Exact Error Rate Analysis of MIMO-MRC System under Cochannel Interference and Imperfect Channel State Information

In this paper, we derive closed-form solution for the bit error rate of multi-input multi-output (MIMO) system with maximum ratio combining. We consider binary PSK modulation suffers from cochannel interference (CCI) and imperfect channel state information (CSI). We assume a propagation model wherein the desired and interfering signals undergo independent and identically distributed (i.i.d.) Rayleigh fading channels. Furthermore, the signal-to-noise ratio (SNR) gain penalty caused by the interference signals and the root mean square of the CSI were demonstrated. The numerical results presented in this paper demonstrate the system performance under very realistic propagation and detection conditions including MIMO system, CCI, imperfect CSI, generalized fading channels, and AWGN. Hence our results are expected to be of significant practical use for such scenarios.     

Exponential Diversity Achieving Spatio–Temporal Power Allocation Scheme for Fading Channels

In this paper, we analyze optimal (in space and time) adaptive power transmission policies for fading channels when the channel-state information (CSI) at the transmitter (CSIT) and the receiver (CSIR) is available. The transmitter has a long-term (time) average power constraint. There can be multiple antennas at the transmitter and at the receiver. The channel experiences Rayleigh fading. We consider beamforming and space-time coded systems with perfect/imperfect CSIT and CSIR. The performance measure is the bit error rate (BER). We show that in both coded and uncoded systems, our power allocation policy provides exponential diversity order if perfect CSIT is available. We also show that, if the quality of CSIT degrades then the exponential diversity is retained in the low SNR region but we get only polynomial diversity in the high SNR region. Another interesting conclusion is that in case of imperfect CSIT and CSIR, knowledge of CSIT at the receiver is very important. Finally, for the optimal power control policy of the uncoded system we find the error-exponents which provide the rate versus diversity-order tradeoff for this policy. This tradeoff is of an entirely different nature than the well-known Zheng-Tse tradeoff.     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

A New Union Bound on the Error Probability of Binary Coded OFDM Systems in Wireless Environments

Orthogonal Frequency Division Multiplexing (OFDM) systems are commonly used to mitigate frequency-selective multipath fading and provide high-speed data transmission. In this paper, we derive new union bounds on the error probability of a coded OFDM system in wireless environments. In particular, we consider convolutionally coded OFDM systems employing single and multiple transmit antennas over correlated block fading (CBF) channels with perfect channel state information (CSI). Results show that the new union bound is tight to simulation results. In addition, the bound accurately captures the effect of the correlation between sub-carriers channels. It is shown that as the channel becomes more frequency-selective, the performance get better due to the increased frequency diversity. Moreover, the bound also captures the effect of multi-antenna as space diversity. The proposed bounds can be applied for coded OFDM systems employing different coding schemes over different channel models.     

Performance of Transmit and Receive Antenna Selection in the Presence of Channel Estimation Errors

This letter considers the effect of channel estimation errors on the performance of space-time coded (STC) systems with transmit and receive antenna selection over quasi-static flat fading channels. By performing pairwise error probability analysis and presenting numerical examples, we show that the diversity order achieved with perfect channel state information (CSI) is still achievable with imperfect CSI used both at the antenna selection and the space-time decoding processes. We note that our results apply to general STC systems with both transmit and/or receive antenna selection based on largest received powers which can be estimated by any channel estimator.     

Impact of channel-state information on coded transmission overfading channels with diversity reception

We study the synergy between coded modulation and antenna-diversity reception on channels affected by slow Rician fading. Specifically, we assess the impact of channel-state information (CSI) on error probability. We show that with a good coding and constant envelope modulations (for example, phase-shift keying) scheme the loss in performance when CSI is not available is moderate (around 1.5 dB). Moreover, as the diversity order grows, the channel tends to become Gaussian     

Differential and coherent decorrelating multiuser receivers for space-time-coded CDMA systems

