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

We investigate the exact error performance of hard minimum mean-squared error (MMSE) detection in multipleinput multiple-output (MIMO) systems. To facilitate the analysis, we first conduct error analysis for a general system with decision statistic, z = ax + u, where a >; 0, x is the transmitted signal, and u is the arbitrarily distributed noise component which is independent of x. For this general system, we derive the exact and closed-form bit-error rate (BER) expressions for M-ary pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) signalings, which include the well-known BER result in [12] as a special case. For the first time in the literature (to the best of our knowledge), we then derive the exact and closed-form instantaneous BER and symbol-error rate (SER) expressions for hard MMSE detection. Finally, the validity of the derived error probability expressions is verified through our own Monte Carlo simulations and the simulation results reported in the literature.

The bit error rate (BER) performance of orthogonal space-time block codes (STBC) in correlated multiple input multiple output (MIMO) channels is studied. We derive closed-form exact BER equations for pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM), and phase shift keying (PSK) constellations in a correlated Rayleigh MIMO channel. The BER expressions can be easily evaluated without any numerical methods.

We derive closed-form expressions for the exact average bit error rate (BER) of hierarchical square M-ary quadrature amplitude modulations (M-QAMs), when these modulation schemes are used along with orthogonal space-time block coding (STBC) over correlated multiple-input multiple-output (MIMO) Nakagami-m fading channels with arbitrary fading parameters. The derived formulae can be used to assess the effects of spatial correlation on the BER performance of hierarchical M-Q AM.

The performance analysis of multiuser multiple-input multiple-output (MIMO) system with rate-adaptive modulation and antenna selection over Rayleigh fading channels is presented. By means of exact expression of bit error rate (BER), the suboptimal switching thresholds (ST) of fading gain subject to a target BER constraint are derived. It is shown that this suboptimal ST are very close to the optimal ST, and is more accurate than the conventional ST based on approximate BER expression. By the ST, we obtain exact closed-form expressions of the spectrum efficiency (SE) and average BER. Moreover, a tightly approximate BER is derived to simplify the calculation of exact BER, which has more accuracy than the existing approximate BER. Simulation results for SE and BER are in good agreement with the derived theoretical expressions. The results show that the multiuser MIMO with adaptive modulation can provide better SE than the single user counterpart, and the system SE using suboptimal ST is also higher than that using conventional ST.

The symbol error rate (SER) and the bit error rate (BER) of orthogonal space-time block codes (OSTBCs) with antenna selection over keyhole fading channels are examined. Considered are receive antenna selection, transmit antenna selection, and joint antenna selection at both the transmitter and the receiver. The exact SERs of OSTBCs for M-PSK and square MQAM constellations are obtained using the technique of moment generating function (MGF). By applying the Bonferroni-type bounds, tight lower and upper bounds for both the SER and BER are provided in closed-form expressions with finite-range single integrals. The bounds can be applied to arbitrary constellations and mappings. Numerical results show that the bounds can be used to provide practically the exact SER and BER over a wide range of the signal-to-noise ratio.

In recent literature, performance analyses of multiple-input multiple-output (MIMO) multiuser systems using orthogonal space-time block coding (OSTBC) over Nakagami-m fading via bit error rate (BER) estimation have been obtained. In addition, analyses of the average channel capacity of these systems were carried out. From these findings, it was reported that closed-form expressions of the average channel capacity are difficult to obtain because of the presence of a finite product of an incomplete Gamma function. This paper shows that a new closed-form upper bound expression on the average channel capacity for non-integer values of m can be derived which gives insights into performance of OSTBC MIMO systems. The new bound is shown to be tight and valid with sensible numerical results.

Precoding techniques can be used in multiple input multiple output (MIMO) system to assign resources such as power and information optimally. This paper is concerned with limited feedback in precoded orthogonal space time block code (OSTBC) systems, which is a precoding technique for incomplete channel information response. The conventional approach to design the precoding codebook is based on the discrete Fourier transform (DFT) matrix, which has high computational complexity. In this paper, a new approach to design the precoding codebook for the limited feedback precoded OSTBC systems is proposed, which is based on the discrete fractional sine transform (DFRST) matrix. The proposed DFRST-based precoding codebook design approach has lower computational complexity comparing to that of the DFT-based design with very similar bit error rate (BER) performance.

