We adopt a stochastic geometry-based model for the distribution of satellites in a constellation, and we investigate the distance and outage properties of these satellites, relative to a ground user, with respect to their order after they are ordered according to their distance from the user.

The industry standard for single-track detection in magnetic recording is partial-response equalization followed by a trellis-based sequence detector. We extend for the first time the partial-response paradigm to the case of multitrack detection when the multiple tracks being jointly detected were written asynchronously, with different bit phases and bit rates. We propose a multiple-input multiple-output (MIMO) partial-response equalizer that equalizes the unsynchronized samples of the multiple readback waveforms to a time-varying MIMO target, thereby enabling a trellis-based rotating-target (ROTAR) detector that accounts for the asynchrony. We evaluate the proposed equalization strategy on a two-dimensional magnetic-recording channel, and find that the proposed receiver outperforms a conventional receiver that detects one track at a time, by a 30% reduction in the bit-error rate, and that it closely matches the performance of a fictitious system in which the tracks are perfectly synchronous.

The industry standard for single-track detection in magnetic recording is partial-response equalization followed by a trellis-based sequence detector. We extend for the first time the partial-response paradigm to the case of multitrack detection when the multiple tracks being jointly detected were written asynchronously, with different bit phases and bit rates. We propose a multiple-input multiple-output (MIMO) partial-response equalizer that equalizes the unsynchronized samples of the multiple readback waveforms to a time-varying MIMO target, thereby enabling a trellis-based sequence detector that is based on the resulted time-varying target to account for the asynchrony. We evaluate the proposed equalization strategy on a two-dimensional magnetic-recording channel, and find that the proposed receiver outperforms a conventional receiver that detects one track at a time, and that it closely matches the performance of a fictitious system in which the tracks are perfectly synchronous.

The granular nature of the recording medium in magnetic recording leads to a type of noise known as media noise; it arises because each magnetic grain can take on only one of two polarities, which causes the boundary of each written bit to be random in shape, coinciding with the boundaries of the randomly sized grains. A key feature of media noise is that it depends on the data being written, and in particular is more pronounced in the vicinity of bit transitions. A widely used strategy for mitigating media noise in a trellis-based detector is pattern-dependent noise prediction (PDNP); in this approach, each bit pattern (which determines a trellis branch) will have its own set of branch metric parameters (including the signal levels, noise predictor coefficients, and residual variances). Traditionally these detector parameters are chosen according to some form of a minimum-mean-squared-error (MMSE) criterion. In this paper, we propose the adaptive minimum-bit-error rate (AMBER) algorithm for adapting these pattern-dependent parameters with the aim of minimizing BER. The AMBER algorithm updates the parameters whenever the add-compare-select operation in the Viterbi detector selects an incorrect path instead of the correct path; the parameters are then updated so as to increase the metric of the incorrect path, and reduce the metric of the correct path. Numerical results based on a set of quasi-micromagnetic simulated channel waveforms show that the AMBER PDNP detector provides at least a 20% BER decrease and an 8% increase in areal density over a traditional MMSE PDNP detector.

The advent of multiple readers in magnetic recording opens the door to multitrack detection, in which multiple tracks are detected jointly. Multitrack detection is a key enabler for both coding across tracks (including modulation and error-control codes) and crosstrack noise prediction, neither of which can be fully exploited using single-track detectors. In this paper, we propose the two-dimensional pattern- dependent noise-prediction (2D-PDNP) algorithm as a solution to the joint maximum-likelihood multitrack detection problem in the face of pattern-dependent autoregressive Gaussian noise. The solution takes the form of the Viterbi algorithm over a trellis that models the combined memory of the channel and noise, with a branch metric that can be interpreted as 2D pattern- dependent noise prediction, where noise is predicted in both downtrack and crosstrack directions, taking into account transitions occurring in both downtrack and crosstrack directions. Numerical results show that, on a set of quasi-micromagnetic simulated channel waveforms with a pair of readers and a multitrack detector detecting two tracks simultaneously, the 2D-PDNP algorithm provides a 4% increase in areal density.

This paper addresses the problem of weighted sum rate (WSR) maximization in dense wireless networks with cooperative access points (APs) subject to a per-AP power constraint. We propose a combined optimization procedure that performs both user selection and MIMO weight calculation and scales well as the number of users increases. User selection eliminates some undesirable users, while MIMO weight calculation determines the precoders and combiners for all active nodes. A new performance metric, which takes into account available power, channel quality and orthogonality, and user weights, is used to perform an initial phase of user selection. A WSR maximization algorithm is then executed to optimize MIMO weights of selected users. The proposed algorithm includes additional user selection, i.e. certain users not eliminated in the first phase will be assigned zero-power stream during its execution. Numerical results show that our proposed algorithm achieves about 25% higher aggregate performance than the best existing algorithm while having a substantially lower running time. In fact, the running time is nearly constant as the number of users increases due to the very fast initial user selection phase.

A bottleneck in multiple-input multiple-output communications systems is the complexity of detection at the receiver. The complexity of optimum maximum-likelihood detection is often prohibitive, especially for large numbers of antennas and large alphabets. A suboptimal tree-search-based detector known as the K-best detector is an effective scheme that provides a flexible performance-complexity tradeoff. In this paper, we identify scalar list detection as a key building block of the K-best detector, and we propose an efficient low-complexity implementation of the scalar list detector for M-ary QAM using a slicing operation. Embedding the slicing list detector into the K-best framework leads to our proposed slicing K-best detector. Simulation results show that the proposed detector offers comparable performance to the conventional K-best detector, but with significantly reduced complexity when K is less than the QAM alphabet size M. Since the slicing list detection is performed at each visited node in the detection tree, the complexity reduction is especially significant when the number of antennas and the alphabet size are large, making the proposed detector a competitive option for high spectral-efficiency wireless systems.

