Fading Correlation Analysis in MIMO-OFDM Troposcatter Communications: Space, Frequency, Angle and Space-Frequency Diversity Ergin Dinc, Student Member, IEEE, Ozgur B

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IEEE TRANSACTIONS ON COMMUNICATIONS 1 Fading Correlation Analysis in MIMO-OFDM Troposcatter Communications: Space, Frequency, Angle and Space-frequency Diversity Ergin Dinc, Student Member, IEEE, Ozgur B. Akan, Senior Member, IEEE

Abstract—The capacity gain of MIMO systems significantly problems under low coverage. In addition, the employment depends on the fading correlation between antennas, and there of relay nodes has security problems due to possible hostile is no analytical study which considers the fading correlation attacks. Since the troposcatter communication provides a direct in the troposcatter communications. In this paper, we develop an analytical model, ring scatter model (RSM), to derive the communication link with microsecond transmission delays [2], fading correlation in the troposcatter systems as a function of the modern b-LoS communication requiring high data rates spatial, frequency and angular separations for the first time in can utilize the troposcatter communications. the literature. In addition, we compare the effects of the diversity Troposcatter medium is a lossy wave-guide due to high path techniques that are suitable for troposcatter communications: lengths and scattering. Thus, the implementation of diversity space, frequency, angle and space-frequency diversity techniques by deriving the distribution of their achievable data rates with techniques is required to provide reliable and high data rate transmit beam-forming. To this end, we extend our previously b-LoS troposcatter systems. The main diversity techniques for introduced troposcatter channel model [1] for the implementation troposcatter communications are space, frequency and angle of MIMO-OFDM and the diversity techniques. diversity. In addition, the combination of diversity techniques Index Terms—Electromagnetic scattering, Correlation, Com- may be utilized to increase the spectral efficiency with less munication channels, Diversity methods, MIMO systems cost. For example, the space-frequency diversity employs horizontally placed antennas utilizing frequency diversity. Since the frequency diversity receivers can be mounted on the same I.INTRODUCTION parabolic reflector, quad diversity can be achieved with only ROPOSCATTER is the scattering of the propagating 2 antennas in each side. Therefore, the main objective of T signals due to atmospheric irregularities. Although most this paper is to analyze the correlation between antennas in of the scattered power is directed to the forward direction, these diversity techniques to determine the proper spacings to it is possible to receive some of the scattered power at the achieve the desired gains for the first time in the literature. receiver by pointing the antennas to the horizon as can be seen The contribution of this paper is twofold: Firstly, we de- from Figure 1. The intersection of the antenna beam-widths velop an analytical model for the fading correlation of the are denoted as troposcatter common volume and the receiver troposcatter antennas utilizing space, frequency and angle and can receive the scattered rays only in this region. Therefore, space-frequency diversity techniques for the first time. These troposcatter can be used as a communication medium for high diversity techniques are employed by the modern troposcatter data rate beyond-Line-of-Sight (b-LoS) communications [1]. systems [2], but there are no analytical fading correlation studies. Therefore, we develop the Ring Scatter Model (RSM) QIIQJQC%IV to analyze the fading correlation in troposcatter links and H: V`V` compare our results with the empirical values provided by the industry [2], ITU [3], and the experimental results [4]–[9].

`:JI1 V` VHV10V` In addition, one of the most important contributions of this work is the prediction of 50% coherence bandwidth based :` . on the frequency separation results. In this way, the fading behavior of the channel can be determined for a given channel Fig. 1. Troposcatter b-LoS paths. parameters. Secondly, we compare the employment of different diversity techniques with the distribution of achievable data Troposcatter communication is a promising candidate for rates by extending our previously proposed ray-based channel b-LoS communications with its low transmission delays and model approach for troposcatter communications [1]. Our ray- high capacity. The available b-LoS communications mostly based channel model is a ray-tracing method which calculates utilize satellite communications (SATCOM) or relay nodes. the power and delay of each ray to generate power delay SATCOM has excessive transmission delays and capacity proﬁle (PDP). The novelty of our approach is to use the real world measurements for atmospheric modeling, thus each ray E. Dinc and O. B. Akan are with the Next-generation and Wireless is subjected to different conditions according to its height (For Communications Laboratory, Department of Electrical and Electronics En- gineering, Koc University, Istanbul, 34450 Turkey (e-mail: [email protected]; more details, see [1]). In this work, we extend our approach [email protected]). to implement the diversity techniques and MIMO-OFDM. IEEE TRANSACTIONS ON COMMUNICATIONS 2

