Closed-form Bit Error Rate Research Articles

Closed-form BER results for multiple-chip-rate CDMA systems based on the simplified improved gaussian approximation

We consider very general code-division-multiple- access (CDMA) systems, namely multiple-chip-rate CDMA systems, where signals can be transmitted at different chip rates, carrier frequencies, processing gains, and transmitted powers to satisfy the given quality of service (QoS) requirements. Also, nonzero and possibly different carrier frequency offsets are assumed for different users. For these systems, a closed-form bit error rate (BER) expression is derived based on the simplified improved Gaussian approximation. Numerical result demonstrates that the proposed method provides much more accurate BER values compared to the standard Gaussian approximation.

A Closed-Form BER Expression for BPSK Using MRC in Correlated CCI and Rayleigh Fading

An exact closed-form expression for the average bit error rate (BER) of coherent BPSK using maximal ratio combining (MRC) with correlated branches in the presence of cochannel interference (CCI) and noise is derived. This expression is valid for an arbitrary correlation structure under the assumption that the branch gains of the desired user signal and interfering signals experience correlated Rayleigh fading with the same correlation eigenvector matrix.

Precise BER analysis of π/4-DQPSK OFDM with carrier frequency offset over frequency selective fast fading channels

An exact closed-form bit error rate (BER) expression is derived for an orthogonal frequency-division multiplexing system with π/4-shifted differentially encoded quadrature phase shift keying (π/4-DQPSK) in the presence of carrier frequency offset over frequency-selective fast Rayleigh fading channels. Different system configurations, including time domain differential modulation, frequency domain differential modulation, single channel reception, and multi-channel reception with maximal ratio combining diversity, are considered in the exact BER analysis. For a small number of subcarriers, the BER expression can be calculated directly. A Monte Carlo method is designed to evaluate the BER for a large number of subcarriers. The analytical expression can be used to investigate the effect of several channel parameters, including mean delay spread and maximum Doppler spread, on the system BER performance. Particularly, the effect of carrier frequency offset on the system performance, and the differences and opportunities to use frequency domain differential modulation or time domain differential modulation, can be studied in a quantitative way for a more realistic wireless channel environment model. By using the exact closed-form BER expression, an optimum number of subcarriers can be found, and the allowable carrier frequency offset, Doppler spread, and mean delay spread for given operating conditions can be determined.

Adaptive IIR Filters for Single Interference Suppression in a BPSK DS CDMA System In Rayleigh Fading Channel

In this paper, effect of a single narrow-band interference (NBI) on bit error rate (BER) performance for a binary phase shift keying (BPSK) synchronous direct-sequence code-division multiple access (DS CDMA) communication system operating in a frequency nonselective Rayleigh fading channel is analyzed. Second-order adaptive infinite impulseresponse (IIR) notch filters with plain gradient algorithm (GA) for suppression of NBI in the DS CDMA system are proposed. A general closed-form BER expression for the DS CDMA system with NBI suppression second order adaptive IIR notch filters is derived based on the standard Gaussian approximation (SGA) method. BER expressions are then derived for the allpass filter-based adaptive IIR notch filter and adaptive IIR notch filter with constrained poles and zeros, the two structures that are commonly found in literature. It is observed that both adaptive IIR notch filter structures exhibit comparable BER performance. Extensive computer simulation results are presented to verify the accuracy and limitations of the analysis.

Closed-form BER analysis for antenna selection using orthogonal space-time block codes

Despite significant research efforts, closed-form bit error rate (BER) expressions for multiple-input multiple-output (MIMO) systems employing transmit antenna selection and orthogonal space-time block codes (OSTBCs) are not available. We thus derive exact closed-form expressions for the BER of Gray-coded M-ary one and two-dimensional amplitude modulations when an OSTBC is employed and N transmit antennas out of total Lt antennas are selected for transmission. We also derive tight closed-form approximate BER for M-PSK constellations. Our BER expressions are valid for a frequency-flat Rayleigh fading MIMO channel and can be evaluated without numerical integration methods.

Closed-form BER analysis for antenna selection using orthogonal space-time block codes

Despite significant research efforts, closed-form bit error rate (BER) expressions for multiple-input multiple-output (MIMO) systems employing transmit antenna selection and orthogonal space-time block codes (OSTBCs) are not available. We thus derive exact closed-form expressions for the BER of Gray-coded M-ary one and two-dimensional amplitude modulations when an OSTBC is employed and N transmit antennas out of total Lt antennas are selected for transmission. We also derive tight closed-form approximate BER for M-PSK constellations. Our BER expressions are valid for a frequency-flat Rayleigh fading MIMO channel and can be evaluated without numerical integration methods.

