Ubiquitous Computing And Communication Journal_128

FREQUENCY SELECTIVITY PARAMETERS ON MULTI-CARRIER WIDEBAND WIRELESS SIGNALS Víctor M Hinostroza, José Mireles and Humberto Ochoa Institute of Engineering and Technology, University of Ciudad Juárez Valle del tigris # 3247,Ciudad Juárez Chihuahua México C. P. 32306 [email protected], [email protected], [email protected]

ABSTRACT. This work is a study of the effects of frequency selectivity on multi-carrier wideband signals in three different environments; indoors, outdoor to indoor and outdoors. The investigation was made using measurements carried out with a sounder with a 300 MHz bandwidth. The main part of this work is related to evaluate the contribution of several parameters; frequency selective fading, coherence bandwidth and delay spread on the frequency selectivity of the channel. A description of the sounder parameters and the sounded environments are given. The 300 MHz bandwidth is divided in segments of 60 kHz to perform the evaluation of frequency selective fading. Sub channels of 20 MHz for OFDM systems and 5 MHz for WCDMA were evaluated. Figures are provided for a number of bands, parameters and locations in the three environments. It is also shown the variation of the signal level due to frequency selective fading. The practical assumptions about the coherence bandwidth and delay spread are reviewed and a comparison is made with actual measurements. Statistical analysis was performed over some of the results. Keywords. modulation .

Coherence bandwidth, frequency correlation, frequency selective fading and multi-carrier

I. INTRODUCTION. To simulate and evaluate the performance of a wireless mobile system a good channel model is needed. Mobile communication systems are using larger bandwidths and higher frequencies and these characteristics impose new challenges on channel estimation. The channel models that have been developed for the mobile systems in use may not be applicable anymore. To validate that the old models can be used for future systems or to design new models, it is necessary to answer the question about how the same parameters performs at higher bandwidths? Also, we have to be able to measure and validate some parameters and compare them to well known practical assumptions. Measurements for analysis of the fading statistics at common frequencies have been performed before, but they have been performed at small bandwidths, it is necessary to update the models with higher bandwidths. As the data rate (the bandwidth) increases the communication limitations come from the Inter Symbol Interference (ISI) due to the dispersive

characteristics of the wireless communications channel. The dispersive channel characteristics arise from the different propagation paths, i.e. multipath, between the receiver and the transmitter. This dispersion could be measured, if we could measure the channel impulse response (CIR). As a general rule the effects of ISI on the transmission errors is negligible if the delay spread is significantly shorter than the duration of the transmitted symbol. Due to the expected increase in demand of higher data rates, wideband multicarrier systems such as; OFDM and WCDMA are expected to be technologies of choice [1], [12] and [14]. This is because these two technologies can provide both; high data rates and an acceptable level of quality of service. However, these systems need first to address better the problem regarding channel prediction or estimation, because this condition is the main boundary for higher data rates. The study of correlation of the mobile radio channel in frequency and time domains has helped to understand the problem of channel estimation. One of this work objectives is to evaluate frequency selective fading (FSF) in several environments. This work begins with the results of

measurements made with a sounder that uses the chirp technique for sounding.

E{H (t1 ; f1 ) * H (t2 ; f 2 )} = ∞ ∞

∫ ∫ E{h(t ;τ ) * h(t ;τ )}e 1

Multipath fading channels are usually classified into flat fading and frequency selective fading according to their coherence bandwidth relative to the one of the transmitted signal. Coherence bandwidth is defined as the range of frequencies over which two frequency components remain in a strong amplitude correlation. Physically, it defines the range of frequencies over which the channel can be considered “flat”. The analytic issue of coherence bandwidth was first studied by Jakes [1] where by assuming homogeneous scattering, his work revealed that the coherence bandwidth of a wireless channel is inversely proportional to its root-mean-square (rms) delay spread. The same issue was subsequently studied by various authors [4], [8], [9], [10]. Since many practical channel environments can significantly deviate from the homogeneous assumption, various measurements were conducted to determine multipath delay profiles and coherence bandwidths [19], [20], [21], [22], aiming to obtain a more general formula for coherence bandwidth. In this work the variations of this formula are reviewed and compared with actual results and a comparison is provided. The rest of this document is structured as follow; in part II the theoretical foundations of the channel impulse response frequency selective fading and coherence bandwidth are reviewed. Also in this part, the characteristics of the three environments sounded are described. In part III, the frequency selective fading evaluation and analysis are presented. Plots of the dependency of fading deep and frequency separation of two specific points in the response are studied. At part IV, data about the relationship between delay spread and coherence bandwidth are provided. At the end in part V, conclusions and future work are mentioned. II. MATHEMATICAL BACKGROUND 2.1 The wideband channel model. The radio propagation channel is normally represented in terms of a time-varying linear filter, with complex low-pass impulse response, h(t, τ). Its time-varying low-pass transfer function is [4] [6] [8] [10]: ∞