Multiple input multiple output (MIMO) system is one of the most promising wireless technologies that can achieve wide coverage, high throughput and improved reliability. Low density parity check (LDPC) codes can achieve capacity near Shannon's limit with good error correcting performance. In this paper, we combined LDPC codes with orthogonal space time block codes (OSTBC) in MIMO systems. The performance of LDPC codes depends on the structure of the parity check matrix and decoding algorithms. In this paper, we analyzed the bit-error rate (BER) performance of different LDPC codes like Quasi Cyclic (QC) and random which differs in their parity check matrix structures. For low complexity decoding, log domain Sum Product Algorithm (log-SPA) is used which has messages in the form of log-likelihood ratios (LLR). Further, the approximate BER expressions are derived and verified for above mentioned system with different antenna configurations.

Multiple-input multiple-output (MIMO) systems employing both maximal-ratio transmission and receive antenna selection (MRT&RAS) are studied in this paper. The examination has been done for independent and identically distributed (i.i.d.) flat Nakagami-m fading channels. Exact bit error rate (BER) expressions for binary phase shift keying (BPSK), differential binary phase shift keying (DBPSK) and binary frequency shift keying (BFSK) signals are derived by using the moment generating function (MGF)-based analysis method. By deriving upper bounds for exact BER expressions, it is shown that the investigated systems achieve full diversity orders at high signal-to-noise ratios (SNRs). Also, the ergodic system capacity and outage probability of MRT&RAS scheme have been analyzed. Exact BER results for different system and channel conditions are validated by Monte Carlo simulations.

The issue of channel state information at the transmitter is investigated using MIMO channel measurements and by deriving expressions for ergodic and outage capacity in a Rayleigh fading channel. Expressions for bit error rates in Rayleigh fading channels are also presented for orthogonal space time block codes and for beamforming where the bit error rates in the beamforming case follow from the distribution of the largest eigenvalue to Wishart matrices. We demonstrate by measurements that Rayleigh fading is a valid assumption in non line-of-sight channels, although a Nakagami-m distribution showed to be a more appropriate distribution model in both line-of-sight and NLOS environments. It was also demonstrated that channel state information at the transmitter is less useful in high SNR scenarios but is more useful in line-of-sight channels compared to non line-of-sight environments. (6 pages)

Starting from three transmit antennas and Nr receive antennas (3Tx-Nr Rx, generally defined as MIMO) system employing orthogonal space-time block coding (STBC-MIMO), the paper analyzes the solution procedure of complex orthogonal weighting channel matrix (OWCM) and decoupling method of the signals received for the resulting pre-coding system, and concludes an algorithm process using computer simulation to generate the complex OWCM. Employing the orthogonal OWEM, we can decouple easily received signals at receiver terminals. Utilizing such decoupled received signals, the paper provides a normal expression of the average output signal-noise-ratio (SNR) for the interest systems. Taking a sample of precoding 2Tx-1Rx STBC system, in the three cases of channel gain x1 and x2 are uncorrelated, order statistics x1gesx2, and the 2 out of 3 transmit antennas with x1gesx2gesx3, respectively, the three exact closed-form bit error rate (BER) expressions are presented. According to these analytical BER expressions, 4 sets of curves are presented to illustrate the performance results. Except the case of x1 and x2 are uncorrelated / no order statistic, the numerical results show that perfect power allocation for transmit antennas selected can effectively enhance system bit error performance. Meanwhile, increasing transmit antennas power related to the best channel can improve obviously system error performance. But if k=W1/W2 is enough large, the BER performance improvement is not obvious, this conclusion makes guidance function for the MIMO systems of using pre-coding STBC technique.