Previously, we proposed a differential space-code modulation (DSCM) scheme that integrates the strength of differential space-time coding and spreading to achieve interference suppression and resistance to time-varying channel fading in single-user environments. In this paper, we consider the problem of multiuser receiver design for code-division multiple-access (CDMA) systems that utilize DSCM for transmission. In particular, we propose two differential receivers for such systems. These differential receivers do not require the channel state information (CSI) for detection and, still, are resistant to multiuser interference (MUI) and time-varying channel fading. We also propose a coherent receiver that requires only the CSI of the desired user for detection. The coherent receiver yields improved performance over the differential receivers when reliable channel estimates are available (e.g., in slowly fading channels). The proposed differential/coherent receivers are decorrelative schemes that decouple the detection of different users. Both long and short spreading codes can be employed in these schemes. Numerical examples are presented to demonstrate the effectiveness of the proposed receivers.     

Chaos-Coded Modulations Over Rician and Rayleigh Flat Fading Channels

In this brief, we analyze a kind of chaos-coded modulations over both Rician and Rayleigh frequency non-selective uncorrelated fading in the presence of additive white Gaussian noise. We provide bounds both for the case when perfect channel-state information (CSI) is available at the decoder and when there is no CSI. We show that the bounds proposed can be tight enough to give reason of the behavior of these systems in a flat fading channel. We compare the results with a related trellis-coded modulation and show that the degradation in performance can be at least as low as with conventional coded modulation systems.     

Impact of diversity reception on fading channels with codedmodulation. II. Differential block detection

For pt. I see ibid., vol.45, no.6, p.563-572, 1997. We study coded modulation with block differential detection in an arbitrarily correlated Rician fading channel with space diversity. Coded differential q-PSK is included in our analysis as a special case. A metric is chosen that is optimum for perfect interleaving, slow fading, and independent diversity branches. For slow fading, we compare the the cutoff rates of the channels resulting from different choices of block length N and diversity index M. Specifically, we show that block detection with diversity may or may not generate a better coding channel than usual differential detection, according to the code selected and the combination of values of M and N. In particular, for low-diversity orders (M=1,2) and for low-to-medium code rates, differential detection is still an optimal or near-optimal solution, while for high-diversity orders (M⩾2) and medium-to-high code rates (up to uncoded modulation) block detection with N>2 can provide a significant gain. An error floor always exists when fading is fast. It decreases exponentially with the product of code diversity and space diversity, so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading. Performance examples based on actual coding schemes are also shown     

Capacity of MIMO channels in the presence of co‐channel interference

This paper presents analytical results on the capacity of multiple‐input‐multiple‐output (MIMO) fading channels in the presence of co‐channel interference (CCI). We consider the scenario in which the desired and CCI users are all subject to Rayleigh fading. We assume that channel realizations of both the desired and CCI users are known at the receiver. Moreover, we consider the case where the transmitter does not have any CSI and as such equal‐power allocation among transmit antennas is used. Given this setup, we derive the moment generating function (MGF) and the mean of the mutual information (MI). We then study the complementary cumulative distribution function of the MI using a Gaussian approximation. Finally, we present and discuss numerical examples to illustrate the mathematical formalism and to show the effect of various parameters on the capacity of MIMO channels in the presence of CCI. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance of M-PSK with GSC and EGC with Gaussian weighting errors

Using a moment-generating function (MGF)-based approach, we study the performance of M-ary phase-shift keying (M-PSK) with generalized selection combining (GSC) and equal gain combining (EGC) in fading channels (including Rayleigh, Rician, Nakagami-m, and Nakagami-q fading) with independent and identically distributed (i.i.d) branches. Analytical expressions for the error and outage probabilities, the signal-to-noise-ratio (SNR) statistics, and the channel capacity of M-PSK diversity receivers are derived, taking into account the effects of Gaussian weighting errors and all relevant system and channel parameters. Unlike the case of perfect channel-state information (CSI), the outage probability for the case of imperfect channel estimation (ICE) is not only a function of the normalized SNR with respect to the SNR threshold, but also a function of the operating SNR itself. The SNR loss of the M-PSK GSC and EGC receivers due to ICE and the relation between the receiver input and output SNRs for ICE are derived. Our results show that, even with ICE, GSC and EGC are effective in improving the output SNR and significantly reduce the error floor and the channel-capacity loss caused by ICE.     

