Firouz Behnamfar

Tight error bounds for space-time orthogonal block codes under slow Rayleigh flat fading

The performance of space-time orthogonal block (STOB) codes over slow Rayleigh fading channels and maximum-likelihood (ML) decoding is investigated. Two Bonferroni-type bounds (one upper bound and one lower bound) for the symbol error rate (SER) and bit error rate (BER) of the system are obtained. The bounds are expressed in terms of the pairwise error probabilities (PEPs) and the two-dimensional pairwise error probabilities (2-D PEPs) of the transmitted symbols. Furthermore, the bounds can be efficiently evaluated and they hold for arbitrary (nonstandard) signaling schemes and mappings. Numerical results demonstrate that the bounds are very accurate in estimating the performance of STOB codes. In particular, the upper and lower bounds often coincide even at low channel signal-to-noise ratios, large constellation sizes, and large diversity orders.

Channel-Optimized Quantization With Soft-Decision Demodulation for Space–Time Orthogonal Block-Coded Channels

We introduce three soft-decision demodulation channel-optimized vector quantizers (COVQs) to transmit analog sources over space-time orthogonal block (STOB)-coded flat Rayleigh fading channels with binary phase-shift keying (BPSK) modulation. One main objective is to judiciously utilize the soft information of the STOB-coded channel in the design of the vector quantizers while keeping a low system complexity. To meet this objective, we introduce a simple space-time decoding structure that consists of a space-time soft detector, followed by a linear combiner and a scalar uniform quantizer with resolution q. The concatenation of the space-time encoder/modulator, fading channel, and space-time receiver can be described by a binary-input, 2q-output discrete memoryless channel (DMC). The scalar uniform quantizer is chosen so that the capacity of the equivalent DMC is maximized to fully exploit and capture the systems soft information by the DMC. We next determine the statistics of the DMC in closed form and use them to design three COVQ schemes with various degrees of knowledge of the channel noise power and fading coefficients at the transmitter and/or receiver. The performance of each quantization scheme is evaluated for memoryless Gaussian and Gauss-Markov sources and various STOB codes, and the benefits of each scheme is illustrated as a function of the antenna-diversity and soft-decision resolution q. Comparisons to traditional coding schemes, which perform separate source and channel coding operations, are also provided

MAP decoding for multi-antenna systems with non-uniform sources: exact pairwise error probability and applications

We study the maximum a posteriori (MAP) decoding of memoryless non-uniform sources over multiple-antenna channels. Our model is general enough to include space-time coding, BLAST architectures, and single-transmit multi-receive antenna systems which employ any type of channel coding. We derive a closed-form expression for the codeword pairwise error probability (PEP) of general multi-antenna codes using moment generating function and Laplace transform arguments. We then consider space-time orthogonal block (STOB) coding and prove that, similar to the maximum likelihood (ML) decoding case, detection of symbols is decoupled in MAP decoding. We also derive the symbol PEP in closed-form for STOB codes. We apply these results in several scenarios. First, we design a binary antipodal signaling scheme which minimizes the system bit error rate (BER) under STOB coding. At a BER of 10-6, this constellation has a channel signal-to-noise ratio (CSNR) gain of 4.7 dB over conventional BPSK signaling for a binary nonuniform source with p0 Delta= P(0) = 0.9. We next design space-time linear dispersion (LD) codes which are optimized for the source distribution under the criterion of minimizing the union upper bound on the frame error rate (FER). Two codes are given here: one outperforms V-BLAST by 3.5 dB and Alamoutis code by 12.3 dB at an FER of 10-2 for a binary source with p0 = 0.9, and the other outperforms V-BLAST by 4.2 dB at an FER of 10-3 for a uniform source. These codes also outperform the LD codes of constructed under a different criteria. Finally, the problem of bit-to-signal mapping is studied. It is shown that for a binary source with p0 = 0.9, 64-QAM signaling, and SER = 10-3, a gain of 3.7 dB can be achieved using a better-than-Gray mapping. For a system with one transmit and two receive antennas that uses trellis coding with 16-QAM signaling, a 1.8 dB gain over quasi-Gray mapping and ML decoding is observed when MAP decoding is used for binary sources with p0 = 0.9.