The reminder of the paper is organized as follows. Section RSM fading correlation analysis are developed for single- II presents the related work. Section III provides the RSM user to single-user communication link. Troposcatter link has fading model. In Section IV, the ray-based channel model is Mt,r antennas at the transmitter and receiver sides, respec- reviewed. Section V and VI include the formulation and sim- tively. Therefore, the channel response in frequency domain ulation results for the data rates for the diversity techniques, (HMr ×Mt [k]) can be represented as respectively. The conclusions are presented in Section VII. r[k] = H[k]s[k] + v[k], (1) where r is the received signal vector, s represents II.RELATED WORK Mr ×1 Mt×1 the transmit vector, vMr ×1 is additive-white-Gaussian-noise Although the fading correlation is well studied especially (AWGN). in mobile links [10], [11], [13], there is no theoretical study The remainder of the section includes the scattering model, which considers the fading correlation in the troposcatter links. and the RSM method for the diversity techniques. Therefore, our main aim is to analyze the fading correlation in different diversity schemes: space, frequency, angle, and A. Scattering Model space-frequency diversity techniques. On the other hand, there The troposcatter power depends on both the path geometry are empirical recommendations for these diversity techniques and the atmospheric turbulence. Therefore, both of these in order for the antennas to be uncorrelated [2], [3]. In addi- factors will have strong effects on the correlation analysis. tion, there are available experimental studies which considers The troposcatter is caused by the atmospheric scintillations the fading correlation in the troposcatter links. [6], [7] provides due the the changes in the refractive index of the atmosphere. the fading correlation results for space diversity along with the According to the turbulence characteristics, the scattering can fading statistic of the channel. According to their results, the be modeled as single or multiple scattering [16], [27]. The channel shows Rayleigh fading under low integration times. microwave propagation in the troposphere is related to the [4], [5] focus on frequency correlation in the troposcatter links. tenuous distribution of the particles, and it can be modeled The correlation and path-loss results for the angle diversity with the first order multi-scattering approximation in the systems are provided in [8], [9]. We utilize these empirical tenuous medium for a unit particle as [16], [27] suggestions and experimental studies to to validate our results. 2 ˆ To model the fading correlation, there are several methods. Pr λ Gt(i)Gr(ô) ˆ = 3 2 2 σV (i, o,ˆ n) exp(−τt − τr), (2) For this purpose, the fading correlation can be determined Pt (4π) Rt Rr by channel sounding experiments [10]. However, the cost of where λ is the wavelength, Pt,r are the transmitter and receiver channel sounding experiments for troposcatter is too high power. Gt,r are the antenna gains which are modeled with due to the requirement for high power amplifiers and large Gaussian pattern. Rt,r are the distances between scattering antennas. Therefore, the correlation between antennas may be point to transmitter and receiver respectively. σV (î, o,ˆ n) is the determined via analytical studies. This is the main reason for scattering cross-section, where î is the incoming ray vector, oˆ this paper. In addition, one of the most popular fading correla- is the scattered ray vector, and n is the index of refraction. tion model is “One Ring” model, which is first introduced in τt,r are the optical distances for Rt,r [16]. [13]. In this model, the receiver is assumed to be surrounded In correlation calculations, the constant terms can be omitted by local scatterers and the correlation between the antennas to simplify the model because they will have no effect: λ2 are determined by using channel geometry calculations. How- and (4π)3 in (2). In addition, the terms that have very slight 2 2 ever, the scatterers in troposcatter channel are located in the changes can be eliminated. Rt Rr term in of (2) will also show troposcatter common volume as in Figure 1 unlike the one very slight changes due to narrow beam-widths. For 250 km ring model. Therefore, we develop the RSM for the fading range and 1.5◦ beam-width, the ratio of the minimum path over Min Max correlation in the troposcatter system based on the methodol- maximum path (Rt /Rt ) is found as 0.9992. Thus, this ogy in [11], [13] by using the troposcatter channel geometry term can be eliminated to simplify the model. Furthermore, the [14]. We extend RSM to analyze space, frequency, angle and τt,r are the path integral of the Rt and Rr over the index of space-frequency diversity fading correlation calculations. refractions and and they represents the effect of the scattering particles between the antennas and the common volume. Since III.RING SCATTER MODELFOR TROPOSCATTER FADING the expected antenna spacing in space diversity (≈ 100λ CORRELATIONS R), and no spacing for the frequency and angle diversity, the To achieve the desired gains with MIMO, the antennas values for optical distances will be almost the same for each exp(−τ − τ ) should have desired correlation values. Thus, we develop an ray. Therefore, we eliminate the t r in (2) as well. To model the atmospheric turbulence, we use Booker- analytical model, ring scatter model (RSM), to investigate the Gordon model [16] instead of the Kolmogorov theory which fading correlations in the main diversity techniques that are is utilized in [1] because the correlation within the atmo- suitable for the b-LoS troposcatter communications: space, spheric turbulence can be directly modeled with Booker- frequency and angle diversity. In addition, the combination Gordon model. In this model, the correlation function of the of diversity techniques also has a potential to provide higher atmospheric scintillations is modeled with the exponential achievable data rates. Therefore, space-frequency diversity function, and it is given as [16] which is the combination of space and frequency diversity c c is introduced and investigated as well. Bn(lx, ly) ≈ exp −lx/lx − ly/ly , (3) IEEE TRANSACTIONS ON COMMUNICATIONS 3

