting the similarity in structure between the X and Y data matrices.>

Two methods are developed for computing the generalized eigenvalues and eigenvectors associated with the matrix pair{A,B}, where A and B are singular hermitian matrices with the range space of A a subset of the range space of B. Conventional methods of solution break down for this case. An application is described based on the recently reported Estimation of Signal Parameters by Rotational Invariance Techniques (ESPRIT) algorithm. ESPRIT possesses remarkable advantages over other high-resolution direction-of-arrival estimation algorithms in terms of speed, storage, and indifference to array calibration.

Two methods are developed for computing the generalized eigenvalues and eigenvectors associated with the matrix pair {A, B}, where B is a singular Hermitian matrix and A is a matrix, not necessarily Hermitian, the range space of which is a subset of the range space of B. Conventional methods of solution break down for this case. An application is described based on the recently reported ESPRIT algorithm, a method of high-resolution direction-of-arrival estimation.