An Efficient Algorithmic Lower Bound for the Error Rate of Linear Block Codes

We present an efficient algorithmic lower bound for the block error rate of linear binary block codes under soft maximum-likelihood decoding over binary phase-shift keying modulated additive white Gaussian noise channels. We cast the problem of finding a lower bound on the probability of a union as an optimization problem that seeks to find the subset that maximizes a recent lower bound - due to Kuai, Alajaji, and Takahara - that we will refer to as the KAT bound. The improved bound, which is denoted by LB-s, is asymptotically tight [as the signal-to-noise ratio (SNR) grows to infinity] and depends only on the codes weight enumeration function for its calculation. The use of a subset of the codebook to evaluate the LB-s lower bound not only significantly reduces computational complexity, but also tightens the bound specially at low SNRs. Numerical results for binary block codes indicate that at high SNRs, the LB-s bound is tighter than other recent lower bounds in the literature, which comprise the lower bound due to Seguin, the KAT bound (evaluated on the entire codebook), and the dot-product and norm bounds due to Cohen and Merhav.

Optimal linear-time algorithm for uplink scheduling of packets with hard deadlines in WiMAX

This paper focuses on a recent application of real-time scheduling in wireless communications industry; i.e., uplink scheduling for WiMAX systems. We address the problem of maximizing the number of packets to be sent in uplink such that the expectations from the system are guaranteed. In this work, we present, for the first time, a formal model for the general problem. Then, we use the properties of the application and derive an algorithm which has two highly favorable features: it finds the optimal solution in linear time. Finally, we present a method to fine-tune our general model in order to make sure that the model represents the actual system. This approach guarantees that the optimal algorithm for the model is indeed the optimal scheduler for the system.

Optimal linear-time QoS-based scheduling for WiMAX

We address a recent application of realtime scheduling in wireless communication industry; namely, the uplink scheduling problem for WiMAX systems. More specially, we have worked on the problem of maximizing the number of data packets to be sent through an uplink subframe such that the expectations from the system are guaranteed. We argue that this problem is NP-hard. Thus far, only a number of heuristic algorithms have been developed for special cases of the problem and the problem has not been modeled formally. In this work, we present two formal models for the system. Then, we derive an algorithm for uplink scheduling which has two highly favourable features: it finds the optimal solution in linear time.

Error analysis of space-time codes for slow Rayleigh fading channels

A communication system which employs L/sub T/ transmit and L/sub R/ receive antennas is considered. The channel is assumed to be quasistatic Rayleigh flat fading. It is assumed that only the receiver has knowledge of the path gains. The additive noise at receiver j at symbol interval t, N/sup j//sub t/, is assumed to be complex Gaussian with i.i.d. real and imaginary parts. We consider the pairwise error probability (PEP) of space-time orthogonal block (STOB) codes, and then generalize the solution to space-time trellis (STT) codes, linear dispersion (LD) codes, and BLAST with ML decoding.

Performance analysis of MAP decoded space-time orthogonal block codes for non-uniform sources

We derive a closed-form expression for the exact pairwise error probability (PEP) of a non-uniform memoryless binary source transmitted over a Rayleigh fading channel using space-time orthogonal block codes and maximum a posteriori (MAP) detection. The expression is easy to evaluate and holds for any signaling scheme. We then use this result to minimize the bit error rate of the binary antipodal signaling scheme. Numerical results for the case of binary antipodal signaling (BPSK and optimal) verify the accuracy of our formula and quantify substantial gains of MAP decoding over maximum likelihood (ML) decoding for sources with strong non-uniformity.

Progressive image communication over binary channels with additive bursty noise

A progressive method for transmission of images over a bursty noise channel is presented. It is based on discrete wavelet transform (DWT) coding and channel-optimized scalar quantization. The main advantage of the proposed system is that it exploits the channel memory and hence has superior performance over a similar scheme designed for the equivalent memoryless channel through the use of channel interleaving. In fact, the performance of the proposed system improves as the noise becomes more correlated, at a fixed bit error rate. Comparisons are made with other alternatives which employ independent source and channel coding over the fully interleaved channel at various bit rates and bit error rates. It is shown that the proposed method outperforms these substantially more complex systems for the whole range of considered bit rates and for a wide range of channel conditions.

Optimal Linear-Time Algorithm for Uplink Scheduling of Packets with Hard or Soft Deadlines in WiMAX

We present, for the first time, a formal model for the general problem of uplink scheduling of a set of packets with various QoS classes and soft or hard deadlines. Our goal is to maximize the number of packets to be sent in uplink such that the expectations from the system are guaranteed. We use our general model and the properties of the application to derive an algorithm which has two highly favorable features: it finds the optimal solution in linear time. Finally, we present a method to fine-tune our general model in order to make sure that the model represents the actual system. This approach guarantees that the optimal algorithm for the model is indeed the optimal scheduler for the system.