Two-dimensional magnetic recording promises to increase areal density through the joint detection of multiple tracks of interest. This paper concerns the problem of joint detection of multiple tracks that are written asynchronously, meaning that neither the bit boundaries (phase) nor the bit rate (frequency) are aligned between neighboring tracks. We propose the rotating-target (ROTAR) algorithm for jointly detecting multiple asynchronous tracks from one or more readback waveforms. The proposed approach is based on the joint Viterbi algorithm and a time-varying target that results when the asynchrony of the tracks is absorbed into the underlying target. Timing estimation for the tracks being detected is embedded inside the joint Viterbi detector using per-survivor processing. Performance results show that the proposed algorithm closely matches the performance of a fictitious system in which neighboring tracks are synchronous, and further that it significantly outperforms a previously reported detector that separately detects the two tracks.

Two-dimensional magnetic recording promises to increase areal density through the joint detection of multiple tracks of interest. This paper concerns the problem of joint detection of multiple tracks that are written asynchronously, meaning that neither the bit boundaries (phase) nor the bit rate (frequency) are aligned between neighboring tracks. We propose the rotating-target algorithm for jointly detecting multiple asynchronous tracks from one or more readback waveforms. The proposed approach is based on the joint Viterbi algorithm and a time-varying target that results when the asynchrony of the tracks is absorbed into the underlying target. Timing estimation for the tracks being detected is embedded inside the joint Viterbi detector using per-survivor processing. Performance results show that the proposed algorithm closely matches the performance of a fictitious system in which neighboring tracks are synchronous, and further that it significantly outperforms a previously reported detector that separately detects the two tracks.

We propose an algorithm whose goal is to maximize the sum rate of a set of interfering multiple-input multiple-output (MIMO) links by jointly optimizing which subset of transmitters should transmit, the number of streams for each transmitter (if any), and the beamforming and combining weights that support those streams. We present numerical results to illustrate that our algorithm achieves a sum rate higher than previously reported algorithms at high interference, and that it achieves comparable performance to the top-performing algorithms at medium and low interference. In one high-interference example with many links, our algorithm achieves a 65% higher sum rate than previously reported algorithms.

We analyze the general form of the extrinsic information transfer curve of polar codes viewed as multilevel codes with multistage decoding. Based on this analysis, we propose a graphical design methodology to construct polar codes for intersymbol interference channels. The method matches the extrinsic information transfer curve of the code to that of the intersymbol interference channels, so that there is an open convergence tunnel between the two. We show that polar codes can provide such a matching to the channel curve under soft-cancellation decoding and propose one such method to achieve it. Example code designs are presented to demonstrate that polar codes that are optimized for an ISI channel can significantly outperform polar codes that are designed for an AWGN channel.

The state-of-the-art soft-output decoder for polar codes is a message-passing algorithm based on belief propagation, which performs well at the cost of high processing and storage requirements. In this paper, we propose a low-complexity alternative for soft-output decoding of polar codes that offers better performance but with significantly reduced processing and storage requirements. In particular we show that the complexity of the proposed decoder is only 4% of the total complexity of the belief propagation decoder for a rate one-half polar code of dimension 4096 in the dicode channel, while achieving comparable error-rate performance. Furthermore, we show that the proposed decoder requires about 39% of the memory required by the belief propagation decoder for a block length of 32768.

In this paper, we study the performance of hybrid automatic repeat request (HARQ) with incremental redundancy over double Rayleigh channels, a common model for the fading amplitude of vehicle-to-vehicle communication systems. We investigate the performance of HARQ from an information theoretic perspective. Analytical expressions are derived for the e-outage capacity, the average number of transmissions, and the average transmission rate of HARQ with incremental redundancy assuming a maximum number of HARQ rounds. Moreover, we evaluate the delay experienced by Poisson arriving packets for HARQ with incremental redundancy. We provide analytical expressions for the expected waiting time, the packet's sojourn time in the queue, the average consumed power, and the energy efficiency. In our study, the communication rate per HARQ round is adjusted to the average signal-to-noise ratio (SNR) such that a target outage probability is not exceeded. This setting conforms with communication systems in which a quality of service is expected regardless of the channel conditions. Our analysis underscores the importance of HARQ in improving the spectral efficiency and reliability of communication systems. We demonstrate as well that the explored HARQ scheme achieves full diversity. Additionally, we investigate the tradeoff between energy efficiency and spectral efficiency.

We propose an algorithm to allocate streams and find the corresponding beamforming and combining weights that maximize the sum rate of a set of interfering multiple-input multiple-output (MIMO) links. Our algorithm iteratively computes the beamforming and combining weights of each link and determines how many streams, if any, are allocated to each link. Assigning zero streams to a link is desirable whenever the interference introduced by activating that link outweighs the throughput contributed by the link. We present numerical results to illustrate that our algorithm achieves a sum rate higher than previously reported algorithms at high interference, and that it achieves similar performance to the top-performing algorithms at medium and low interference. In one high-interference example with many links, our algorithm achieves a 65% higher sum rate than the best-known alternative.

A widely used soft-output decoder for polar codes is a message-passing algorithm based on belief propagation, which performs well at the cost of high processing and storage requirements. In this paper we propose a low-complexity alternative for soft-output decoding of polar codes that offers comparable performance but with significantly reduced processing and storage requirements. In particular we show that the complexity of the proposed decoder is about 5% of the total complexity of the belief propagation decoder for the dicode channel, while achieving comparable error-rate performance. Furthermore, we show that the proposed decoder requires about 39% of the memory required by the belief propagation decoder for a block length of 32768.

