Exact Closed-Form BER Analysis of MIMO Multiplexing under Channel Prediction Errors

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.

Multiple-input multiple-output (MIMO) has been accepted as a promising technology for its potential to achieve low bit error rate (BER) by space time coding [1] or to achieve large capacity by multiplexing [2]. MIMO multiplexing has been widely adopted to realize high speed data communications. The capacity of MIMO systems in the point-to-point transmission without external interferences has been studied in [3, 4] to show that large capacity can be achieved in a rich scattering environment. In a cellular environment, the same frequency/frequencies can be used in neighboring cells. As a result, co-channel interference exists and the channel between the base-station (BS) and the mobile-station (MS) is changed from noise-limited channel to interference-limited channel. Recently, the capacity of MIMO systems in the cellular environment has attracted much interest. Uplink (transmission from MS to BS) capacity with variable-rate transmissions is studied in [5]. By modeling the co-channel interference as additive white Gaussian noise (AWGN), the uplink capacity is also studied in [6, 7]. On the other hand, from the users’ stand point, the downlink capacity may be more interesting. However, the results for the downlink capacity of cellular MIMO systems presented in the literature are mainly based on the simulation results. Very detailed simulation results for the downlink MIMO capacity in 3G FDD WCDMA cellular systems can be found in [8]. By assuming single-frequency-reuse (the frequency reuse factor (FRF) equals to 1), the capacity of downlink cellular MIMO systems is studied by simulations and the results are presented in [9, 10]. These results are given in terms of the number of antennas, the modulation schemes, the propagation parameters as well as the cell size. However, FRFs other than 1 are not considered. By taking various FRFs into consideration, a comparative study on the capacity of cellular MIMO systems is presented in [11]. A comprehensive comparison between the capacity of SISO, SIMO, STBC-MISO and MIMO systems in a cellular environment is made based on the simulation results. In general, fixed FRF has been considered in cellular systems. It is reported in [12] that a flexible FRF may help to improve the capacity for cellular single antenna (SISO) systems. However, flexible design of FRF for cellular MIMO systems is rarely available in the literature. In this chapter, the downlink capacity of cellular MIMO systems is theoretically analyzed in terms of both the ergodic and outage capacities. The theoretical results of the best and worst situation capacities suggest that the greatest capacities may be achieved by using FRF 1 or FRF 3 adaptively according to the situations. Therefore, a hybrid frequency reuse scheme is

Closed form expressions for the bit error rate (BER) for a multiple input multiple output (MIMO) relay system employing maximum likelihood (ML) based decode and forward (DF) cooperative diversity are obtained. The DF operation at the relay involves maximal ratio combining (MRC) on the source-relay link and space-time coding (STC) on the relay-destination link. Exact expressions of the BER are obtained for the case of a single relay supporting two antennas. For a system employing a large number of relays, each having two antennas, approximate expressions for the BER are obtained using the piecewise linear (PL) approximation for the ML detector. This is done by finding the statistics of conditionally Gaussian random variables, that appear in the decision variable. The validity of the analytical expressions is then verified through simulations. Through numerical results obtained from the BER expressions for large number of relays, it is then shown that the loss in diversity order due to DF can be compensated by using multiple antennas at the relay.

MIMO (Multiple input–Multiple Output) technology is a promising and upcoming technology for the future wireless generation system, as it has got high throughput and diversity gain. MIMO makes antennas work smarter by enabling them to combine data streams arriving from different paths and at different times to effectively increase receiver signal-capturing power. MIMO is used in modern wireless standards, including in IEEE 802.11, 3GPP LTE, and mobile WiMAX systems.Sphere decoding algorithm is a lattice reduction algorithm introduced for low complexity MIMO detection SD is a powerful and attractive tool to achieve a high performance close to the Maximum Likelihood (ML),Zero Forcing (ZF) but with less complexity. This paper presents a simulation study on the sphere decoding method and compares the performance with other classical MIMO scheme such as VBLAST and Zero forcing receivers. The simulation tool used is MATLAB communication tool box version 7.1. The performance metric considered is Bit Error Rate (BER) and the channel is assumed to be Rayleigh fading. It is inferred that detection is possible with complexity and gives a better result in terms of Bit Error Rate when comparing general sphere decoding and MMSE.

The demand for higher data rate and better quality of service (QoS) in wireless communications was growing fast in the past few years. Obtaining these requirements becomes challenging for wireless communication systems due to the problems of channel multi-path fading, higher power and bandwidth limitations. One of the most promising solutions to this problem is Multiple Input Multiple Output (MIMO) system. This paper proposed a combined spatial multiplexing MIMO scheme with beamforming for high data rate wireless communication. The proposed transmission scheme combines the benefits of both techniques and the system was able to transmit parallel data streams as well as providing beamforming gain. Actually, these diverse techniques, share the same requirement of multiple antenna elements, but differ in the antenna element spacing necessary for the different schemes to work. Thus, smart antenna array was proposed as a possible solution and was adopted at the both transmitter and the receiver. The hybrid technique provides higher spectral efficiency and improve better Bit error rate (BER) of the system than the conventional MIMO, spatial multiplexing and beamforming techniques under the same simulation environment.