H (t , f ) =

− j 2πf ∫ h(t;τ )e τ dτ

−∞

(1) Where τ represents delay, using (1) the frequency correlation function for the channel can be written as:

1

2

2

− 2πf1τ 1 + j 2πf 2τ 2

e

dτ 1dτ 2

− ∞− ∞

(2) By considering the channel to have uncorrelated scattering (US) and to be wide sense stationary (WSS), the subscript for τ is eliminated and f1 and f2 can be replaced by f + ∆f and t1 and t2 replaced by t + ∆t, then: ∞

∫R

R H (∆t ; ∆f ) =

h

(∆t ;τ )e − j 2π∆fτ dτ

−∞

(3) In (3) RH and Rh represents the correlation of random variations in the channels transfer function and its impulse response respectively. If there are US, then ∆t is 0 then:

{

Rh (0;τ ) = E h (0;τ )

2

}= E {h(τ ) } 2

(4) substituting into (3) gives:

∫ E {h(τ )

∞

R H ( ∆f ) =

2

}e

− j 2π∆fτ

dτ

−∞

(5)

{

E h (τ )

2

}

is the average Power Delay where Profile PDP of the channel. So, under the above conditions, RH is the Fourier transform of the average PDP. 2.2 Coherence bandwidth. The multipath effect of the channel, the arrival of different signals in different time delays causes the statistical properties of two signals of different frequencies to become independent if the frequency separation is large enough. The maximum frequency separation for which the signals are still strongly correlated is called coherence bandwidth (Bc). Besides to contribute to the understanding of the channel, the coherence bandwidth is useful in evaluating the performance and limitations of different modulations and diversity models. The coherence bandwidth of a fading channel is probed by sending two sinusoids, separated in frequency by ∆f = f1- f2 Hz, through the channel. The coherence bandwidth is defined as ∆f, over which the cross correlation coefficient between r1 and r2 is greater than a preset threshold, say, η0= 0.9. Namely:

Cov( r1, r 2) = η0 var(r1) var(r 2)

C r1,r 2 = (6)

Then, using (2) ∞

∞

0

0

R( s, τ ) = r1r 2 = ∫

∫ r1r 2 p(r1, r 2)dr dr 1

2

(7) Where p(r1,r2) is 2π 2π

p( r1, r 2) =

∫ ∫ p(r1, r 2, θ , θ 1

2

)dθ1dθ 2

(8)

It is possible to see in this expression that the correlation decreases with frequency separation. This formula has been substituted by several practical expressions some of them are the following [4], [8], [9], [10].

BC =0.9 =

⎡ r + r ⎤ ⎛ r1r 2 λ ⎞ r1r 2 I ⎜ exp⎢− ⎟ 2 2 ⎥ 0⎜ 2 ⎟ µ (1 − λ ) ⎣ 2 µ (1 − λ ) ⎦ ⎝ µ 1 − λ ⎠ 2 1

2 2

2

Where I0(x) is the modified Bessel function of zero order. Then, substituting (8) in (7) and integrating

π

1 1 R( s,τ ) = b0 F ( − ,− ;1; λ2 ) 2 2 2 this may also be expressed as

π

⎛ λ2 ⎞ R( s, τ ) = b0 ⎜⎜1 + ⎟⎟ 2 ⎝ 4⎠

[r

2 1

(10)

R ( s, τ ) − r1 r 2 − r1

2

][ r

2 2

⎛2 λ ⎞ ⎟ R( s,τ ) = b0 (1 + λ ) E ⎜⎜ ⎟ ⎝1+ λ ⎠

− r2

BC =0.9

1

(13) BC =0.5 =

1

(14)

50σ rms 5σ rms 1 1 (15) BC = (16) = 8σ mean 2πσ rms

In general

BC =

k

σ rms

(17)

It will be shown, comparing with practical measurements that none of these expressions are accurate and it is difficult to obtain a comprehensive expression for all environments.