We describe an error-correcting system that combines polar codes with turbo equalization for partial response channels. The successive cancellation decoder, originally proposed by Arikan for polar codes, does not produce the soft outputs needed for turbo processing. The belief propagation decoder, on the other hand, requires many iterations and has high computational complexity. In this paper, we propose a soft-input soft-output variant of the successive cancellation decoder that produces the soft information required for turbo architectures, while keeping the computational complexity low. Numerical results show that the proposed decoder performs better than the hard-output successive cancellation decoder and the belief propagation decoder in the context of turbo equalization. The proposed decoder achieves this performance gain with lower complexity compared to belief propagation and maximum-likelihood decoders. Additionally, we prove that Arikan's successive cancellation decoder is a fast-polarizing instance of our soft-input soft-output successive cancellation decoder.

We tackle the problem of determining the beamforming and combining weights in a network of interfering multiple-input multiple-output (MIMO) links. We classify any strategy for computing these weights as either unilateral or bilateral. A unilateral strategy is one for which the responsibility of cancelling interference from one node to another is preassigned to lie solely with only one of the two nodes, so that the other node is free to ignore the interference. Many existing strategies for managing interference in a network of MIMO nodes adopt the unilateral approach. In contrast, a bilateral strategy is one for which the responsibility of cancelling interference from one node to another is not preassigned, but is instead shared by both sides as the weights are computed. We present numerical examples to illustrate that bilateral strategies can significantly outperform unilateral strategies, especially for large networks and high interference. In one example, a bilateral approach delivers an aggregate capacity that is 227% higher than that of the best unilateral approach. We conclude that, although unilateral strategies are useful for determining whether or not the streams allocated in a network of MIMO links can coexist, the weight computation should be done bilaterally to prevent throughput loss.

In this paper, we study the performance of hybrid automatic repeat request (HARQ) with incremental redundancy (IR) over double Rayleigh channels. Such channels can be used to model the fading amplitude for vehicle-to-vehicle (V2V) communications. We study the performance of HARQ from an information theoretic perspective. Analytical expressions are derived for the e-outage capacity, the average number of trans missions, and the average transmission rate for HARQ with IR, assuming a maximum number of rounds for the HARQ protocol. In our study, the communication rate per HARQ round is adjusted to the average signal-to-noise ratio (SNR) such that a target outage probability is not exceeded. This setting conforms with communication systems in which a quality of service is expected regardless of the channel conditions. It is well known that the ergodic capacity is achievable only if the power is adapted to the channel conditions, which requires channel state information (CSI) at the transmitter. We demonstrate that HARQ allows to communicate at a rate close to the ergodic capacity even in absence of CSI at the transmitter. Our analysis underscores the importance of HARQ in improving the spectral efficiency and reliability of communication systems.

Because each golden code codeword conveys four information symbols from an M-ary QAM alphabet, the complexity of an exhaustive-search decoder is proportional to M4. In this paper we prove that the golden code is fast-decodable, meaning that maximum-likelihood decoding is possible with a worst-case complexity proportional to only M2.5. The golden code retains its fast-decodable property regardless of whether the channel varies with time. We also present an efficient implementation of a fast maximum-likelihood decoder that exhibits a low average complexity.

We propose a new family of high-rate space-time block codes called embedded orthogonal space-time (EOS) codes. The family is parameterized by the number of transmit antennas, which can be any positive integer, and by the rate, which can be as high as half the number of transmit antennas. The proposed codes are based on a new concept called embedding, whereby information symbols of a traditional space-time code are replaced by codewords from a second space-time code. The EOS codes use orthogonal designs as this second code, which induces orthogonality in an effective channel matrix and leads to reduced-complexity decoding. The EOS codes have lower decoding complexity than previously reported space-time codes for any number of transmit antennas, and for any rate. Furthermore, simulation results show that the EOS codes outperform previous constructions for certain number of antennas and certain rates, when performance is measured by error probability in quasistatic Rayleigh fading.

This paper presents the field-programmable gate array (FPGA) implementation of a variant of the Lenstra-Lenstra-Lovasz (LLL) lattice reduction (LR) algorithm, known as the Clarkson's Algorithm (CA), and its application to uncoded multiple input-multiple output (MIMO) detection. The CA provides practically the same performance as the LLL algorithm while having a considerably lower complexity, especially for MIMO systems with a large number of transmit and receive antennas. The algorithm has been implemented in real-time using a rapid prototyping methodology, greatly reducing its development time. Implementation results indicate that the variable complexity and the sequential nature of LR algorithms, like the CA, remain their main drawbacks from an implementation point of view.

Soft-output detection of the golden code is an important but computationally difficult task. We propose a low-and fixed-complexity soft-output detector for the golden code that uses linear equalization to simplify the task of finding a list of candidate values for one pair of information symbols, and then - for each pair on the list - it uses decision-feedback equalization to find candidate values for the remaining pair of information symbols. We propose a simple ordering algorithm that exploits the golden code's structure to ensure that the overall algorithm performs well. Numerical results indicate that the proposed algorithm is significantly less complex than previously reported algorithms, yet performs comparably.

Over the last two decades, wireless communications has gained enormous popularity, offering attractive options for many personal and organizational communication needs due to major intrinsic characteristics such as flexibility, cost effectiveness, and mobility.

Three desirable properties of a four-antenna spacetime block code are full rate, full diversity, and single-symbol decodability. Previously reported space-time codes that achieve all three properties do so at the expense of the peak-to-average power ratio (PAPR). A fourth desirable property of a space-time block code is that its PAPR be the same as that of the underlying quadrature-amplitude modulation alphabet. In this letter we introduce space-time codes for three and four transmit antennas that achieve all four properties; these codes use a diversity technique based on constellation stretching. Numerical results for quasistatic Rayleigh-fading channels show that, despite their low PAPR, the proposed codes are comparable in SNR performance to the best-performing single-symbol decodable space-time codes for three and four transmit antennas.

