Mao-Ching Chiu

Predistorter Based on Frequency Domain Estimation for Compensation of Nonlinear Distortion in OFDM Systems

An orthogonal frequency-division-multiplexing signal is very sensitive to the nonlinear distortion of the power amplifier (PA) as a result of its high peak-to-average power ratio. Predistortion, which is an effective countermeasure for balancing off the nonlinearity of a PA, is usually necessary for the sake of mitigating the in-band distortion and the spectrum regrowth. In general, a feedback path is required to estimate the PA characteristic, and a memoryless polynomial is used in modeling the PA characteristic or constructing the predistorter. The polynomial coefficients are solved by least-square (LS) estimation or adaptive identification algorithms in the time domain. In this paper, we examine the estimation problem from the frequency domain and propose five predistortion schemes. The advantage of using frequency-domain estimation is that it is much easier to compensate the delay effect caused by the transmission and receiving filters in the feedback path. Two different criteria are used in the proposed algorithms. The first one is based on the minimization of the square error of the PA input, which is termed as the PA-input-LS criterion. The second one is based on the minimization of the square error between the input of the predistorter and the output of the PA, which is termed as PA-output-LS criterion. We also propose an easy method to cope with the delay effect caused by the transmission and receiving filters in the feedback path. The performances of the proposed schemes are compared in the simulation. The simulation results show that by using the proposed schemes, the power efficiency of the PA can be increased by at least 7 dB in the sense of total degradation for a practical IEEE 802.11a wireless local area network system with a 64-quadrature-amplitude-modulation signal constellation.

On Unequal Error Protection of Convolutional Codes From an Algebraic Perspective

In this paper, convolutional codes are studied for unequal error protection (UEP) from an algebraic theoretical viewpoint. We first show that for every convolutional code there exists at least one optimal generator matrix with respect to UEP. The UEP optimality of convolutional encoders is then combined with several algebraic properties, e.g., systematic, basic, canonical, and minimal, to establish the fundamentals of convolutional codes for UEP. In addition, a generic lower bound on the length of a UEP convolutional code is proposed. Good UEP codes with their lengths equal to the derived lower bound are obtained by computer search.

Constructions of Asymptotically Optimal Space–Frequency Codes for MIMO-OFDM Systems

Constructions of space-frequency (SF) codes for multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems with nt transmit antennas and Q subcarriers are considered in this paper. Following the pairwise-error-probability analysis, it is known that in addition to the conventional rank distance criterion, the minimum column distance of (nttimesQ) SF codes serves as another benchmark in code design. SF codes with larger minimum column distance are expected to have better performance. Following this principle, the rate-diversity tradeoff for the MIMO-OFDM channels as well as two SF code constructions are presented. The first construction is obtained by right-multiplying the code matrices in a maximal rank-distance (MRD) code by a fixed (QtimesQ) nonsingular matrix. Codes obtained from this construction are called linearly transformed MRD (LT-MRD) codes. Minimum column distance of the LT-MRD codes, when averaged over all code ensembles, is shown to meet the Gilbert-Varshamov bound. For the case of constructing the (2times256) quadrature phase-shift keying (QPSK)-modulated SF codes, it is shown that the LT-MRD codes can provide a much larger minimum column distance at the value of ges50, compared to the values of 3,5, or 6 obtained by other available constructions. The second code construction, termed cyclotomic construction, is reminiscent of the construction of the Reed-Solomon codes except that the code polynomials are now selected according to the cyclotomic cosets of the underlying field. Exact minimum rank distances of the resultant codes are presented. It is shown that this newly constructed code is asymptotically optimal in terms of rate-diversity tradeoff. Bounds on the minimum column distance of these codes are also given

DC-free error-correcting codes based on convolutional codes

A new construction of direct current (DC)-free error-correcting codes based on convolutional codes is proposed. The new code is constructed by selecting a proper subcode from a convolutional code composed of two different component codes. The encoder employs a Viterbi algorithm as the codeword selector so that the selected code sequences satisfy the DC constraint. A lower bound on the free distance of such codes is proposed, and a procedure for obtaining this bound is presented. A sufficient condition for these codes to have a bounded running digital sum (RDS) is proposed. Under the assumption of a simplified codeword selection algorithm, we present an upper bound on the maximum absolute value of the RDS and derive the sum variance for a given code. A new construction of standard DC-free codes, i.e., DC-free codes without error-correcting capability, is also proposed. These codes have the property that the decoder can be implemented by simple symbol-by-symbol hard decisions. Finally, under the new construction, we propose several codes that are suitable for the systems that require small sum variance and good error-correction capability.

Decision-feedback soft-input/soft-output multiuser detector for iterative decoding of coded CDMA

The optimal decoding scheme for a code-division multiple-access (CDMA) system that employs convolutional codes results in a prohibitive computational complexity. To reduce the computational complexity, an iterative receiver structure was proposed for decoding multiuser data in a convolutional coded CDMA system. At each iteration, extrinsic information is exchanged between a soft-input/soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders. However, a direct implementation of the full-complexity SISO multiuser detector also has the exponential computational complexity in terms of the number of users. This paper proposes a low-complexity SISO multiuser detector based on tentative hard decisions that are made and fed back from the channel decoders in the previous iteration. The computational complexity of the proposed detector is linear in terms of the number of users and can be adjusted according to the complexity/performance tradeoff. Simulation results show that even with this simple feedback scheme, the performance of the coded multiuser system approaches that of the single-user system for moderate to high signal-to-noise ratios (SNRs).