(9)

ρ ( s, τ ) =

(12)

0

0

=

⎛2 λ ⎞ π ⎟− (1 + λ ) E ⎜⎜ 1 + λ ⎟⎠ 2 ⎝ ρ ( s, τ ) = π 2− 2 2 J (ω τ ) = λ2 = 0 2m 2 1+ s σ

2

] (11)

Where E(x) is the complete elliptic integral of the second kind. The expansion of the hyper geometric function gives a good approximation to (9). After several reductions and considerations, the correlation coefficient becomes

2.3 Sounder systems environment description.

characteristics

and

The sounder system used to make the measurements of this work was developed at UMIST in Manchester UK and is described in [2] and [3]. This sounder uses the FMCW or chirp technique. The generated chirp consists of a linearly frequency modulated signal with a bandwidth of 300 MHz and a carrier frequency of 2.35 GHz. The chirp repetition frequency is 100 Hertz, which allows having 50-Hertz Doppler range measurements. The receiver has the same architecture than the transmitter. But in the receiver, the generated chirp is not transmitted but mixed with the incoming signal from the antenna, which are the multi-path components of the transmitted chirp. This mixing allows having the multi-path components at low frequencies, these low frequencies can be sampled, digitized and stored in a computer to perform the required analysis. The three environments where the measurements took place were the following: 1) Indoors, in

different floors around a building in an eight stories building. Each floor form a rectangle with four long corridors; two 66 m long and two 86 m long, the width of the corridors is 3 m, the total covered area was 912 square meters and the ceiling height is 5 meters. The transmitter was static and the receiver was moved around the corridors and in different floors, measurements were taken at specific distances in each corridor. 2) From a building to different building. These two buildings are eight stories high, they have about the same high and they are separated by about 200 meters. The transmitter was located in the top of one of the buildings and the receiver was moved around specific locations inside the second building in all eight different floors. 3) An urban environment around the city center, a commercial area with several high rising buildings. Each location in each environment was sampled during one second and 100 impulse responses were stored for this specific location. When the measurements were taken, every location was sampled with 100 impulse responses, an impulse response (IR) was taken on that specific location every 10 milliseconds. III. FREQUENCY SELECTIVITY PARAMETERS To carry out the calculation of frequency selective fading, each processed IR was split in samples of 60 kHz, which was the minimum sampled frequency, each 300 MHz bandwidth was sampled 5000 times every 10 milliseconds, this means that a sample was taken every 2 microseconds or every 60 kHz. Each IR was averaged over the complete second, meaning that every frequency was averaged 100 times for each IR. The level of the frequency response of each 60 kHz segment was calculated and recorded In each environment the channel transfer function for about 50 different locations were calculated and recorded. Each transfer function has 5000 sampled frequencies, i.e. 5000 segments for each location. Every sample represents the signal level on that segment, relative to the maximum over the complete 300 MHz bandwidth. The outdoors environment has a bandwidth of 120 MHz, the indoors and indoor to outdoor environments has 300 MHz bandwidth. The fading characteristics in each of the environments were calculated. For each of the locations the fading characteristics that were calculated were; average delay spread, RMS delay spread, coherence bandwidth, channel transfer function and frequency correlation. Using the channel transfer function for each IR, specific fading characteristics for sub channels of 5 and 20

MHz were calculated. Figure 1 shows a typical channel transfer function. In figure 2 are shown the fading characteristics for a 20 MHz sub channel, in this figure there are 15 different lines, each one corresponds to a 20 MHz sub channel in a 300 MHz bandwidth. To get this figure, the following has been done; first, the fading information of the complete 300 MHz bandwidth was divided in 15 segments of 20 MHz each. Then, each point on that segment, that represents a 60 kHz sample, was measured and the result was compared to the next sample, then the next sample was compared and so on up to the complete 20 MHz bandwidth was compared. After that, a second 20 MHz sub channel was applied the same procedure and so on up to the end of the 300 MHz bandwidth. To form figure 3, the same procedure was followed, but in this case the sub channel bandwidth was of 5 MHz, then this figure has 60 different lines which come from the 300 MHz total bandwidth. Figure 2 shows that the maximum fading deep within the 20 MHz sub channel is lower than 14 dB in all the bandwidth. On the other hand, in the 5 MHz bandwidth the maximum fading deep was of 18 dB. It is possible to see in figure 2, that most of the lines follows a pattern, which means that the fading in all sub channels is about the same. In figure 2, most of the lines stay below 5 dB and only a few lines go higher than 6 dB; this could mean that deep fading in this bandwidth is rare.

Figure 1. Typical channel transfer function. Figure 3 shows the calculations of fading characteristics for the second environment with 15 different 20 MHz sub channels, this figure shows that there are more dispersion of the lines, which means there are more deep fading in the responses of the IR. Since this environment is the measurement of the propagation for the penetration of the signal in different floors in a building, higher delay spread, (time dispersion) than the former environment was expected and therefore more fading.

Another way to look at the statistics of the fading is to calculate the CDF of this parameter. To make the calculations of these CDF’s figures, the mean of all locations in the involved environment were used. Figure 4 shows the CDF of the building-tobuilding environment for both, the 20 and 5 MHz bandwidths, this figure shows that the fading deep for a 20 MHz sub channel is below 7 dB for 90% of the time. On the other hand, for the 5 MHz sub channel, the fades are below 5 dB for 90% of the time.

