Frequency-flat Rayleigh Fading Channels Research Articles

Error probabilities of noncoherent and coherent FSK in the presence of frequency and phase offsets for two-hop relay networks

We analyze the error performance of two-hop relay networks adopting frequency shift keying (FSK) over frequency flat Rayleigh fading channels. It is assumed that relay networks consist of a source, a relay, and a destination without a direct path signal from the source to the destination and the relay adopts the amplify-and-forward protocol with a fixed gain. Firstly, considering imperfect frequency and phase synchronization, we obtain the exact error probability expressions for noncoherent and coherent binary FSK (BFSK). Secondly, assuming perfect frequency and phase synchronization, we derive a closed-form error probability approximation for coherent M-ary FSK (MFSK). The proposed methods can also be used for the error performance analysis of classical one-hop FSK systems with perfect/imperfect frequency and phase synchronization. The obtained error probability expressions will help the design of two-hop relay networks adopting FSK in determining the system parameters such as the transmission power at the source, the amplifying coefficient at the relay, and the maximum affordable frequency and phase offsets to satisfy the required error performance.

An exact error probability analysis of OFDM systems with frequency offset

In this paper, we derive exact closed form bit error rate (BER) or symbol error rate (SER) expressions for orthogonal frequency division multiplexing (OFDM) systems with carrier frequency offset (CFO). We consider the performance of an OFDM system subject to CFO error in additive white Gaussian noise (AWGN), frequency flat and frequency selective Rayleigh fading channels. The BER/ SER performances of BPSK and QPSK modulation schemes are analyzed for AWGN and frequency-flat Rayleigh fading channels while BPSK is considered for frequency-selective Rayleigh fading channels. Our results can easily be reduced to the respective analytical error rate expressions for the OFDM systems without CFO error. Furthermore, the simulation results are provided to verify the accuracy of the new error rate expressions.

Estimation of autoregressive fading channels based on two cross-coupled H ∞ filters

This paper deals with the on-line estimation of time-varying frequency-flat Rayleigh fading channels based on training sequences and using H∞ filtering. When the fading channel is approximated by an autoregressive (AR) process, the AR model parameters must be estimated. As their direct estimations from the available noisy observations at the receiver may yield biased values, the joint estimation of both the channel and its AR parameters must be addres- sed. Among the existing solutions to this joint estimation issue, Expectation Maximization (EM) algorithm or cross- coupled filter based approaches can be considered. They usually require Kalman filtering which is optimal in the H2 sense provided that the initial state, the driving process and measurement noise are independent, white and Gaussian. However, in real cases, these assumptions may not be satis- fied. In addition, the state-space matrices and the noise variances are not necessarily accurately estimated. To take into account the above problem, we propose to use two cross- coupled H∞ filters. This method makes it possible to provide

Error Performance of MT System Using Adaptive Modulation with Guard Period

The increasing demand on modern communications systems and the associated services together with the scarce frequency radio recourses have put a great deal of pressure on frequency utilization techniques to accommodate such high and dramatically increasing consumer demand. The impetus of this research is the hypothesis that high-bit rate transmission technique is a means of increasing the capacity of wireless communications systems and hence solves the problems of spectrum congestions and high consumer demand. Multitones (MC) channel transmission is one of the techniques used for high-speed digital transmission; a study of the performance of this technique is evaluated by means of bit error rate (BER). BER results are presented for offset quadrature phase shift keying (OQPSK) using guard period (GP). GP is used to alleviate the effect of multipath delay, associated with radio mobile communications, for frequency flat Rayleigh fading channels and for two-path fading channels in the presence of additive white Gaussian noise (AWGN) by means of a complete simulation model.