`R R 1

[^`5%_ % ` ` 1R ^`5%_ 1R = ` 1 R7 R7 R R _ ^`5%_ C _ C

Fig. 2. Geometry of RSM method.

where lx,y are the horizontal and vertical distance to the where Rt is the path between the center of the rings and c 3dB 10dB reference point, and lx,y are the correlation distances of the transmitter. wt and wt are the transmitter 3 dB and c turbulence for vertical and horizontal axis. For troposcatter, ly 10 dB beam-widths, respectively. is approximately ≈ 50 m and it varies 20 − 130 m according To maximize the received power, the 3 dB beam-widths of c to the atmospheric conditions [16]. Since lx is much greater the antennas are adjusted to the radio horizon as in Figure c than ly as in [16], we assume that lx = 4 × ly [16]. 2 [1], [14]. Therefore, the lower part of the ring (the darker The geometry dependency of the scattering cross-section region in Figure 2) will be blocked by the path geometry due can be determined with sin(Ψ)−11/3 as experimentally val- to the curvature of the earth. Since RSM method utilizes the 10 idated in [9]. With the proposed simplifications for the dB beam-widths, the lower part of the ring will be eliminated correlation analysis, the resulting power relationship in the from the correlation calculations as described in Appendix A. troposcatter channel is found as Due to the troposcatter geometry, the path-loss observed by the both end of the communication is symmetrical [2]. The −11/3 ˆ Pr/Pt ≈ sin(Ψ) Bn(lx, ly)Gt(i)Gr(ô), (4) troposcatter links generally utilize the same type of antennas at the both ends. For these reasons, we assume that the where DTj is the distance between scatterer (S(r, θ)) and 3dB 3dB troposcatter path is symmetrical. Thus, we have wt = wr transmitter j, and DRi is the distance between scatterer S(r, θ) 10dB 10dB and receiver i as in Figure 2. Since the antenna gains will and wt = wr that imply RT = RR as [1] change dramatically for 10 dB beam-widths, we include the RT,R = Rsin(β0)/sin(α0 + β0), (6) antenna gains in the model as well. The scattering model which is considered in this paper is where α0 and β0 are the elevations of the antenna beams with developed for the clear air atmospheric turbulence between 1− respect to horizon for transmitter and receiver, respectively [1]. 10 GHz because the atmospheric correlation model is valid for R is the horizontal distance between transmitter and receiver. the clear air conditions and the scattering power relationship Since the b-LoS troposcatter communication does not have depends on the Rayleigh scattering which is more accurate for any line-of-sight component, only the scattered rays are con- 1 − 10 GHz [16]. In addition, we assume that the transmitter sidered in RSM and the power of the scattered rays are deter- and receiver have the same vertical orientation for simplicity. mined by (4). Suppose that there are K effective scatterers in Therefore, we consider only the symmetrical troposcatter paths each ring and L rings within the common volume. Thus, the in this paper. However, our model can be extended for non- normalized path gain Hi,j is represented as [11] symmetrical cases with geometrical approximations. 10dB L K Z r Z 2π X X Hi,j = δ(θ − θk)δ(r − rn)ζ(r, θ) B. RSM Model 0 0 n=1 k=1 −11/3 In troposcatter, only the scattered rays inside the troposcatter Gt(r, θ)Gr(r, θ) sin(Ψ(r, θ)) Bn(lx, ly) common volume can be received due to path geometry as in exp −j2π/λ(DTj + DRi ) + jφ(r, θ) dθdr, (7) Figure 1. The scattered rays outside of this region will reach the receiver with either lower or higher angles than the 10 dB ζ(r, θ) is defined to exclude the lower part of the ring as beam-width of the receiver. Although the scattering particles described in Appendix A. Gt,r(r, θ) are the antenna gains, as are located through the troposphere, we only consider the defined in Appendix B. In Section III-A, the multi-scatter na- scatterers that are located in a ring within the intersection of ture of the troposcatter is approximated by the single scattering the transmitter and receiver 10 dB beam-widths as in Figure [16]. Therefore, the phase (φ(r, θ)) is assumed as uniformly 2. The boundaries for the scatterers is given as θ in [−π, π) distributed [−π, π) and iid. Thus, phase term is canceled in and r in [0, r10dB]. The radius of the rings are given by the correlation analysis as in [11]. For the fading correlation analysis, HM ×M matrix is 3dB 3dB r t r = Rt sin(wt /2), reshaped into hbMr Mt×1 vector. In this case, the fading corre- 10dB 10dB r = Rt sin(wt /2), (5) lation between different antenna pairs becomes the covariance IEEE TRANSACTIONS ON COMMUNICATIONS 4

1 1 1 1 l =30 l =20 m l =20 m y 0.8 y y 0.8 l =50 l =50 m l =50 m y 0.6 y y 0.5 0.6 l =130 l =130 m 0.5 l =130 m y 0.4 y y 0.4 0.2 [7] [6] 3dB ° 0 w =0.6 0 Correlation Correlation 0.2 0 3dB ° Correlation w =1 Correlation −0.2 w3dB =1.5 ° 0 −0.4 w3dB =2.6 °

−0.5 −0.6 −0.5 0 50 100 150 0 50 100 0 50 100 150 0 50 100 150 d/ λ d/ λ d/ λ d/ λ (a) (b) (c) (d) Fig. 3. Fading correlation vs. spatial separation (a) for different beam-widths, and (b) for different correlation distance, (c) and (d) for the comparison with the experimental measurements.