Figure 2 Indoor to outdoor fading Characteristics for a 20 MHz sub channel

correlation coefficient, the coherence bandwidth (Bc) is lower than 10 MHz most of the locations. This is corroborated in figure 6, this figure shows the average Bc for all locations in the indoors environment. Figure 7, shows the RMS delay spread for all locations for the same environment. Quick calculations comparing figure 11 results and expression (13) show that, few calculated values of the versions of expression (13) match with the measured values of figure 7.

Figure 4. Fading CDF for indoor to outdoor for a 5 MHz sub channel

Figure 3. Outdoor to indoor fading Characteristics For a 5 MHz sub channel Figure 5. Coherence bandwidth for indoors IV. COHERENCE BANDWIDTH EVALUATION. Figure 5 shows the frequency correlation of all locations in the indoors environment. To make this figure the following was done; first the PDP of all locations was calculated. Then a Fourier transform was performed on the PDP, which gave us the frequency correlation for all locations. Then the frequency correlation for each location was plotted in figure 5. On this figure, the thick and dashed line is the line for the maximum coherence bandwidth, when the transmitter and receiver are connected directly. In figure 5, one can see that at 0.9

Figure 6. Average of coherence bandwidth for indoors Figure 8 shows the frequency correlation for the outdoor to indoor environment, this figure shows that in this environment the Bc at frequency correlation of 0.9 is higher than the indoor environment, although the delay spread is not different is both environments. Figure 9, shows the average Bc for the outdoors to indoors environment, one can see in this figure, that the coherence bandwidth is higher than the indoor environment, which was an expected result, but the difference is higher than expected. In indoors the coherence bandwidth is not bigger than 20 MHz in average. In the other hand, in the outdoor to indoor, the average is about 100 MHz, here is relation of 5 to 1. The difference in RMS delay spread is 100 nS versus 200 nS, there is a relation of 2 to 1.

Figure 8. Coherence bandwidth for outdoor to indoor

Figure 9. Average of coherence bandwidth for indoor to outdoor Figure 7. RMS delay spread for indoors Figure 11 shows the frequency correlation for the outdoors environment. Figure 12, shows the Bc at frequency correlation of 0.9. In this case the Bc can not be compared to the Bc for the other two environments, since in this environment a lower bandwidth is evaluated, 120 MHz instead of 300 MHz. Despite this difference and observing figures 11 and 12, Bc is not significantly lower even when we have higher distances and higher delay spread. In outdoors the Bc is not bigger than 2 MHz in average. In the other hand, the RMS delay spread is 1.5 µS in average.

Table 1, shows the comparisons of Bc for the three environments with the different versions of expressions 13 -16 and measured results. This table shows that the values of the expressions are always lower than the measured results, which induce to conclude that the expressions were underestimated, at least in these environments. Moreover, it is possible to conclude that these expressions were deduced with not enough measured results. Also, table 1 show that the relationship between delay spread and coherence bandwidth, not necessarily is a single constant.

Figure 11. Coherence bandwidth for outdoors

Figure 10. RMS delay spread for outdoors to indoors V. CONCLUSIONS. In this work the results of analysis of frequency selective fading on two indoor and one outdoor environment have been presented. The three environments analyzed demonstrate that the fading is within specific limits, these results could help to the designers of adaptive receivers to estimate the channel more accurately. The division of the channel impulse bandwidth in segments of 20 and 5 MHz bandwidths, allow the calculation of fading in the bandwidth of interest for OFDM and WCDMA transmission. Plots of the frequency selective fading will help for this assessment. The analysis of coherence bandwidth show that the expressions accepted in the literature for its calculation are not accurate and the accepted direct relationship between delay spread and coherence bandwidth is not simple. Also, additional work is require on try to determine how much the combined effect of Doppler spread, time variability and frequency offsets affects the transmission on multi-carrier signals as the ones on OFDM y CDMA

Figure 12. Average of coherence bandwidth for outdoors Table 1. Coherence bandwidth calculations Value from Indoors Outdoors Outdoors to indoors (13) 400 kHz 200 kHz 30 kHz (14) 4 MHz 2 MHz 300 kHz (15) 3.3 MHz 2.5 MHz 250 kHz (16) 3.2 MHz 1.6 MHz 212 kHz Measured0.9 5.3 MHz 12 MHz 300 kHz Measured0.5 19 MHz 72 MHz 5.6 MHz

Figure 13. RMS delay spread for outdoors References. 1. 2.

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