Performance comparison of selection combining schemes for binary DPSK on nonselective Rayleigh-fading channels with interference

This paper is concerned with the error performance analysis of binary differential phase shift keying (DPSK) with differential detection over the nonselective Rayleigh-fading channel with selection diversity reception and with an additive, correlated, Gaussian interference process in each diversity channel. The fading process is assumed to have an arbitrary Doppler spectrum with arbitrary Doppler bandwidth. The selection schemes investigated are: 1) the selection combining (SC) scheme based on signal-to-noise power ratio (SNR); 2) the SC scheme based on signal-plus-noise (S+N); and 3) the SC scheme based on maximum output (MO). New, exact, closed-form bit-error probability (BEP) expressions are derived, and a performance comparison among the three SC schemes and combining diversity reception is given. The results obtained reduce to previously known results when the correlated interference process is absent, and when the fading process does not fluctuate over the duration of several symbol intervals. The results indicate that the performance of each scheme depends on the tradeoff between the number of diversity branches, the SNR, the interference level, and the correlation of the interference process. However, the SC-(S+N) scheme generally performs worse than the SC-SNR scheme, the SC-MO scheme and combining diversity reception scheme. The findings presented here are not only of fundamental theoretical value, but are also of practical interest to the designers of future mobile communication systems.     

Improved cochannel interference cancellation for MFSK/FH-SSMAsystems

There has been much interest in the application of frequency hopping-spread spectrum multiple access (FH-SSMA) to wireless systems because of its frequency diversity and resistance to the near-far problem. In FH-SSMA systems, cochannel interference (CCI) is the dominant factor limiting the user capacity. Various techniques used to resolve the CCI problem have been extensively investigated. We propose several multiuser detection schemes based on canceling CCI to increase user capacity in a multilevel frequency shift keying (MFSK)/FH-SSMA system. The performance of systems with the proposed interference cancellers over a Rayleigh fading channel are analyzed and compared with those of the conventional and other interference cancellers. Our results show that the proposed schemes have the best performance in both nonfading and fading channels     

Maximal Ratio Combining (MRC) in Shadowed Fading Channels in Presence of Shadowed Fading Cochannel Interference (CCI)

Simultaneous existence of multipath fading and shadowing leads to worsening conditions in wireless channels. This is further compounded by the interference from other base stations operating at the same frequency. The effect of this cochannel interference (CCI) and shadowed fading in error rates is studied when maximal ratio combining is used to mitigate short term fading. The CCI channels were also treated as undergoing shadowed fading. The generalized K distribution was used to model the signal-to-noise ratio of composite shadowed fading channel. The probability density functions of the signal-to-noise ratio taking into account the presence of multipath fading, shadowing and CCI were derived and used for the estimation of error rates. Results demonstrated the existence of degradation in the channel manifested as increased error rates and higher error floors. The improvements in the channel obtained through diversity were also demonstrated. The approach presented here can be easily adapted to the analysis of other diversity schemes in shadowed fading channels.     

Comparison of diversity with simple block coding on correlatedfrequency-selective fading channels

We investigate the effects of correlation on the performance of diversity systems in wideband wireless radio environments. Specifically, the average bit error rate (BER) performance of M-ary differential phase shift keying (MDPSK) on correlated frequency-selective slow Rayleigh fading channels is analyzed. A two-branch diversity receiver with postdetection equal gain combining is considered. Nyquist pulse shaping is used and differential detection is employed at the receiver. The effects of cochannel interference on the system performance are assessed using a Gaussian interference model. To further enhance the system performance, the effects of combined diversity and forward error correction (FEC) coding on the average BER are investigated. Results using short cyclic block codes with perfect bit interleaving are obtained. The effects of the root mean square (RMS) delay spread, the amount of correlation, and the level of modulation, M, on the average BER are investigated in detail for both coded and uncoded systems. The results show that dual branch diversity combining with a correlation coefficient of 0.5 outperforms (in terms of BER) short block codes with perfect bit interleaving, and that combined diversity and coding strategies are effective in combatting the effects of frequency-selective fading     