∗ between hbi,j and hbl,q that can be represented as E[hbi,jhbl,q] antennas becomes dTx = dRx = 0. Since the troposcatter where (.∗) is the conjugate operation [11]. channel is symmetrical for transmit and receive sides, the correlation calculations that are developed for one side will be C. Space Diversity valid for the other side as well. For this reason, we only focus on the correlation between two receivers which are communi- We assume that there are inﬁnitely many scatterers inside cating with the same transmitter. This condition implies that the scattering common volume, thus L and K in (7) go to dTy = 0. By using (8), (10) and geometrical approximations, inﬁnity. By using (7), the spatial fading correlation between the correlation for horizontally spaced receivers is given as different troposcatter antenna pairs is represented as Z r10dB Z 2π Z r10dB Z 2π ∗ 2 ∗ 2 E[hbi,jhbi,l] = ξ(r, θ)Bn(|r sin(θ|), |r cos(θ)|) E[hbi,jhbl,q] = Bn(|r sin(θ)|, |r cos(θ)|) 0 0 0 0 ζ(r, θ)G (r, θ)G (r, θ) exp −j2π/λd r/R sin(θ) dθdr. G (r, θ)G (r, θ)ζ(r, θ)ξ(r, θ) t r Ry t t r (11) exp −j2π/λ(∆DT + ∆DR ) dθdr, (8) j,q i,l (11) can be solved with numerical integration on MATLAB. where ∆DTj,q = DTj − DTq is the path length differ- The calculated correlation results are normalized based on the ence between local scatterer to transmitters j and q, and zero spacing value which has the correlation of 1.