The golden code is a full-rate full-diversity space-time code for two transmit antennas that has a maximal coding gain. Because each codeword conveys four information symbols from an M-ary QAM alphabet, a maximum-likelihood decoder based on a conventional sphere detector has a worst-case complexity of M4. In this paper we present a new algorithm for maximum-likelihood decoding of the golden code that has a worst-case complexity of only 2M3. We thus prove that the golden code is fast decodable, a fact that has evidently been overlooked in prior work. Furthermore, in contrast to the overlaid Alamouti codes, which are fast decodable on quasistatic channels but not on time-varying channels, the golden code is fast decodable on both quasistatic and rapid time-varying channels.

Consider a communications system where the detector generates a mix of hard and soft outputs, which becomes fed to a soft-input channel decoder. In such a setting, it is of interest to find the optimal soft representation for the hard detected bits, which minimizes the probability of error at the decoder output. In this contribution we prove that for repetition codes transmitted over the AWGN channel using antipodal signaling, the optimal soft representation is given by the error probability at the detector output. This provides an indication of how "LLR clipping levels" should be chosen, e.g., in the context of list based detection of multiple-input multiple-output (MIMO) signals.

Suboptimal detection schemes, such as list MIMO detection, often face the challenge of having to ldquoguessrdquo at the decision reliability for some of the detected bits. A simple yet effective way of doing this is to set the maximum magnitudes of the associated log-likelihood-ratios (LLRs) to a certain predefined value: LLR clipping. However, the choice of the clipping level has a significant impact on the system performance. A majority of prior approaches attempted to determine appropriate clipping levels by manual optimization. In this work we propose to use an SNR-aware approach for calculating the LLR clipping levels in list MIMO detection. The proposed scheme exploits knowledge of the channel state information to determine the instantaneous bit error probability of the list detector, and from this an appropriate level for clipping of the LLRs. Simulation results show that this strategy outperforms schemes using a fixed clipping level.

Three desirable properties of a four-antenna space-time block code are full rate, full diversity, and single-symbol decodability. Previously reported space-time codes that achieve all three properties do so at the expense of the peak-to-average power ratio (PAPR). A fourth desirable property of a space-time block code is that its PAPR be the same as that of the underlying quadrature-amplitude modulation alphabet. In this paper we introduce space-time codes for three and four transmit antennas that achieve all four properties; these codes use a diversity technique based on constellation stretching. Numerical results for quasistatic Rayleigh-fading channels show that the proposed codes are comparable in SNR performance to the best-performing single-symbol decodable space-time codes for three and four transmit antennas.

The fifteen articles in this special issue are devoted to new equalization techniques for wireless communications, including new the latest theories and applications.

Orthogonal-frequency-division multiplexing (OFDM) transforms a frequency-selective multiple-input multiple-output (MIMO) fading channel into a MIMO-OFDM channel that has a well-defined outage capacity. A transmitter with channel knowledge can achieve this capacity by a combination of eigenbeamforming and water-filling; the eigenbeamforming transforms the MIMO-OFDM channel into a parallel bank of scalar channels, and the water-filling procedure optimally allocates rate and energy to the scalar channels - a form of adaptive modulation. This paper shows that the water-filling procedure is not necessary to approach the zero-outage capacity of the MIMO-OFDM channel; it is sufficient instead to use a combination of eigenbeamforming and a fixed (nonadaptive) rate allocation. The fixed allocation depends only on the statistics of the channel and is independent of the particular channel realization. This paper proves that the capacity penalty incurred by the fixed allocation approaches zero as the number of antennas grows large. Numerical results indicate that the convergence is fast; for example, the fixed allocation suffers an SNR penalty of less than 0.2 dB for a 6-input 6-output Rayleigh-fading MIMO-OFDM channel at 8 bits per signaling interval, when the channel is assumed to be uncorrelated between antennas and between channel taps. A main conclusion is that eigenbeamforming is the most valuable way to exploit knowledge of the channel at the transmitter, and that any subsequent adaptive modulation has minimal relative value.

We propose a new cooperation protocol for the fading multiple-access channel called space-division relay (SDR). It is similar to the protocol of Laneman, Tse and Wornell (LTW), except that the relays use space- division instead of time-division multiplexing. The result is a nonorthogonal cooperation protocol with a higher rate that nevertheless achieves the full diversity of the two-user Rayleigh-fading cooperative multiple-access channel, a result that is proven in this paper. We examine the SDR protocol with two types of relays: the amplify-and- forward (AF) relay and the amplify/decode-and-forward (ADF) relay. We derive the outage probability of the proposed scheme with AF relays. We present numerical results for the two-user channel at 1 bps/Hz which show that SDR-ADF outperforms all previously reported cooperative schemes. In particular, in terms of the SNR required to achieve a 10-3outage probability, the SDR-AF protocol outperforms the LTW-AF protocol by 1.9 dB, while the SDR-ADF protocol outperforms another non- orthogonal protocol called NAF [4] by 1 dB, falling only 2.3 dB short of the ideal cooperation bound.

The BLAST-ordered decision-feedback (BODF) detector is a nonlinear detection strategy for multiple-input multiple-output (MIMO) channels that can significantly outperform a linear detector. However, for some applications even the BODF detector is too complex. We propose the partial decision-feedback (PDF) detector, a stripped-down version of the BODF detector that only feeds back one decision. The PDF detector performs close to the BODF detector, with complexity comparable to the linear detector. For example, over a 3-input 3-output Rayleigh-fading channel with 64-QAM inputs, the PDF detector is 21% less complex than the BODF detector, yet requires only 0.3 dB more average signal energy to reach a bit-error rate of 10-3

Lattice basis reduction is a powerful technique that enables a hard-output detector for a multiple-input multiple-output channel to approach maximum-likelihood performance with low complexity. In this work we propose a soft-output detector that combines lattice- reduction-aided detection and list decoding. The proposed algorithm performs nearly as well as the list-sphere detector but with much lower complexity. Numerical results reveal that the complexity per bit for the proposed algorithm decreases as the size of the QAM alphabet increases.