A coded beamforming scheme for frequency-flat MIMO fading channels

In this paper, a coded beamforming scheme is considered for frequency-flat multiple-input-multiple-output (MIMO) fading channels. With channel state information (CSI) available at the transmitter, this scheme combines coded modulation (CM) with downlink transmission beamforming to exploit both diversity and coding advantages. In order to identify the appropriate code design criteria, the exact pairwise error probability and bit error rate upper bounds are derived for both frequency-flat slow and fast MIMO Rayleigh fading channels. It is shown that the minimum squared Euclidean distance of the code should be maximised in slow-fading channels, whereas the minimum effective code length and the product distances should be maximised in fast-fading scenarios. This conclusion indicates that the conventional Ungerboeck's trellis-coded modulation codes originally designed for additive white Gaussian noise channels and single-antenna Rayleigh fading channels could be directly utilised in the proposed scheme for slow and fast MIMO fading channels, respectively. This eliminates the need for complicated code design. Simulation results are provided to substantiate the theoretical analysis. For an example, it is demonstrated that a trellis-coded beamforming scheme can outperform the published space-time trellis coded beamforming schemes by up to 4 dB, although it has a simpler encoder structure and requires no specific code design. Interference free is assumed in the analysis, while the impact of the imperfect CSI and antenna correlation on the system error performance is evaluated.

Near-optimum transmit power allocation for space–time block encoded wireless communication systems

Space–time block codes (STBCs) allow the diversity provided by multiple-input–multiple-output (MIMO) communication channels to be utilised, thereby increasing the capacity over ergodic fading channels or decreasing the outage probability over non-ergodic fading channels. The authors consider the deployment of orthogonal STBCs in spatially distributed mesh networks where the potentially different average sub-channel gains from any transmit to any receive antenna are assumed to be known at the transmitting elements. To optimise performance in terms of capacity or outage probability, heavy signal processing is required at each transmit element as only numerical optimisation is known to yield the optimum performance. In the paper, explicit near-optimum transmit power allocation strategies for distributed STBCs operating over ergodic and non-ergodic frequency-flat Rayleigh fading channels are introduced which reduce the required signal processing considerably.

MRC reception of rectangular M-ary QAM signals over frequency-flat Rayleigh fading channels with distinctive branch fading amplitudes

The usual approach to calculate the symbol error rate (SER) for multilevel (M-ary) signalling over a fading channel is to first find the average SER in an additive white Gaussian noise channel conditioned on a fixed fading parameter and then average this SER over the fading parameter (averaging over the fading parameter at the last stage). This usual approach is called the postaveraging method. A different approach, called the preaveraging method, that is the averaging over the fading parameter is performed on the probability density function of per symbol estimate error in an earlier stage of the derivation process. By doing so, it is possible to obtain an exact closed-form expression of SER for the special case of maximal ratio combining reception of arbitrary rectangular M-ary quadrature amplitude modulation (QAM) signalling over frequency-flat Rayleigh fading channels, which has not been obtained using the usual postaveraging method. For the case under study, it is assumed that all diversity channels have independent, but distinctive, fading amplitudes. The SER results can be applied to any M-size rectangular QAM constellation. The method can be readily extended to square M-ary QAM, M-ary pulse amplitude modulation (PAM) and binary antipodal signalling. It is thought that this method and the closed-form SER result have never been treated and exposed elsewhere for the arbitrary rectangular QAM case under consideration. Monte Carlo simulations prove to be in excellent agreement with the theoretical results.

A BEM-Based Algorithm for Soft-In Soft-Output Detection of Co-Channel Signals

In this paper, a soft-in soft-out multiuser detector for synchronous co-channel signals transmitted over frequency-flat Rayleigh-fading channels is described. The derivation of the proposed algorithm is based on a generalization of the expectation-maximization (EM) algorithm, called Bayesian EM. Performance results for both uncoded and coded phase shift keying transmissions show the efficacy of the proposed multiuser detection technique over slowly time-varying fading channels in a two-user system.

Analysis and Design Criteria for Trellis-Coded Modulation With Differential Space-Time Transmit Diversity

In this letter, concatenation of trellis-coded modulation (TCM) with differential space-time block codes (DSTBC) is considered under frequency-flat Rayleigh-fading channels with and without perfect interleaver. It is shown that the design criteria of TCM concatenated with DSTBC are exactly the same as that of TCM concatenated with space-time block codes (STBC) in perfectly known channels. They are effective code length over span two symbol intervals and minimum product-sum distance over span two symbol intervals. Based on the design criteria, several new rate-2/3 systematic Ungerboeck's TCM schemes have been found by computer search. They outperform existing optimal TCM schemes designed for additive white Gaussian noise or flat fading channels.