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.

In this paper, frequency-domain one-tap weight control for single-carrier multiple access with multiple antennas is considered. Adaptive antenna array (AAA) weight control, diversity combining (DC) weight control and least square (LS) weight control are studied. These three weight control algorithms belong to multiple-input multiple-output (MIMO) beam forming, MIMO diversity and MIMO multiplexing, respectively. The weight control algorithms will be evaluated and compared in terms of computational complexity as well as bit error rate (BER) performance in a frequency-selective Rayleigh fading channel.

Multiple input multiple output (MIMO) systems can be designed for two operational modes: to improve bit error rate (BER) or to increase capacity without consuming additional power or bandwidth. In this paper, MIMO space-time-frequency (STF) conjugate two-path transmission orthogonal frequency division multiplexing (OFDM) systems with precoders are presented to combat inter-carrier interference and to adaptively switch between these two modes in mobile fading channels. First, the STF architecture is developed to form a 2 × 1 STF-OFDM system. Second, a conjugate cancellation (CC) two-path transmission scheme is integrated with the STF-OFDM system to form a new 2 × 1 STFCC-OFDM system. This system improves BER without expanding power or bandwidth in comparing with the CC scheme. Third, Walsh–Hadamard (WH) transform is employed as the precoder to form the 2 × 1 WHSTFCC-OFDM system. Finally, a 2 × 2 WHSTFCC-OFDM architecture is designed. It can be used to improve BER or switch to two 2 × 1 WHSTFCC-OFDM systems to increase capacity as needed. Simulations indicate that the 2 × 1 WHSTFCC-OFDM system has the best BER, the STFCC-OFDM system, and the STF-OFDM system follow in order. Similarly, the BER of the 2 × 2 WHSTFCC-OFDM system outperforms the 2 × 1 WHSTFCC-OFDM, and the 2 × 2 STFCC-OFDM system follow in order. All these STFCC- and WHSTFCC-OFDM schemes are simple and backward compatible with the existing OFDM system. They may serve as baseband building blocks in OFDM transceivers and can be adaptively switched between 2 × 1 and 2 × 2 architectures as required for the fourth generation and the future planned fifth generation MIMO systems. This adaptive MIMO system can also be applied to the regular or bad weather environment in the disaster conditions for increasing capacity or enhancing the reliability of the communication system.

The free space optical (FSO) communication system has attracted many researchers from different countries, owning to its advantages such as high security, high speed and anti-interference. Among all kinds of the channels of the FSO communication system, the atmosphere channel is very difficult to deal with for two typical disadvantages at least. The one is the scintillation of the optical carrier intensity caused by the atmosphere turbulence and the other is the multipath effect by the optical scattering. A lot of studies have shown that the MIMO (Multiple Input Multiple Output) technology can overcome the scintillation of the optical carrier through the atmosphere effectively. So the background of this paper is a MIMO system which includes multiple optical transmitting antennas and multiple optical receiving antennas. A number of particles such as hazes, water droplets and aerosols exit in the atmosphere widely. When optical carrier meets these particles, the scattering phenomenon is inevitable, which leads to the multipath effect. As a result, a optical pulse transmitted by the optical transmitter becomes wider, to some extent, when it gets to the optical receiver due to the multipath effect. If the information transmission rate is quite low, there is less relationship between the multipath effect and the bit error rate (BER) of the communication system. Once the information transmission rate increases to a high level, the multipath effect will produce the problem called inter symbol inference (ISI) seriously and the bit error rate will increase severely. In order to take the advantage of the FSO communication system, the inter symbol inference problem must be solved. So it is necessary to use the channel equalization technology. This paper aims at deciding a equalizer and designing suitable equalization algorithm for a MIMO free space optical communication system to overcome the serious problem of bit error rate. The reliability and the efficiency of communication are two important indexes. For a MIMO communication system, there are two typical equalization methods. The first method, every receiving antenna has an independent equalizer without the information derived from the other receiving antennas. The second, the information derived from all of the receiving antennas mixes with each other, according to some definite rules, which is called space-time equalization. The former is discussed in this paper. The equalization algorithm concludes training mode and non training mode. The training mode needs training codes transmitted by the transmitter during the whole communication process and this mode reduces the communication efficiency more or less. In order to improve the communication efficiency, the blind equalization algorithm, a non training mode, is used to solve the parameter of the equalizer. In this paper, firstly, the atmosphere channel is described focusing on the scintillation and multipath effect of the optical carrier. Then, the structure of a equalizer of MIMO free space optical communication system is introduced. In the next part of this paper, the principle of the blind equalization algorithm is introduced. In addition, the simulation results are showed. In the end of this paper, the conclusions and the future work are discussed.