∆DRi,l = DRi − DRl is the path length difference between Figure 3(a) shows the correlation vs. antenna spacing to local scatterer to receivers i and l. ξ(r, θ) function represents c wavelength ratio (d/λ) by (11) for 250 km range and ly = 50 −11/3 −11/3 the sin(Ψ1) × sin(Ψ2) term as a function of r and m. As noticed, the increase in the beam-width decreases the θ as defined in Appendix C. Bn is the correlation function (3). correlation at the same ratio. The increase in the beam-width Since the reference point is assumed as the center of the ring, increases r10dB by virtue of (5), and this condition also in- the vertical and horizontal distance from the reference can be creases the troposcatter common volume. As the common vol- simply find by |r sin(θ)| and |r cos(θ)|, respectively. ume increase, the separations between scatterers have higher Since troposcatter paths use low beam-widths and elevation distances and less correlation. Figure 3(b) shows the spatial angles, (8) can be simplified by using geometrical approxi- correlation results for different vertical correlation distances ◦ mations. For low beam-widths, ∆DTj,q ≈ dTx cos(Ω(r, θ)) + for 1.5 3 dB beam-widths. As noticed, there is a inverse dTy sin(Ω(r, θ)), where sin(Ω(r, θ)) ≈ r/Rt sin(θ), and relationship between the correlation distance and correlation. 1 2 1 2 cos(Ω(r, θ)) ≈ 1 − 4 (r/Rt) + 4 (r/Rt) cos(2θ) = According to [2], the antennas should be placed at least 100λ or higher distance apart to achieve low correlation ξ(r, θ) where dTx,y are the vertical and horizontal spacing of 100λ the transmitters. Rt is the distance between transmitter and the values. Our results in Figure 3(a) also show that spacing ◦ ◦ center of the troposcatter common volume as in Figure 2. Since is required for 1 and 1.5 beam-widths to achieve low 4.7 3 the troposcatter path is assumed as symmetrical, Rt = Rr and correlation values. Since GHz troposcatter system with m antenna diameter has ≈ 1.5◦ beam-width (w = 70λ where given as Dant 3dB sin(β + w /2) Dant is the antenna diameter [12]), we can conclude that the R = R 0 t . t,r 3dB (9) our analytical results are consistent with the empirical results. sin(α0 + β0 + wt ) In addition, Figure 3(c) and 3(d) provides the comparison By using the geometrical approximations, ∆D +∆D Tj,q Ri,l of the RSM results with the experimental results for 258 km term in (8) is represented as and 2.6◦ 3 dB beam-width (Figure 3 in [7]), and for 321 km and 2.13◦ 3 dB beam-width (Figure 7 in [6]). As noticed, our ∆DTj,q + ∆DRi,l = dTy r/Rt sin(θ) + dTx ξ(r, θ) + correlation results with the same channel parameters in Figure + d r/R sin(θ) + d ξ(r, θ). (10) Ry r Rx 3(c) and 3(d) are consistent with the experimental results We only consider horizontal space diversity because it is presented in [6], [7]. However, some deviations between the the most common type of spatial diversity for troposcatter. theoretical and experimental results can be observed in these Therefore, x axis component of the receive and transmit figures. Since the RSM considers the clear air propagation, the IEEE TRANSACTIONS ON COMMUNICATIONS 5 real world atmospheric conditions may causes changes in the By using (12), (13) and (16), the covariance expression for correlation values. On the other hand, the general trend of the frequency diversity is given as correlations can be well-estimated with RSM. r10dB 2π ∗ Z Z E[hbi,jhbl,q] = ξ(r, θ)ζ(r, θ)Gt(r, θ)Gr(r, θ) 0 0 D. Frequency Diversity 2 Bn(|r sin(θ|), |r cos(θ)|) exp − j2π (∆f/c For frequency diversity, the effect of the frequency separation is reflected in the system with the small change in (2Rr − r cos(θ − α) + r cos(θ + β))) dθdr. (17) wavelength (λ) in (7). In this way, the wavelength for antenna pairs will slightly differ. Therefore, the resulting covariance of Figure 5(a) presents the fading correlation vs. the fre- (7) for antennas having frequency separation is represented as quency separation for different beam-widths in a 250 km and correlation distance 50 m troposcatter link. As in the r10dB 2π ∗ Z Z space diversity, the increase in the beam-width decreases E[hbi,jhbl,q] = Gt(r, θ)Gr(r, θ)ξ(r, θ) 0 0 the correlation due to the increase in the common volume. 