A paradigm for multiple-input multiple-output (MIMO) channel modeling demands diversity technique to compensate the effects of fading and shadowing. In this paper, error performance of MIMO system is analyzed with orthogonal space time block code (OSTBC) and maximal ratio combining (MRC) techniques over Weibull-gamma (WG) fading channel. WG distribution forms a composite channel model which is used to determine the effects of multipath as well as shadowing. In this scenario, exact analytical expressions for symbol error rate (SER) are computed for MIMO systems using OSTBC and MRC. Consequently, the effects of fading severity by varying shape parameters are also shown by simulation and analytical results.

In this paper we present a new simple cooperative relaying scheme. The proposed scheme is compared with simple cooperative schemes with virtual orthogonal space time block coding (OSTBC) and quasi orthogonal space time block coding (QOSTBC). Every of these three schemes includes one base station with two antennas, two relay stations each with a single antenna and one mobile station with a single antenna. The aim of the proposed scheme is to preserve, as much as it is possible bit error rate (BER) performance of the cooperative scheme with virtual OSTBC, but with increased code rate. It is shown that the presented scheme obviously outperforms simple cooperative scheme with virtual QOSTBC, while in comparison with simple cooperative scheme with virtual OSTBC has very similar BER performance and increased code rate.

Diversity is an integral technique in the advancement of wireless communications. Multiple-input multiple-output (MIMO) technology continues to occupy a pivotal position in the fourth-generation (4G) standards and beyond. With the advent of full-dimension (FD) MIMO and massive MIMO, new paradigms are being targeted in the disruptive technology. Third-generation partnership project (3GPP) has also emphasized the advanced MIMO technology for achieving its vision of International Mobile Telephony (IMT) 2020. However, implementing multiple antennas can be cumbersome due to limiting factors such as size, cost, and hardware limitations. In such a scenario, where implementing many antennas is not feasible, the benefits of diversity can be reaped by employing cooperative communication. Single antenna mobiles can share their mobile stations giving rise to a virtual MIMO system. In this paper, the authors have analyzed the performance of cooperative mobile stations in a frequency selective channel. Orthogonal frequency division multiplexing (OFDM), known for its robustness against multipath fading, is the modulation technique employed to circumvent the hazardous effects of intersymbol interference (ISI). MIMO is the key technology for achieving capacity advantage and improving link reliability. The blend of these two cutting edge technologies in a cooperative relay system presents encouraging results and inferences. Maximal Ratio Combining (MRC) is employed at the relay and the receiver to maximize the signal-to-noise ratio (SNR). Decode and forward (DF) protocol is used at the relay node owing to its regenerative nature and adaptability. The closed-form expressions for bit error rate (BER) and outage probability (Pout) are derived and compared with the experimental results. The effect of power decay factor is analyzed and simulation is done for 2 × 2, 2 × 3, and 2 × 4 transmit and receive antennas. The number of antennas at the relay is kept as 2. The analytical results agree with the simulation results.

Transmit antenna selection is a promising technique to simplify hardware and computational complexity of MIMO wireless communication systems. In this paper, we derive expressions for outage probability and bit error rate of two-hop relaying systems incorporated with transmit antenna selection at source and relay node. A closed form expression for outage probability and an infinite expression for bit error rate are derived for two hop cooperative communication system for BPSK modulation scheme. In the analysis, received signals are assumed to be collection of signals received as a result of multiple reflections having a line of sight component. Such channels can be well approximated by к-μ fading distribution which is generalized assumption to model fading channels with a dominant or line of sight component. To analyze the performance of the system at high SNR conditions, the expression of asymptotic BER is also derived in closed form from the expression for exact BER. The transmit antenna is selected at the source and relay nodes such that the received signal to noise ratio at the destination node is maximized. Maximal ratio combining is considered at the relay and destination nodes. The bit error rate results obtained from analytical expressions and Monte Carlo simulations are plotted for different values of fading parameters, к and μ. The analytical results are found to be in close agreement with simulation results.