# An Adaptive Channel Model for VBLAST in Vehicular Networks

- Ghassan M. T. Abdalla
^{1}Email author, - Mosa A. Abu-Rgheff
^{1}and - Sidi-Mohammed Senouci
^{2}

**2009**:328706

**DOI: **10.1155/2009/328706

© Ghassan M. T. Abdalla et al. 2009

**Received: **6 May 2008

**Accepted: **1 February 2009

**Published: **19 March 2009

## Abstract

The wireless transmission environment in vehicular ad hoc systems varies from line of sight with few surroundings to rich Rayleigh fading. An efficient communication system must adapt itself to these diverse conditions. Multiple antenna systems are known to provide superior performance compared to single antenna systems in terms of capacity and reliability. The correlation between the antennas has a great effect on the performance of MIMO systems. In this paper we introduce a novel adaptive channel model for MIMO-VBLAST systems in vehicular ad hoc networks. Using the proposed model, the correlation between the antennas was investigated. Although the line of sight is ideal for single antenna systems, it severely degrades the performance of VBLAST systems since it increases the correlation between the antennas. A channel update algorithm using single tap Kalman filters for VBLAST in flat fading channels has also been derived and evaluated. At 12 dB , the new algorithm showed 50% reduction in the mean square error (MSE) between the actual channel and the corresponding updated estimate compared to the MSE without update. The computational requirement of the proposed algorithm for a VBLAST is 6 real multiplications and 4 real additions.

## 1. Introduction

Crash prevention, road traffic control, route guidance, internet on the road as well as multimedia services, and others are the promising applications of vehicular ad hoc networks (VANET). Such applications require high data rates and high reliability with minimum human interaction. Although the technology used in wireless communication such as IEEE 802.11 has reached a high level of maturity and is capable of providing high bit rates, its performance in high speed transmission and adaptability to channel conditions ranging from strong line of sight to Rayleigh fading are of concern. Multiple-input multiple-output (MIMO) systems, including diversity, space-time coding, and BLAST algorithms, have been thoroughly studied and have shown superior performance [1] compared to single antenna systems for mobile communications in rich scattering, no line of sight, and slowly varying channel conditions. However, the conditions are different in VANET, and an accurate channel model is required to study the performance of MIMO systems. Moreover, since MIMO algorithms require accurate channel state information, the issue of channel tracking is raised.

In this paper, we adapt the elliptical model introduced in [2] to simulate the MIMO channel in VANET. The channel Doppler spectrum was calculated and compared to that of the classical Jakes model [3]. As will be shown, the Doppler spectrum is different from that of Jakes' model due to the movement of the scatterers. The correlation between antennas was also studied under various line of sight conditions. The results show that an antenna separation of 3 or more, represents the wavelength, can achieve a correlation less than 0.5 unless a very strong line of sight exists. A novel channel update algorithm to track the channel is then introduced. The new algorithm improves the bit error rate (BER) performance of MIMO systems with a minor increase in hardware complexity.

The paper is organised as follows. Some of the existing models and their applications are discussed in the next section. Section 3 is a detailed description of the proposed channel model. In Section 4, a comparison between the proposed model and Jakes' model is provided as well as correlation results for a broadside antenna array. The channel update algorithm is derived and assessed in Section 5. Finally, Section 6 concludes the paper.

## 2. An Overview of Existing Channel Models

where
is the maximum Doppler shift, *v* is the relative transmitter receiver speed, and
is the zero-order Bessel function.

To simulate the received signal at a mobile terminal from a basestation, or vice versa, in marcocells, Lee's model is usually used [5]. Since the basestation is positioned over high buildings, the number of surroundings is small, while for a mobile terminal at street level, a large number of surroundings are available. Therefore, Lee modelled the channel by a ring of scatterers uniformly distributed around the terminal which affects both the terminal and basestation [6]. Lee's model was extended to model ad hoc networks in [7]. Since in ad hoc networks the transmitter and receiver are usually peers, both are assumed to be surrounded by scatterers; therefore, the authors of [7] developed a two-ring model which uses one ring of scatterers around the transmitter and another around the receiver. The two-ring model was extended to three dimensions in [8] to study the performance of vertical antenna arrays. The three-dimensional model assumes that the terminals are surrounded by scatterers of various heights, and the authors used cylinders instead of rings to model the channel. An elliptical model was introduced in [2] to study the angle of arrival (AOA) and angle of departure (AOD) as well as the performance of antenna arrays at basestations in microcells. Basestations in microcells are at street lights heights and, therefore, are more affected by the surroundings than those in macrocells. The probability of line of sight communication in microcells is also much greater than in macrocells. The model places the transmitter and receiver at the foci of an ellipse. The two-ring and three-dimensional channel models are ideal for urban areas under heavy traffic conditions where there are a large number of surroundings and no line of sight. However, in suburban areas, open areas, or light traffic conditions, the assumptions of large number of surroundings and no line of sight become invalid and, therefore, a more realistic channel model is required.