Performance analysis of space-time block coded cooperative wireless transmission in Rayleigh fading channels

This paper studies theoretically the bit error rate (BER) performance of cooperative transmission using space-time block code (STBC) in a fully distributed manner. Specifically, we first propose a STBC-based cooperative signaling structure to make the cooperation of three single-antenna terminals possible. Then, we derive the closed-form BER expressions for both cooperation and noncooperation schemes under flat Rayleigh fading channel plus additive white Gaussian noise (AWGN). The validity of these expressions is verified by Monte-Carlo simulations. A variety of numerical and simulation results reveal that the cooperative transmission achieves higher diversity gain and better performance than the direct transmission for the same total transmit power.

Exact BER analysis of OSTBCs in spatially correlated MIMO channels

The bit-error rate (BER) performance of orthogonal space-time block codes (STBCs) in correlated multiple-input multiple-output (MIMO) channels is studied. We first derive closed-form exact BER equations for pulse amplitude modulation, quadrature amplitude modulation, and phase-shift keying constellations in a correlated Rayleigh MIMO channel. The BER expressions can be easily evaluated without any numerical methods. Then we consider correlated MIMO channels where the line of sight components exist and they suffer from shadowing, namely, correlated shadowed Rician MIMO channels. For three practical channel scenarios, the BER is analyzed, and closed-form BER equations are presented.

Performance analysis of asynchronous MC-CDMA systems with a guard period in the form of a cyclic prefix

This letter presents an analysis of asynchronous multicarrier code-division multiple-access (MC-CDMA) systems with a guard period (GP) in the form of a cyclic prefix over frequency-selective multipath fading channels, which results in closed-form bit-error rate performance. Furthermore, it confirms that the frequency diversity of MC-CDMA systems is identical to the path diversity. The analytical approach proposed here is extended to the case without a GP. The derived analytical results show that a GP is required for MC-CDMA systems in order to mitigate not only the effect of intersymbol interference and intercarrier interference, but also the desired signal power degradation.

Closed-form BER results for MRC diversity with channel estimation errors in Ricean fading channels

Closed-form expressions for computing the average bit error rate (BER) for a class of modulation schemes in Ricean flat fading channels with maximal-ratio combining diversity and channel estimation errors are derived. The results are valid for a general multichannel model that includes Ricean and Rayleigh fading channels. The results are applicable to channel estimators that are jointly Gaussian with the channel gain. The BER performance of pilot symbol-assisted modulation is studied. The effects of estimation error on the diversity system are examined as well as the influences of varying the Ricean factor K and changing the number of diversity branches L.

Analytical Study of QAM With Interference Cancellation for High-Speed Multicode CDMA

In this paper, we consider the multilevel quadrature amplitude modulation (M-QAM) for forward link of multicode code-division multiple-access (CDMA) systems with interference cancellation to support high data rate service, and provide an analytical bit error rate (BER) performance of the system. In the current third-generation (3G) wide-band CDMA systems, in addition to multicode transmission, M-QAM is employed for high-speed downlink packet access (HSPDA) due to its high spectral efficiency. In frequency-selective fading channels, multipath interference seriously degrades the system performance, therefore interference cancellation technique is employed at the receiver. In this paper, an analytical closed-form BER of multicode CDMA systems with QAM is presented, where two important factors (channel estimation error and additive interference) on system performance are considered. Numerical results show that the system is very sensitive to additive multipath interference. With the help of interference cancellation technique, M-QAM can be adaptively employed in high signal-to-noise ratio cases to increase system throughput, within 5 MHz bandwidth. Meanwhile, simulation results are shown to illustrate the accuracy of the analytical method. Moreover, it is found that extra pilot power should be invested for more accurate channel estimation and consequently better BER performance when using the interference cancellation technique.

Effect of Channel-Estimation Error on QAM Systems With Antenna Diversity

This paper studies the effect of channel estimation error and antenna diversity on multilevel quadrature amplitude modulation (M-QAM) systems over Rayleigh fading channels. Based on the characteristic function method, a general closed-form bit-error rate (BER) for M-QAM systems is presented. The effect of the inaccurate channel estimation on the performance for pilot-symbol-assisted modulation M-QAM systems with antenna diversity is investigated. Simulation results for M-QAM (M = 4, 16, 64, 256, etc.) show that the analytical method can accurately estimate the system performance. Moreover, numerical results show that with the antenna-diversity technique, the BER performance improves significantly, especially in perfect channel-estimation cases. It is also found that the channel-estimation error limits the benefit of antenna diversity. By increasing the length of the channel estimator and the amplitude of the pilot symbol, more accurate channel estimation can be achieved, so that the BER performance is improved.