2 According to the empirical recommendations provided by ITU ζ(r, θ)Bn(|r sin(θ|), |r cos(θ)|) [3], the frequency spacing between antennas (∆f) should DT + DR DT + DR exp −j2π j i − q l dθdr, (12) be ∆f = 1.44f(D2 + 152)1/2/θR Mhz, where f is the λ λ ant j q carrier frequency in Hz and R is the range in m. For 4.7 GHz carrier frequency, 3 m antenna diameter and 250 km where λj = c/(f + ∆f), λq = c/f, and ∆f is the frequency separation. Therefore, the path calculations in (12) becomes range, the recommended frequency spacing is 13 MHz. For the same antenna diameter (1.5◦ curve in Figure 5(a)), 10 MHz and greater frequency separations allow the antennas to (DT + DR )(f + ∆f)/c − (DT + DR )f/c = j i q l be uncorrelated in the frequency diversity systems. (D + D )∆f/c + (∆D + ∆D )f/c. (13) Tj Ri Tj,q Ri,l In addition, [4], [5] provides experimental frequency correlation results for the troposcatter links. To this end, Figure 5(c) Firstly, we assume there is no spatial separation between provides the experimental frequency correlation results (Figure receivers to investigate the effects of frequency diversity. 9 in [5]) along with the RSM results by using the experimental Therefore, (∆D + ∆D )f/c term in (13) disappears. Tj,q Ri,l channel parameters: 192 km and 1.17◦ 3 dB beam-width at D and D are found by using their relationship with R . Tj Ri r 7.6 GHz. As noticed, the trend of the experimental and RSM Since the distance between antennas and scattering common results are similar. However, the results of the RSM model volume is much higher than the radius of common volume is higher than the experimental results. This situation can be (R r10dB), we can use far distance approximation in t,r caused by the atmospheric conditions of the experiment site. which R and D are assumed to be parallel to each other. t Tj However, the behavior of the frequency correlation can be In the same way, R and D also become parallel as shown in r Ri well-captured with the RSM method. Figure 4. By performing the required geometrical calculations, The frequency separation formula (17) depends on the range the D and D is represented as Tj Ri by (9) as in the ITU’s formula [3]. Figure 5(b) presents the fading correlation vs. range and frequency separation with the D = R − r cos(θ − α), (14) Tj t RSM for 1.5◦ 3 dB beam-width and 50 m vertical correlation D = R + r cos(θ + β). Ri r (15) distance. According to our results, the increasing range decreases the fading correlation at the same frequency separation The proof of these equations are left to the reader. Since the value because the increasing range also cause increase in troposcatter path is assumed as symmetrical, Rt = Rr. Thus, the troposcatter common volume. Also, the ITU’s frequency D + D term becomes Tj Ri separation formula is inversely proportional to range. Most importantly, the analytical fading calculations for the D + D = 2R − r cos(θ − α) + r cos(θ + β). (16) Tj Ri r frequency diversity can be utilized to derive the coherence bandwidth of the channel for 50% correlation. According to our results, 250 km troposcatter link at 4.7 GHz and 3 m antenna diameter have Bc(50) ≈ 2 MHz. Therefore, the ` channel will have frequency-selective fading for bandwidths = 1 3LUR% %UR3L greater than 2 MHz. In such cases, the channel requires the implementation of orthogonal-frequency-division-multiplexing % ` (OFDM) to mitigate the effects of frequency-selective fading. In this paper, we focus on the high data rate employments of troposcatter communications. Thus, we use higher bandwidths than the coherence bandwidth and introduce OFDM capacity Fig. 4. Channel geometry for the frequency diversity. calculations for the troposcatter systems by using our previously developed ray-based method [1] in Section V. IEEE TRANSACTIONS ON COMMUNICATIONS 6