We propose an adaptive reduced-rank solution for decoding spatial multiplexed multiple-input multiple-output (MIMO) wireless communications based on the multi-stage Wiener filter (MSWF). Spectral efficiency gains promised by spatial multiplexing schemes, such as vertical Bell Labs space time (V-BLAST) and space-division multiple access (SDMA), are difficult to realize for military applications where extreme channel conditions such as co-channel interference and intentional jamming can be expected. We show that the MSWF combined with successive interference (SIC) for spatial demultiplexing leads to significant signal subspace compression or rank-reduction. We propose for the MSWF-SIC a novel rank-reduction stopping rule that adapts to channel correlation and interference converges much faster than full rank methods permitting shorter training length and robustness to co-channel interference and jamming. Also, significant computational reduction is realized making this method a good candidate for portable applications where computational resources are limited. Bit error rate (BER) versus SNR for the correlated channel and for co-channel interference and SINR versus the MSWF rank-reduction and length of training interval are presented.

The spatial and intertap correlation matrices of fading channels are first estimated for underwater multiple input multiple output (MIMO) systems using real experimental data. We confirm that underwater MIMO channels exhibit strong spatial and temporal correlation. The bit error rate (BER) performance of the MIMO system at different correlation scenarios are also evaluated with computer simulation. At BER=0.01%, the required SNR of highly correlated channel is 5 dB higher than the i.i.d. channel. BER results of the experimental data also quantitatively show the performance degradation caused by the correlation.

– This paper analyses the performance of Multiple Input Multiple Output (MIMO) wireless communication system by combining it with an efficient algorithm Diagonal Reduction (DR). DR is a powerful tool to achieve more efficiently a high performance with less complexity. This paper proposes a DR algorithm in order to reduce its complexity named Greedy Diagonal Reduction (GDR) algorithm which gives reduced complexity with efficient performance at the receiver using the MATLAB communication tool box version 7.0 as a simulation tool. From the simulation results of various reduction algorithms it is observed that, DR can reduce the number of iterations using size reduction operations. Proposed DR algorithm gives identical Bit Error Rate (BER) performance with LLL algorithms when applied to Successive Interference cancellation (SIC) decoding. Greedy DR reduces the computational complexity in Multiple Input Multiple Output systems by improving the efficiency in terms of size reduction operations. Sphere Decoding (SD) technique gives better BER performance on comparing with Successive Interference cancellation decoding technique.

In the present paper, the bit error rate (BER) performance of hybrid power line communication (PLC) and multiple‐input multiple‐output (MIMO) visible light communication (VLC) system (HPMV) has been investigated using line‐of‐sight (LOS) and LOS plus first reflection (L‐R1) signals for room size of 5 m × 5 m × 3 m (configuration A) and 7.5 m × 7.5 m × 3.5 m (configuration B). In the work, Rayleigh fading and Barry channel models have been considered for PLC and VLC channels respectively. The BER has been analysed by varying separations between LEDs as 0.2 m, 0.6m and 1m for both configurations. The results show that the BER for LOS and L‐R1 signals decreases upto optimal separation of 0.6 m for configuration A. However, the result indicates that the required optimal separation for configuration B is more than configuration A. The channel frequency response of MIMO‐VLC and HPMV system has been inspected and it supports the results of BER simulation. It has been found that, with increase in spatial separation between LEDs, the deep notches and attenuation in the frequency response of MIMO‐VLC system decrease. The overall investigation shows that even though OFDM is resilient to frequency selective fading, an optimum separation between LEDs must be chosen according to the room size for the HPMV system.

This paper proposes likelihood function generation of complexity-reduced maximum likelihood detection with QR decomposition and M-algorithm (QRM-MLD) suitable for soft-decision turbo decoding and investigates the throughput performance using QRM-MLD with the proposed likelihood function in multipath Rayleigh fading channels for orthogonal frequency and code division multiplexing (OFCDM) with multiple-input multiple-output (MIMO) multiplexing. Simulation results show that by using the proposed likelihood function generation scheme for soft-decision turbo decoding following QRM-MLD in 4-by-4 MIMO multiplexing, the required average received signal energy per bit-to-noise power spectrum density ratio (E/sub b//N/sub o/) at the average block error rate (BLER) of 10/sup -2/ at a 1-Gbps data rate is significantly reduced compared to that using hard-decision decoding in OFCDM access with 16 QAM modulation, the coding rate of 8/9, and 8-code multiplexing with a spreading factor of 8 assuming a 100-MHz bandwidth. Furthermore, we show that by employing QRM-MLD associated with soft-decision turbo decoding for 4-by-4 MIMO multiplexing, the throughput values of 500 Mbps and 1 Gbps are achieved at the average received E/sub b//N/sub o/ of approximately 4.5 and 9.3 dB by QPSK with the coding rate of R = 8/9 and 16 QAM with R = 8/9, respectively, for OFCDM access assuming a 100-MHz bandwidth in a twelve-path Rayleigh fading channel.