The complexity of a turbo equalizer based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is manageable only for mildly dispersive channels having a small amount of memory. To enable turbo equalization of highly dispersive channels, we propose the soft-feedback equalizer(SFE). The SFE combines linear equalization and soft intersymbol-interference cancellation. Its coefficients are chosen to minimize the mean-squared error(MSE) between the equalizer output and the transmitted sequence, under a Gaussian approximation to the a priori information and the SFE output. The resulting complexity grows only linearly with the number of coefficients, as opposed to the quadratic complexity of previously reported minimum-MSE structures. We will see that an SFE-based turbo equalizer consistently outperforms another structure of similar complexity, and can outperform a BCJR-based scheme when complexity is taken into account.

We consider the problem of timing recovery for bandlimited, baud-rate sampled systems with intersymbol interference and a timing offset that can be modeled as a combination of a frequency offset and a random walk. We first derive the Cramer–Rao bound (CRB), which is a lower bound on the estimation-error variance for any timing estimator. Conventional timing recovery is based on a phase-locked loop (PLL). We compare the conventional timing recovery method with the CRB for realistic timing parameters for the magnetic recording channel, and observe a 7 dB signal-to-noise ratio gap between the two. Next, we propose a PLL postprocessor based on the maximum a posteriori estimation principle that performs to within 1.5 dB of the CRB. This postprocessor performs time-invariant filtering and time-varying scaling of the PLL timing estimates. The refined timing estimates from the postprocessor are then used to get refined samples by interpolating the samples taken at the PLL's timing estimates. Finally, we present suboptimal implementations that allow a performance-complexity tradeoff.

We consider the problem of timing recovery for bandlimited, baud-rate sampled systems with intersymbol interference and a timing offset that can be modeled as a combination of a frequency offset and a random walk. We first derive the Crameacuter-Rao bound (CRB), which is a lower bound on the estimation error variance for any timing estimator. Conventional timing recovery is based on a phase-locked loop (PLL). We compare the conventional timing-recovery method with the CRB for realistic timing parameters for the magnetic recording channel, and observe a 7 dB signal-to-noise ratio gap between the two. Next, we propose a PLL postprocessor based on the maximum a posteriori estimation principle that performs to within 1.5 dB of the CRB. This postprocessor performs time-invariant filtering and time-varying scaling of the PLL timing estimates. The refined timing estimates from the postprocessor are then used to get refined samples by interpolating the samples taken at the PLL's timing estimates. Finally, we present suboptimal implementations that allow a performance-complexity tradeoff

We propose space-time active rotation (STAR), a new layered space-time architecture for fading multiple-input multiple-output channels. The vertically layered V-STAR architecture is similar in spirit to the popular V-BLAST architecture, but by rotating the set of active antennas it achieves better performance with comparable complexity. We derive the outage probability and bounds on the diversity order of a V-STAR system. We propose an ordering algorithm that minimizes the outage probability of a successive cancellation decoder for the V-STAR system. Over a 4-input 4-output Rayleigh-fading channel, we show that V-STAR outperforms V-BLAST by 17.7 dB, and that V-STAR outperforms transmitter-optimized V-BLAST by 2.7 dB. The outage probability of V-STAR with successive cancellation decoding is only 1.4 dB away from the optimum outage probability achieved by an unconstrained decoder. This gap drops to 0.6 dB for an 8-input 8-output channel

A (full-complexity) per-survivor iterative timing recovery scheme, which jointly performs timing recovery, equalization, and error-correction decoding, was recently proposed [1] to deal with the problem of timing recovery operating at low signal-to-noise ratio. Although it outperforms other iterative timing recovery schemes, it has very high complexity. In this paper, we propose a reduced-complexity per-survivor iterative timing recovery scheme to make it implementable, in real-life applications. Simulation results indicate that for low to moderate complexity, the reduced-complexity scheme provides a better performance than the full-complexity scheme.

We consider a wireless system over a MIMO Rayleigh-fading channel with successive-cancellation detection. The outage probability (OP) of such a system is strongly dependent on two choices: the order in which the layers are detected, and the rate-allocation strategy at the transmitter. We propose the rate-normalized ordering algorithm, a generalization of the BLAST ordering algorithm that is shown to minimize OP. We further optimize the allocation of rate and energy at the transmitter, for a variety of receiver ordering strategies. Finally, we jointly optimize the receiver ordering and transmitter rate and energy allocations. Our main conclusion is that, for a wide range of data rates and SNR, the OP is minimized by a combination of rate-normalized ordering and a partially uniform rate and energy allocation strategy. The jointly optimum system outperforms the BLAST architecture by 15 dB at 8 b/s/Hz and an outage probability of 10/sup -3/, when operating over a 4-input 4-output Rayleigh-fading channel. Also, this system shows an improvement of 1.5 dB over a recently proposed combination of optimum allocation and fixed ordering.

The performance of a decision-feedback detector on a fading multiple-input multiple-output channel is limited by the low diversity of the first symbol detected. We propose a new family of detection techniques which overcomes this bottleneck by using a list detector for the first symbol; the list detector is then combined with a parallel bank of decision-feedback detectors, one for each element of the list. The detector family is parameterized by the length of the list, which can be adjusted to achieve a wide range of attractive trade-offs between performance and complexity. For example, on a 4-input 4-output Rayleigh-fading channel with uncoded 16-QAM inputs, one version of the proposed detector outperforms the popular minimum-mean-squared-error BLAST-ordered decision-feedback detector by 1.5 dB, while simultaneously requiring 6% fewer computations.