Accumulate codes based on 1+D convolutional outer codes

A new construction of good, easily encodable, and soft-decodable codes is proposed in this paper. The construction is based on serially concatenating several simple 1+D convolutional codes as the outer code, and a rate-1 1/(1+D) accumulate code as the inner code. These codes have very low encoding complexity and require only one shift-forward register for each encoding branch. The input-output weight enumerators of these codes are also derived. Divsalariquests simple bound technique is applied to analyze the bit error rate performance, and to assess the minimal required signal-to-noise ratio (SNR) for these codes to achieve reliable communication under AWGN channel. Simulation results show that the proposed codes can provide good performance under iterative decoding.

Application of space-time codes to OFDM UWB systems with under-sampled receivers

In this paper, the application of space-time codes (STCs) to orthogonal frequency division multiplexing (OFDM) ultra-wideband (UWB) systems with under-sampled receivers is investigated. In this system, the total available bandwidth is divided into M/sub t/ smaller sub-bands. OFDM modulation is adopted in each sub-band, and data are transmitted in all the sub-bands simultaneously. The transmitter properly encodes the data in sub-bands to gain the rich frequency diversity, enabling a low-cost receiver with reduced sampling rate, only one M/sub t/-th of the Nyquist rate. We first show that this system can be analogized to a multiple-input single-output (MISO) system with M/sub t/ transmit antennas, by which the application of STC becomes a natural consequence. We then consider employing low-rate space-time trellis codes (STTCs), which can jointly attain the maximal diversity gain and coding gain based on the two design criteria from the MISO analogy. Simulation results with proposed STTCs have verified the superior performance to the previously proposed coding scheme.

Constructions of space-frequency codes for MIMO-OFDM systems

Constructions of space-frequency (SF) codes for MIMO-OFDM systems with nt transmit antennas and Q subcarriers are considered in this paper. Arising from the pairwise-error-probability analysis, in addition to the rank distance criterion, the minimum column distance of (nt times Q) SF codes serves as another benchmark in code design. Codes with larger minimum column distance are expected to have better performance. Following this observation, two code constructions are presented. The first construction is obtained by right-multiplying the code matrices in a maximal rank-distance (MRD) code by a fixed, (Q times Q) nonsingular matrix. Codes obtained from this construction are called linearly transformed MRD (LT-MRD) codes in this paper. Minimum column distance of the LT-MRD codes, when averaged over all code ensembles, is shown to meet the Gilbert-Varshamov bound. The second construction is reminiscent of the construction of the Reed-Solomon codes except that the code polynomials are now selected according to the cyclotomic cosets of the underlying field. Exact minimum rank distances and bounds on the minimal column distance of these codes are presented

A low-complexity SISO multiuser detector for iterative decoding of asynchronous CDMA systems with convolutional codes

The optimal decoding scheme for asynchronous code-division multiple-access (CDMA) systems that employ convolutional codes results in a prohibitive computational complexity. To reduce the computational complexity, an iterative receiver structure was proposed for decoding multiuser data in a convolutional coded CDMA system. At each iteration, extrinsic information is exchanged between a soft-input soft-output (SISO) multiuser detector and a bank of single-user SISO channel decoders. A direct implementation of the optimal SISO multiuser detector, however, has exponential computational complexity in terms of the number of users which is still prohibitive for channels with a medium to large number of users. This paper presents a low-complexity SISO multiuser detector using the decision-feedback scheme, of which tentative hard decisions are made and fed back to the SISO multiuser from the previous decoding output. In the proposed scheme, the log-likelihood ratios (LLR) as well as the tentative hard decisions of code bits are fed back from the SISO decoders. The hard decisions are used to constrain the trellis of the SISO multiuser detector and the LLRs are used to provide a priori information on the code bits. The detector provides good performance/complexity tradeoffs. The computational complexity of the detector can be set to be as low as linear in the number of users. Simulations show that the performance of the low-complexity SISO multiuser detector approaches that of the single-user system for moderate to high signal-to-noise ratios even for a large number of users.

Bandwidth-Efficient Modulation Codes Based on Nonbinary Irregular Repeat Accumulate Codes

Using nonbinary low-density parity-check (LDPC) codes with random-coset mapping, Bennatan and Burshtein constructed bandwidth-efficient modulation codes with remarkable performance under belief propagation (BP) decoding. However, due to the random nature of LDPC codes, most of the good LDPC codes found in the literature do not have a simple encoding structure. Thus, the encoding complexity of those LDPC codes can be as high as O(N 2), where N is the codeword length. To reduce the encoding complexity, in this paper, nonbinary irregular repeat-accumulate (IRA) codes with time-varying characteristic and random-coset mapping are proposed for bandwidth-efficient modulation schemes. The time-varying characteristic and random-coset mapping result in both permutation-invariance and symmetry properties, respectively, in the densities of decoder messages. The permutation-invariance and symmetry properties of the proposed codes enable the approximations of densities of decoder messages using Gaussian distributions. Under the Gaussian approximation, extrinsic information transfer (EXIT) charts for nonbinary IRA codes are developed and several codes of different spectral efficiencies are designed based on EXIT charts. In addition, by proper selection of nonuniform signal constellations, the constructed codes are inherently capable of obtaining shaping gains, even without separate shaping codes. Simulation results indicate that the proposed codes not only have simple encoding schemes, but also have remarkable performance that is even better than that constructed using nonbinary LDPC codes.