Outage analysis of the hybrid free-space optical and radio-frequency channel

We study the hybrid free-space optical (FSO) and radio-frequency (RF) channel from an information theoretic perspective. Since both links operate at vastly different carrier frequencies, we model the hybrid channel as a pair of parallel channels. Moreover, since the FSO channel signals at a higher rate than the RF channel, we incorporate this key feature in the parallel channel model. Both channels experience fading due to scintillation, which is slow compared to typical signalling rates. Under this framework, we study the fundamental limits of the hybrid channel. In particular, we analyse the outage probability in the large signal-to-noise ratio (SNR) regime, and obtain the outage diversity or SNR exponent of the hybrid system. First we consider the case when only the receiver has perfect channel state information (CSIR case), and obtain the exponents for general scintillation distributions. These exponents relate key system design parameters to the asymptotic outage performance and illustrate the benefits of using hybrid systems with respect to independent FSO or RF links. We next consider the case when perfect CSI is known at both the receiver and transmitter, and derive the optimal power allocation strategy that minimises the outage probability subject to peak and average power constraints. The optimal solution involves non-convex optimisation, which is intractable in practical systems. We therefore propose a suboptimal algorithm that achieves significant power savings (on the order of tens of dBs) over uniform power allocation. We show that the suboptimal algorithm has the same diversity as the optimal power allocation strategy.     

Analysis of DPSK error rate due to multipath delay spread

The intersymbol interference (ISI) produced by multipath channel delay spread can be approximated as Gaussian noise. The equivalent average signal-to-noise power ratio (SNR) is defined. Very simple expressions for average bit error rate (BER) due to delay spread are derived for linear quaternary DPSK (QDPSK) transmission with differential detection over mobile radio Rayleigh fading channels.<>     

Design of trellis coded QAM for flat fading and AWGN channels

The design of trellis coded modulation (TCM) schemes for QAM constellations to counteract simultaneous flat fading and additive white Gaussian noise (AWGN) is considered. Motivated by the results of Divsalar and Simon (see IEEE Trans. Commun., vol.36, p.1004, 1988), and incorporating some recent ideas from Boulle and Belfiore (1992), we develop novel 2-D TCM schemes that attain diversity of order two even for a trellis structure that includes parallel paths with one symbol per edge. An algorithm is described that transforms codes designed for the AWGN channel into codes that achieve significant gains over flat fading channel, while preserving their coding gain over AWGN channel. Their performance is assessed via computer simulation for some representative TCM-QAM schemes under the assumption of uncorrelated fading and perfect channel state information (CSI). Finally, the effects of finite interleaving as well as imperfect CSI on code performance are investigated     

On the Performance of the MIMO Zero-Forcing Receiver in the Presence of Channel Estimation Error

By employing spatial multiplexing, multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. Zero-forcing (ZF) detection is a simple and effective technique for retrieving multiple transmitted data streams at the receiver. However the detection requires knowledge of the channel state information (CSI) and in practice accurate CSI may not be available. In this letter, we investigate the effect of channel estimation error on the performance of MIMO ZF receivers in uncorrelated Rayleigh flat fading channels. By modeling the estimation error as independent complex Gaussian random variables, tight approximations for both the post-processing SNR distribution and bit error rate (BER) for MIMO ZF receivers with M-QAM and M-PSK modulated signals are derived in closed-form. Numerical results demonstrate the tightness of our analysis     

The union bound for turbo-coded modulation systems over fadingchannels

We derive performance bounds for turbo-coded modulation systems over fading channels. We consider a Ricean fading channel model both with and without channel-state information (CSI). This model obviously includes Rayleigh fading channel as a special case. The bounds are extensions of similar bounds derived for additive white Gaussian noise channels. For the special case of a Rayleigh fading channel with CSI, we also derive a tighter version of the bound. We illustrate the use of the new bounds via some numerical examples