An inner space–time code, i.e., one that is complemented by an outer error-control code, calls for vastly different design strategies than a space–time code that stands alone. This letter investigates the design of a linear inner space–time code for a$t$-input$r$-output Rayleigh fading channel by examining its outage capacity, which assumes an idealized outer code. We show that a linear space–time code with rate$R ≪ min(t, r)$can achieve at most a fraction$R/min(t, r)$of the underlying channel's outage capacity at high signal-to-noise ratio (SNR). Conversely, we find that a space–time code with low raw diversity order (as calculated using the rank rule) does not necessarily suffer a capacity penalty. Under very general conditions, a rate of$R = min(t, r)$is sufficient to ensure that the outage capacity of the space–time code approaches that of the underlying channel at high SNR. Simulation results are presented to support the claims.

Performance analysis of iterative timing recovery schemes, which perform timing recovery, equalization, and error-correction decoding jointly, is difficult because of their complexity. In this paper, we apply the extrinsic information transfer chart (EXIT chart) analysis as a tool to compare and predict their performances. Simulation results indicate that the system performance predicted by the EXIT chart coincides with that obtained by simulating data transmission over a complete iterative receiver, especially when the coded block length is large.

We propose a new iterative timing recovery scheme based on per-survivor processing that jointly performs timing recovery and turbo equalization on partial response channels with error-correction codes. The scheme embeds the timing recovery process inside the Bahl, Cocke, Jelinek, and Raviv (BCJR) equalizer, using per-survivor processing. This per-survivor BCJR equalizer then iteratively exchanges soft information with an error-correction decoder. Results indicate that the proposed scheme yields a better performance than a conventional receiver that performs timing recovery and turbo equalization separately, especially when the channel encounters severe timing jitter noise. We also present evidence that suggests that the proposed scheme can correct a cycle slip much more efficiently than the others.

We introduce a new family of detectors for multiple-input multiple-output (MIMO) channels called Chase detectors because of their resemblance to the well-known Chase algorithm for soft decoding of error-control codes. A Chase detector is fully specified by only three simple parameters; nevertheless, it reduces to a wide range of previously reported MIMO detectors as special cases, including the maximum-likelihood and decision-feedback detectors. Based on the Chase framework, we propose two new detectors, the B-Chase and L-Chase detectors, both of which perform well on fading channels. In fact, the L-Chase detector is shown to outperform the BLAST-ordered decision-feedback detector by 9.8 dB, while simultaneously requiring 17% fewer computations, on a 4-input 4-output Rayleigh-fading channel with uncoded 4-QAM inputs. Under the same conditions, the B-Chase detector falls only 0.2 dB short of the minimum-mean-squared-error sphere detector, while requiring 50% fewer computations.

A conventional receiver performs timing recovery and equalization separately. Specifically, conventional timing recovery is based on a phase-locked loop that relies on the decision provided by its own symbol detector. We propose a new timing recovery scheme based on per-survivor processing (PSP) that jointly performs timing recovery and equalization for uncoded partial response channels. In the proposed scheme, each survivor of the Viterbi algorithm maintains its own estimate of the timing offset, and this estimate is updated according to the history data associated with the survivor path. As compared to conventional timing recovery at BER = 10/sup -4/, the proposed scheme can provide a 0.5 dB gain in SNR.

The BLAST ordered decision-feedback (ODF) detector is a nonlinear detection strategy for multiple-input multiple-output channels that can significantly outperform a linear detector at the expense of the increased computational complexity. We propose the partial decision-feedback (PDF) detector, a simplified version of the ODF detector that only feeds back one decision. The PDF detector reduces complexity significantly compared to the ODF detector while suffering limited performance loss. For example, over a 5 /spl times/ 5 Rayleigh fading channel with 64-QAM inputs, the PDF detector is one-third as complex as the ODF detector yet it requires only 0.5 dB more average signal energy to reach a symbol-error rate of 10/sup -3/.

Orthogonal frequency division multiplexing (OFDM) is a popular method for high data rate wireless transmission. OFDM may be combined with antenna arrays at the transmitter and receiver to increase the diversity gain and/or to enhance the system capacity on time-varying and frequency-selective channels, resulting in a multiple-input multiple-output (MIMO) configuration. The paper explores various physical layer research challenges in MIMO-OFDM system design, including physical channel measurements and modeling, analog beam forming techniques using adaptive antenna arrays, space-time techniques for MIMO-OFDM, error control coding techniques, OFDM preamble and packet design, and signal processing algorithms used to perform time and frequency synchronization, channel estimation, and channel tracking in MIMO-OFDM systems. Finally, the paper considers a software radio implementation of MIMO-OFDM.

We present new trellis codes based on multiple-pulse-position modulation (MPPM) for wireless infrared communication. We assume that the receiver uses maximum-likelihood sequence detection to mitigate the effects of channel dispersion, which we model using a first-order lowpass filter. Compared to trellis codes based on PPM, the new codes are less sensitive to multipath dispersion and offer better power efficiency when the desired bit rate is large, compared with the channel bandwidth. For example, when the bit rate equals the bandwidth, trellis-coded (17 2)-MPPM requires 1.4 dB less optical power than trellis-coded 16-PPM having the same constraint length.

We analyze the impact of a time-varying Rayleigh-fading channel on the performance of an Alamouti transmit-diversity scheme. We propose several optimal and suboptimal detection strategies for mitigating the effects of a time-varying channel, and derive expressions for their bit-error probability as a function of the channel correlation coefficient /spl rho/. We find that the maximum-likelihood detector that optimally compensates for the time-varying channel is very tolerant to time-varying fading, attaining full diversity order even for the extreme case of /spl rho/=0. In contrast, although lower in complexity, the suboptimal schemes suffer a diversity penalty and are thus suitable only for slowly fading channels.