Lower Capacity Bound for MIMO Correlated Fading Channels With Keyhole

It is well known that the existence of spatial fading correlation and keyhole effects severely reduces the capacity of multiple-input and multiple-output (MIMO) channels. In this letter, for correlated Rayleigh frequency-flat fading channels with keyholes, a tight lower capacity bound is given in a closed form. For the uncorrelated case, the lower bound can be proved to be tight asymptotically. The tightness of this bound for both correlated and uncorrelated channels is demonstrated by numerical examples.

Error-Bound Formulation for Multichannel Reception of<tex>$M$</tex>-DPSK and Pilot-Aided<tex>$M$</tex>-PSK Over Rayleigh-Fading Channels With Postdetection Combining

Upper bounds for symbol-error probability are developed for multichannel reception of M-ary phase-shift keying (M-PSK) over frequency-flat Rayleigh-fading channels. Differential coherent demodulation of differentially encoded M-PSK (M-DPSK), pilot-tone aided coherent demodulation of M-PSK (PTA M-CPSK) and pilot-symbol aided coherent demodulation of M-PSK (PSA M-CPSK) are considered in the formulation. The bounds enable the investigation of the effects of fading correlation and unequal average power level between channels using postdetection diversity reception with maximal-ratio combining. Error-performance degradation due to imperfect demodulation effects, such as Doppler spread in M-DPSK schemes, noisy reference signals in PTA M-CPSK, and PSA M-CPSK schemes can be taken into account in the formulation. Exact bit-error probabilities for both binary and quaternary phase-shift keying are also derived.

Theoretical Analysis and Performance of the Decorrelating Detector for DS-CDMA Signals in Nonlinear Channels

We analyze the effects of the nonlinear distortions, introduced by the transmitting high-power amplifier (HPA), on the performance of the linear decorrelating multiuser detector in direct-sequence code-division multiple-access (DS-CDMA) downlink systems. By assuming and motivating the Gaussian distribution of the nonlinear distortion noise, the symbol-error rate (SER) and the total degradation (TD) has been derived theoretically in additive white Gaussian noise (AWGN) and frequency-flat Rayleigh fading channels. Simulation results show that the analytical model is quite accurate in many scenarios.

Channel estimation for iterative decoding over fading channels

A method of coherent detection and channel estimation for punctured convolutional coded binary Quadrature Amplitude Modulation (QAM) signals transmitted over a frequency-flat Rayleigh fading channels used for a digital radio broadcasting transmission is presented. Some known symbols are inserted in the encoded data stream to enhance the channel estimation process. The pilot symbols are used to replace the existing parity symbols so no bandwidth expansion is required. An iterative algorithm that uses decoding information as well as the information contained in the known symbols is used to improve the channel parameter estimate. The scheme complexity grows exponentially with the channel estimation filter length. The performance of the system is compared for a normalized fading rate with both perfect coherent detection (corresponding to a perfect knowledge of the fading process and noise variance) and differential detection of Differential Amplitude Phase Shift Keying (DAPSK). The tradeoff between simplicity of implementation and bit-error-rate performance of different techniques is also compared.

Adaptive innovations-based MLSE receiver for frequency-nonselective Rayleigh fading channels

The performance of an adaptive innovations-based maximum likelihood sequence estimation (MLSE) receiver for differentially encoded M-ary differential phase shift keying (M-DPSK) in frequency-flat Rayleigh fading channels is presented. The proposed receiver can be implemented without the knowledge of the channel statistics, yet reveal a robust demodulation performance against the uncertainties associated with the channel dynamics.

MAP symbol estimation on frequency-flat Rayleigh fading channels via a Bayesian EM algorithm

In this paper, an expectation-maximization (EM) technique for maximum a posteriori estimation is employed to devise novel soft-in soft-out algorithms for symbol detection over frequency-flat Rayleigh fading channels. An application of these algorithms to iterative decoding of coded PSK signals is proposed and some performance results are illustrated.