## 3. Proposed Channel Model

*D*is the distance between the transmitter and receiver, and

*c*is the speed of light. The delay spread of VANET has been measured for various roads and traffic conditions in [9, 10]. The minimum mean delay spread measured was 103 nanoseconds. We adopt this value in our model as a worst-case scenario since a larger delay spread leads to smaller antenna correlation.

where and are the heights of the transmitter and receiver antennas, respectively, and is the wavelength. The right-hand side of (3) is the minimum distance for the first Fresnel zone to touch the ground, and thus a ground reflection may exist only if (3) is satisfied [11, 12].

*i*) is given by (4) or (5) [13, 14]. Equation (5) follows from (4) since the last term in (4) is much smaller than the first. Considering the elliptical model in Figure 1, the maximum Doppler shift is no longer defined only by the relative speed of the transmitter/receiver ( ) as in Jakes' model because the surroundings are not fixed [3, 14].

where
is the reflection coefficient,
and
are the excess distance delay and phase, respectively,
is a random phase, *N* is the number of paths, and
is the unit step function. The line of sight is represented by the *i* = 0 term.

## 4. Model Statistics and Antenna Correlation

For our simulations, we use 10 scatterers. The maximum speed was set to 120 km/h with the transmitter moving at 90 km/h and fixed receiver. The ratio of the line of sight component to any of the other scatters is equal to *k*. The delay spread is 103 nanoseconds as measured in [9]. The distance (*D*) between the transmitter and receiver is 1 km, which is the maximum transmission range specified for IEEE 802.11p [15], and the heights of the antennas were set to 1.5 m. The frequency is 5.9 GHz as specified by ASTM [16]. The amplitude distribution of the received signal using our model was found to follow Rayleigh distribution for no line of sight and Rician distribution when a line of sight component exists. This agrees with the statistics obtained from measurements in [11, 17]. The Rician distribution can be approximated by a Gaussian distribution under strong line of sight conditions [4].

*d*is the spacing between the antennas and is the angle of orientation of the array (set to for broadside and 0 for end fire). For mobile terminals, the surroundings are usually assumed to be uniformly distributed in a circle around the terminal (Lee's model) leading to the AOA distribution of the following equation [19]:

Figure 3 compares the correlation between the antennas under various line of sight strengths and no line of sight conditions using the elliptical model with the correlation from (7). As can be seen, (7) gives an optimistic estimate of the correlation due to the assumption of uniform angle distribution which is realistic only in rich scattering channels. We also note that the correlation increases as the line of sight strength increases since the received signal becomes dominated by the line of sight component. The ground reflection reduces the correlation since the attenuation for line of sight is inversely proportional to instead of , thus the contribution of line of sight is reduced [11, 12]. Without ground reflection, the correlation becomes higher, and it is not possible to reduce it unless very large, impractical antenna spacings are used.

## 5. Channel Update

The performance of MIMO systems depends on the accuracy of channel state information (CSI). In a fast varying channel, the channel estimate must be updated more frequently. Generally, a training sequence is used for channel estimation [22–24]; however under fast varying conditions, the interval between successive training sequences becomes small, and thus the efficiency is reduced. Our aim in this section is to develop an algorithm to update the channel estimate using the received signal in order to increase the interval between successive training intervals.

Several channel tracking algorithms are available for single and multiple antenna systems. In [25], a maximum likelihood channel tracking algorithm has been proposed. Kalman filters have been considered in several papers. In [26], the authors combined a Kalman filter with a decision feedback equaliser (DFE). The DFE is used to estimate the transmitted signal, and its output is fed to the Kalman filter for channel tracking. In [27], an autoregressive moving average (ARMA) filter was used to model the channel response based on Jakes' channel power spectral density; this was then used to design a Kalman filter for tracking. The main limitation of these algorithms is complexity. The decoding algorithms for MIMO systems are usually very complicated and, therefore, it is desirable to minimise the channel estimation and tracking complexity. In this section, we develop a simple single tap Kalman filter to update the channel and thus reduce the BER while keeping the increase in hardware complexity to minimum.