Soft-output equalizers that exploit a priori information on the channel inputs play a central role in turbo equalization. Such equalizers are traditionally implemented with the forward-backward or BCJR algorithm, whose complexity is prohibitive for channels with large memory. Many reduced-complexity alternatives to the BCJR algorithm have been proposed that use a linear equalizer and use the a priori information to perform soft intersymbol interference cancellation. In this work, we propose a soft-feedback equalizer (SFE) that combines the equalizer output and the a priori information to improve interference cancellation. Also, by assuming a statistical model for the a priori information and the SFE output, we obtain an equalizer with linear complexity, as opposed to the quadratic complexity of some similar structures. Simulation results show that the SFE may perform within 1 dB of a system based on an BCJR equalizer, within 0.3 dB of quadratic complexity schemes, and consistently outperforms other linear complexity schemes.

Although many space-time codes sacrifice their rate in order to achieve a high diversity order, such a sacrifice is not necessary. Recent work has reported two instances of a linear space-time code that achieves both a full rate of min(t, r) and a full diversity order of tr over a t-input r-output Rayleigh-fading channel (Damen, M.O. et al., IEEE Trans. on Inf. Theory, vol.48, no.3, p.753-60, 2002; Ma, X. and Giannakis, G.B., Proc. 2nd Sensor Array and Multichannel SP Workshop, p.442-6, 2002). We show that such full-rate full-diversity codes are plentiful and can, in fact, be found with probability one by randomly choosing an encoding matrix from an ensemble of matrices with orthonormal columns. However, full rate and full diversity does not guarantee good error-rate performance. Different encoding matrices with the same rate and diversity order can have markedly different error rates. We propose the union bound on word-error rate as an optimization metric and perform constrained optimization to find good space-time codes. For the two-input, two-output Rayleigh channel, we present an optimized code that outperforms the previously reported codes by 1.25 dB at 4 b/s/Hz and a frame-error rate of 10/sup -3/.

Despite the widespread use of forward-error control (FEC) coding, most channel estimation techniques ignore its presence, and instead make the simplifying assumption that the transmitted symbols are uncoded. However, FEC induces structure in the transmitted sequence that can be exploited to improve channel estimates. Furthermore, soft-output decoding can improve decision-driven techniques. We propose a technique for exploiting FEC in channel estimation that combines iterative channel estimation with turbo equalization. We present one example showing that an estimator that exploits FEC can attain the same accuracy as one that ignores FEC, but with an SNR that is 6 dB lower.

We analyze the impact of a time-varying Rayleigh fading channel on the performance of an Alamouti transmit-diversity scheme. We propose several detection strategies for mitigating the effects of a time-varying channel, and derive expressions for their bit-error probability as a function of the channel correlation coefficient /spl rho/.

We propose an iterative solution to the problem of blindly and jointly identifying the channel response and transmitted symbols in a digital communications system. The proposed algorithm iterates between a symbol estimator, which uses tentative channel estimates to provide soft symbol estimates, and a channel estimator, which uses the symbol estimates to improve the channel estimates. The proposed algorithm shares some similarities with the expectation-maximization (EM) algorithm but with lower complexity and better convergence properties. Specifically, the complexity of the proposed scheme is linear in the memory of the equalizer, and it avoids most of the local maxima that trap the EM algorithm.

We consider the design and adaptation of a linear equalizer with a finite number of coefficients in the context of a classical linear intersymbol-interference channel with Gaussian noise and a memoryless decision device. If the number of equalizer coefficients is sufficient, the popular minimum mean-squared-error (MMSE) linear equalizer closely approximates the optimal linear equalizer that directly minimizes bit-error rate (BER). However, when the number of equalizer coefficients is insufficient to approximate the channel inverse, the minimum-BER equalizer can outperform the MMSE equalizer by as much as 16 dB in certain cases. We propose a simple stochastic adaptive algorithm for realizing the minimum-BER equalizer. Compared to the least-mean-square algorithm, the proposed algorithm can provide a substantial reduction in BER with no increase in complexity.

We propose a blind implementation of the finite-tap linear MMSE detector for asynchronous direct sequence CDMA. Unlike partially blind detectors that require knowledge of the signature sequence of the desired user in lieu of a training sequence, the proposed detector requires neither training nor knowledge of any of the signature sequences. Moreover, the detector need not know the number of interfering users, the size of their QAM alphabets, nor the amount of memory in the channel. The detector first transforms the channel into an equivalent higher-dimensional channel without memory by stacking a sufficient number of receiver observations. The three factors in a singular-value decomposition of the MMSE detector are then implemented one by one, with each factor being adapted blindly and independently. Numerical results demonstrate that, unlike many subspace-based detectors, the proposed detector is robust to inaccuracies in its estimate of the signal subspace dimension.

We examine the performance of two decision-feedback equalizers (DFEs) for pulse-position modulation (PPM) on measured nondirected indoor infrared channels with intersymbol interference. PPM offers high average-power efficiency, but on ISI channels, unequalized PPM suffers severe performance penalties. We have previously examined the performance of the maximum-likelihood sequence detector (MLSD), and found that it yields significant improvements. However, the MLSD often requires such large complexity and delay that it may be impractical. We investigate suboptimal, reduced-complexity equalization techniques for PPM, providing a performance analysis of zero-forcing chip-rate and symbol-rate DFEs. Our results show that a symbol-rate DFE provides performance that closely approaches that of the optimal MLSD.

We propose the approximate minimum-bit-error-rate (AMBER) algorithm for adapting the coefficients of a linear equalizer with pulse-amplitude and quadrature-amplitude modulation. While less complex than the least-mean-square algorithm, AMBER very nearly minimizes error probability in white Gaussian noise, and can significantly outperform the minimum-mean-squared-error equalizer when the number of equalizer coefficients is small relative to the severity of the intersymbol interference.

We propose a partial-response precoding scheme for combatting intersymbol interference that is compatible with trellis codes based on multiple-pulse position modulation. The scheme reduces the span of intersymbol interference from a possibly infinite number to two baud periods, significantly reducing the complexity of the receiver equalizer. Numerical results show that, in terms of performance and complexity, the proposed scheme compares favorably to conventional linear equalization, block decision-feedback equalization, and superstate maximum-likelihood sequence detection.