Aspects on single symbol signaling on the frequency flat Rayleigh fading channel

The optimal single symbol detector on the Rayleigh fading channel computes a functional quadratic form in the time continuous received signal. A drawback is that closed-form solutions of integral equations based on the channel statistics are required. This makes simplified discrete receivers attractive. A class of suboptimal receivers that transforms the received random process to a set of discrete observables is derived. The set of observables constitutes a random vector in a finite dimensional receiver signal space. Given this vector, the maximum likelihood detector computes a quadratic form in the received vector. The discretization implies a loss of information, therefore such a detector is not, in general, optimal given the received time continuous signal. The purpose is, however, to achieve close to optimal performance when the number of observables becomes large. This class of detectors is analyzed using exact error probability calculations, which reveal several interesting properties. The length of the observation interval and the number of discrete observables have significant influences on the error probability when the time variations of the fading process are rapid compared with the symbol duration. By increasing the number of observables, the error floor is lowered, and the implicit diversity order is increased. This implicit diversity arises as soon as more than one observable per symbol interval is used and is a consequence of the information bearing signal being a random process. Matched filter receivers use few discrete observables per symbol interval, and thus suffer from high error floors and low implicit diversity orders on fast fading channels. The error probability is highly dependent on the shapes and durations of the modulator waveforms. For instance, pulses of long duration give lower error probabilities than shorter pulses, and for a certain type of orthogonal waveforms there is no error floor.

Differential detection algorithms for MSK signals over AWGN and frequency-flat Rayleigh fading channels

Novel symbol-by-symbol differential detection algorithms are proposed for minimum-shift keying signals transmitted over additive white Gaussian noise and frequency-flat Rayleigh fading channels. They are derived as approximations to the maximum likelihood noncoherent detection strategy. Their error performance is assessed by computer simulation and is compared with that of other noncoherent detectors. It is shown that, with fading channels, the new algorithms outperform the traditional methods.

Further results in carrier frequency estimation for transmissions over flat fading channels

A data-aided feedforward algorithm has been proposed by Kuo and Fitz (see IEEE Trans. Commun., vol.45, p.1412-26, 1997) for carrier frequency estimation in M-ary phase-shift keying (PSK) transmissions over frequency-flat Rayleigh fading channels. Its accuracy is very good but the estimation range may be limited under certain operating conditions. Also, its application requires a knowledge of the Doppler bandwidth. We show that the estimation range can be greatly extended without sacrificing the estimation accuracy and a simple technique is indicated to measure the Doppler bandwidth. This allows the algorithm to operate in an adaptive manner in a time-varying environment.

A space-time coding modem for high-data-rate wireless communications

This paper presents the theory and practice of a new advanced modem technology suitable for high-data-rate wireless communications and presents its performance over a frequency-flat Rayleigh fading channel. The new technology is based on space-time coded modulation (STCM) with multiple transmit and/or multiple receive antennas and orthogonal pilot sequence insertion (O-PSI). In this approach, data is encoded by a space-time (ST) channel encoder and the output of the encoder is split into N streams to be simultaneously transmitted using N transmit antennas. The transmitter inserts periodic orthogonal pilot sequences in each of the simultaneously transmitted bursts. The receiver uses those pilot sequences to estimate the fading channel. When combined with an appropriately designed interpolation filter, accurate channel state information (CSI) can be estimated for the decoding process. Simulation results of the proposed modem, as applied to the IS-136 cellular standard, are presented. We present the frame error rate (FER) performance results as a function of the signal-to-noise ratio (SNR) and the maximum Doppler frequency, in the presence of timing and frequency offset errors. Simulation results show that for a 10% FER, a 32-state eight-phase-shift keyed (8-PSK) ST code with two transmit and two receive antennas can support data rates up to 55.8 kb/s on a 30-kHz channel, at an SNR of 11.7 dB and a maximum Doppler frequency of 180 Hz. Simulation results for other codes and other channel conditions are also provided. We also compare the performance of the proposed STCM scheme with delay diversity schemes and conclude that STCM can provide significant SNR improvement over simple delay diversity.

Double-filtering receivers for PSK signals transmitted over Rayleigh frequency-flat fading channels

This paper describes novel detection algorithms for coded and uncoded M-ary phase shift keying (M-PSK) signals transmitted over frequency-flat fading channels. Fading distortion is estimated with per-survivor methods using the sampled outputs of two receive filters. Some of the proposed algorithms do not require information on the fading statistics and are dubbed blind algorithms. The error rate performance of blind and nonblind algorithms is assessed by simulation for uncoded and trellis-coded phase shift keying (PSK) and is compared to the performance of other detection schemes proposed in the literature.