Performance of Asynchronous MC-CDMA Systems with Maximal Ratio Combining in Frequency-Selective Fading Channels

The bit error rate (BER) performance of the asynchronous uplink channel of multicarrier code division multiple access (MC-CDMA) systems with maximal ratio combining (MRC) is analyzed. The study takes into account the effects of channel path correlations in generalized frequency-selective fading channels. Closed-form BER expressions are developed for correlated Nakagami fading channels with arbitrary fading parameters. For channels with correlated Rician fading paths, the BER formula developed is in one-dimensional integration form with finite integration limits, which is also easy to evaluate. The accuracy of the derived BER formulas are verified by computer simulations. The derived BER formulas are also useful in terms of computing other system performance measures such as error floor and user capacity.

BER for optical heterodyne DPSK receivers using delay demodulation and integration detection

Previous work on the bit error rate (BER) performance of differential phase-shift keying (DPSK) including the effects of additive white Gaussian noise (AWGN) and phase noise has concentrated on the delay demodulator with narrow-band intermediate frequency (IF) bandpass filtering (BPF) and sampling detection. No similar analysis has yet been performed for the delay demodulator with wideband IF bandpass filtering and integration detection. Phase noise is an important consideration in coherent optical communication systems and the most widely accepted model is a Brownian motion process. A closed-form BER expression along with detailed Monte Carlo simulation results are presented for the DPSK delay demodulator with wideband IF bandpass filtering and integration detection filtering including phase noise effects using the Brownian motion model. Analytic expressions are also obtained for the moments of the phase noise component of the decision variable. Using these moments, estimates of the phase noise BER floor are produced. It is found that this receiver has noise performance comparable to receivers with narrowband IF bandpass filtering and sampling detectors for signal-to-noise ratio (SNR) and phase noise in the range of practical interest, but with potentially less degradation due to intersymbol interference (ISI).

Performance of Rake receiver assisted adaptive-modulationbased CDMA overfrequency selective slow Rayleigh fading channels

A closed form expression of the average bit error rate (BER) is derived for a Rake receiver adaptive-modulation scheme over frequency selective slow Rayleigh fading channels. Multidimensional minimisation of a cost function based on the derived closed form BER expression is performed to optimise the switching levels for a constant BER adaptive modulation system.

BER expressions for differentially detected π/4 DQPSK modulation

Closed form bit-error rate (BER) expressions for differentially detected /spl pi//4-shifted differentially encoded quadrature phase-shift keying (QPSK) modulation (/spl pi//4 DQPSK) are derived for both additive white Gaussian noise (AWGN) and Rayleigh-fading channels. The derivations are carried out in an exact and most general manner in that in-phase (I) and quadrature (Q) channel bit-error probabilities P/sub cl/ and P/sub cQ/ are separately obtained in terms of the same-quadrature and cross-quadrature noise Correlation functions, including a measure of noise nonstationarity. We then specialize the general expressions for uncorrelated noise and equal noise powers in successive symbol periods to obtain a useful bit-error probability expression for the AWGN channel in the form P/sub e//spl ap/Q(/spl radic/(1.1716/spl middot/E/sub b//N/sub 0/)) where Q(/spl middot/) is the Gaussian distribution Q-function and E/sub b//N/sub 0/ is the bit energy-to-noise density ratio. Exact BER expressions for the Rayleigh-fading channel that involve the noise parameters are also given and are extended to the case of L-fold diversity combining.

The use of WMC distribution for performance evaluation of APD optical communication systems

In the analysis of the bit-error rate (BER) of an optical communication system with avalanche photodiode (APD) detectors, the Webb, McIntyre, Conradi (1974) distribution has been often used to approximate the APD receiver output statistics. This paper presents new simple and closed form BER expressions as well as an importance sampling technique for optical systems employing APD receivers when the WMC model is used. Comparison of the WMC model with the exact model is also carried out. In particular, it is shown that the WMC distribution is quite accurate and has the advantage of simplicity for both simulation and analysis.

The error performance of Gray encoded QPSK and 8-PSK schemes in a fading channel with cochannel interference

Closed-form BER (bit error rate) expressions are derived for Gray-encoded QPSK (quadrature phase shift keying) and 8-PSK schemes using coherent detection in a slow Rayleigh fading narrowband channel with fading cochannel interference. Earlier work has been limited to deriving the approximate BER using the canonical Stein (1961) receiver concept. The symbol error rate (SER) for the QPSK scheme is also derived. The desired signal and the cochannel interferer are both PSK signals, modulated by different baseband pulses with identical signaling rate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

BER performance of DQPSK in slow Rician fading

A new expression involving an infinte series of finite integral terms is derived for the bit error rate (BER) of DQPSK in slow Rician fading channels. The formula reduces to a new closed form BER expression for DQPSK in Rayleigh fading channels when the K factor (ratio of LOS to multipath power) equals zero.