We propose a blind multiuser detection technique for array processing and code division multiple access (CDMA) systems that does not require knowledge of the array geometry or transmitter signature sequences. The technique has two key elements: an adaptive algorithm for separating the signal subspace from the noise subspace and an adaptive whitener based on linear prediction. The proposed algorithm offers low complexity, fast convergence, compatibility with shaped signal constellations, near-Wiener steady-state performance, and optimal near-far resistance.

Although most linear and decision-feedback equalizers are designed to minimize a mean-squared error (MSE) performance metric, the equalizer that directly minimizes bit-error rate (BER) may significantly outperform the minimum-MSE equalizer, especially for binary antipodal signaling and its biorthogonal extensions, such as four quadrature-amplitude modulation. We show that the performance gain of the minimum-BER equalizer over the minimum-MSE equalizer is most pronounced when the number of equalizer coefficients is small relative to the severity of the intersymbol interference. We propose a simple stochastic gradient algorithm that approximately minimizes BER in the presence of linear intersymbol interference and white Gaussian noise. Computer simulations reveal that the proposed algorithm compares favorably to the popular least-mean-square algorithm in terms of both steady-state performance and complexity.

The use of infrared radiation as a medium for high-speed short-range wireless digital communication is discussed. Available infrared links and local-area networks are described. Advantages and drawbacks of the infrared medium are compared to those of radio and microwave media. The physical characteristics of infrared channels using intensity modulation with direct detection (IM/DD) are presented including path losses and multipath responses. Natural and artificial ambient infrared noise sources are characterized. Strategies for designs of transmitter and receivers that maximize link signal-to-noise ratio (SNR) are described. Several modification formats are discussed in detail, including on-off keying (OOK) pulse-position modulation (PPM), and subcarrier modulation. The performance of these techniques in the presence of multipath distortion is quantified. Techniques for multiplexing the transmissions of different users are reviewed. The performance of an experimental 50-Mb/s on-off-keyed diffuse infrared link is described.

Although multiple pulse-position modulation performs well on ideal channels, its performance on multipath channels is degraded significantly. In an attempt to quantify the inherent penalty due to multipath dispersion, we evaluate upper bounds for the error probability of each modulation scheme in the presence of intersymbol interference, considering both an unequalized receiver and the optimal maximum-likelihood sequence detection receiver. We also present upper and lower bounds of the channel capacity for multiple pulse-position modulation and its variants, PPM and overlapping PPM. Numerical results show that the PPM-based schemes are significantly more sensitive to multipath dispersion than is on-off keying.

We examine the performance of pulse-position modulation (PPM) on measured channels with intersymbol interference (ISI). We summarize the bit-error-rate performance of unequalized systems and review the performance of maximum-likelihood sequence detection (MLSD) for PPM over ISI channels with additive white Gaussian noise. We evaluate the performance of PPM links over 46 experimentally measured indoor infrared channels. Detailed results are presented for 2, 4, 8, and 16-PPM at bit rates of 10 Mb/s and 30 Mb/s, and these techniques are compared to on-off keying. Our results show that when MLSD is employed, 16-PPM provides the best average-power efficiency among the modulation techniques considered in this study.

We consider the capacity C of a continuous-time channel with frequency response H(f) and additive white Gaussian noise. If H(f)|/sup -2/ behaves like a polynomial of order /spl rho/ at high frequencies, we show that the per-symbol capacity approaches /spl rho//2 nats per channel use at high signal powers. If the receiver uses an ideal zero forcing decision-feedback equalizer (DFE) consisting of a sampled whitened-matched filter followed by a zero-forcing tail canceler that is free of error propagation, the overall system is free of intersymbol interference and has a well-defined capacity C/sub ZF/. By comparing this capacity with the capacity C of the underlying channel, we quantify the loss of information inherent in the tail-canceling operation that typifies zero-forcing DFE and zero-forcing precoding systems. For strictly bandlimited channels, we find that the capacity penalty approaches zero in the limit of large signal power. On the other hand, for nonstrictly bandlimited channels, the asymptotic penalty is nonzero; however, with bandwidth optimization, the asymptotic penalty is at most 0.59 dB, and the asymptotic ratio C/sub ZF//C is at least 93.6%, depending on the asymptotic order /spl rho/ of the channel response.

An adaptive space-time processing system for dynamic spatial channels in a CDMA mobile communications network is presented. The proposed system consists of an adaptive sensor array that estimates the desired directions and waveforms, followed by adaptive linear equalizers that refine the waveform estimates by compensating for the mobile radio uplink channel. Capacity gains are achieved through code reuse, which is made possible by performing the spatial processing after the codes have been decorrelated with one another. Simulation results for a two sensor array in a variety of interference scenarios are presented in the form of bit error rate curves.

A recursive method for evaluating the impulse response of an indoor free-space optical channel with Lambertian reflectors is presented. The method, which accounts for multiple reflections of any order, enables accurate analysis of the effects of multipath dispersion on high-speed indoor optical communication systems. A simple algorithm for computer implementation of the technique and computer simulation results for both line-of-sight and diffuse transmitter configurations are also presented. In both cases, it is shown that reflections of multiple order are a significant source of intersymbol interference. Experimental measurements of optical multipath, which help verify the accuracy of the simulations, are discussed.>

Coherent optical communications, an area of research that shows great promise for future high-bandwidth and long-haul applications, is reviewed. Coherent optical receivers, which add light to the received signal as part of the detection process, have numerous advantages over direct-detection receivers, most notably increased sensitivity and increased selectivity, at the cost of increased complexity. The performance of coherent optical receivers under shot-noise-limited conditions is reviewed for a variety of modulation and demodulation formats. In addition, laser phase noise is discussed, and its effect on receiver performance is analyzed.>