*p*×

*q*VBLAST system with

*p*transmit and

*q*receive antennas,

*q*≥

*p*, in a flat fading channel, the received signal vector of length

*q*( ) at time index can be written as

where
is the *q* × *p* channel matrix,
is the column vector of *p* transmitted symbols, and
is the column vector of *q* white noise samples at time
. Unless otherwise specified, bold upper-case characters represent matrices and bold lower-case characters represent vectors while normal lower-case characters represent elements within the matrix/vector of the same character. Our analysis assumes that the antenna separation is large enough for the received signals to be uncorrelated.

where **K** is a *q* × *p* matrix of update parameters and the dot in (13) represents the element-by-element multiplication.

**K**, however, since we assume that the receive antennas are not correlated; we need to optimise for only one antenna. Equation (12) can be rewritten for the elements of the matrix as

*i*) and column (

*j*or

*l*) which represent receive and transmit antennas, respectively, while the superscript (

*n*) denotes the time index. is the element at column

*j*of the row vector ( ). Equation (14) can be expanded using (9) as

*i*, is the average error covariance reduction value, and is a constant that specifies the fraction of noise associated with stream

*j*. The optimum value of is the one that minimises the expression . For , is the symbol duration, the channel autocorrelation function ( ) can be approximated by (20) [29, 30]. The optimum value of is then found using (21) to (24),

We define
as the total SNR if all transmitting antennas transmit the same symbol. We set
and
equal to 1/*p* in (22) since we assume equal average transmit (receive) power for each transmit (receive) antenna. The
parameters are calculated recursively. First, we assume no interference from the other symbols and set
= 0. This is best suited for the last decoded symbol in VBLAST since all the other symbols would be cancelled out by then. We then calculate
and
for this stream. Next, we substitute the new value of
for the next to last decoded symbol and calculate the
then update
. After all the initial
parameters are calculated, the process is repeated again with
from the calculated
. This process converges very quickly, and the final values of
are not very different from the initial ones. The parameters then can be used to update the channel estimate. The algorithm requires the calculation of
parameters, one for each transmit antenna (21) and (24). These can be calculated once at the beginning of the packet and held constant for the duration of the packet.
requires the pseudoinverse of the (*p* × 1) vector **s**, which can be precalculated and stored, and then multiplying it by the term
, (11), which is calculated in the VBLAST algorithm. This multiplication consists of *p* × *q* complex multiplication. The update algorithm, (13), requires *p* × *q* real-by-complex multiplication and *p* × *q* complex addition.

A simple analysis shows that the algorithm requires 6*p* × *q* real multiplications and 4*p* × *q* real additions per update. Assuming a 2 × 4 system, the algorithm then requires 48 multiplications and 32 additions. If channel update is conducted for every symbol, then a chosen 500 MHz DSP processor, which executes a multiplication in 1 cycle, can compute the update in 160 nanoseconds.

We ran a number of simulations using Matlab for a 2 × 4 VBLAST system with a symbol rate of 1 MSymbol/s and the elliptical channel model. The frequency was 5.9 GHz. In our simulations, initially the algorithm would have perfect channel knowledge rather than estimating from a training sequence. This is necessary to isolate any errors that might arise from the use of training sequence estimation. The initial values of were used to reduce complexity, and the channel estimate was updated for every symbol.

## 6. Conclusion

In this paper, we introduced a channel model for vehicular networks. The model was compared to Jakes' model, and it was shown that the Doppler power spectrum extends beyond Jakes' maximum frequency due to the movement of the surroundings, transmitter, and receiver. The correlation between antennas was then studied, and the results show that under very strong line of sight conditions, the correlation is high and, therefore, a small gain is expected from the use of multiple antennas while for moderate and no line of sight conditions the correlation is low. We also developed a simple recursive algorithm to keep track of changes in the channel and update the channel estimation matrix for VBLAST. The update algorithm enhances the channel estimation on a symbol-by-symbol basis, but this can be relaxed for high symbol rates and/or slow fading as the channel coherence time will be large compared to the symbol duration. The proposed algorithm improves system BER and channel estimate MSE via continuous and accurate channel updating and has less computational complexity compared to existing tracking algorithms as a result of using a simplified Kalman filter. Simulation results showed remarkable improvements when using the update algorithm compared to the training of only channel estimation. The algorithm is capable of updating the channel estimation for VBLAST for nodes moving at high speeds thus improving the bit error rate and reliability of VANET.

## Declarations

### Acknowledgment

The authors would like to thank France Telecom and the University of Plymouth for supporting this work as well as the anonymous reviewers for their valuable comments.

## Authors’ Affiliations

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