1 1 ° w3dB =0.6 l =20 m y ° w3dB =1 l =50 m 0.8 y 3dB ° 0.8 w =1.5 l =130 m y [5] Upper 0.6 1 0.6 [5] Median [5] Lower

0.4 0.5 Correlation 0.4 Correlation

Correlation 100 0.2 0 0.2 0 5 200 10 0 0 0 2 4 6 8 15 d (km) 0 2 4 6 8 20 300 ∆ f (MHz) 6 ∆ 6 x 1 0 ∆ f (MHz ) f (MHz) x 1 0 (a) (b) (c) Fig. 5. The fading correlation results for (a) frequency separation, (b) range and frequency separation.

E. Space-frequency Diversity

Troposcatter systems can also use the combination of di- 1 versity techniques. Space-frequency diversity is a promising technique which can provide higher data rates with low 0.5 cost. Space-frequency diversity systems utilize horizontally placed antennas with frequency diversity. Since the frequency Correlation diversity antennas can be mounted on the same parabolic 0 reflector antenna, higher gains can be achieved with the space- 0 frequency diversity by using the same number of parabolic 2 reflector antennas as in space diversity. Therefore, we derive 150 4 100 analytical expressions for the correlation between antennas as 50 6 0 a function of spatial and frequency separation. ∆ f (MHz) d/ λ By using (12) and (13), the fading correlation for space- frequency diversity can be found directly using the same Fig. 6. Fading correlation vs. spatial and frequency separations. methodology as in the frequency diversity part.For the 2 receivers that are communicating with the same transmitter, volumes. In addition, the angle diversity receivers can be ∆D = 0. Therefore, by combining (12), (13) and (16) Tj,q mounted on the same parabolic reflector. Therefore, the cost of for horizontally placed antennas (d = 0), the covariance Rx additional antennas will be low compared to space diversity. expression for the space-frequency diversity is found as When the angle spacing of the antennas are higher than the Z r10dB Z 2π beam-width of the antennas, the troposcatter common volumes ∗ 2 E[hbi,jhbl,q] = ζ(r, θ)Bn(|r sin(θ|), |r cos(θ)|) will not intersect, and there will be low correlation between the 0 0 troposcatter common volumes. However, in practical employ- ∆f ments, troposcatter systems use very low angular separations exp − j2π (2Rr − r cos(θ − α) + r cos(π − θ − β)) c because higher angular separation causes increase in the path ξ(r, θ)Gt(r, θ)Gr(r, θ) exp −j2π/λdRy r/Rt sin(θ) dθdr. lengths, and results in more path loss. In angle diversity, the (18) source of the correlation between antennas is the intersection of two different troposcatter common volumes as in Figure 7. (18) is calculated with numerical integration on MATLAB.

Figure 6 shows the fading correlation for space-frequency

diversity for 250 km range, 50 m vertical correlation distance and 1.5◦ 3 dB beam-width. As noticed, the required frequency separation for low correlation decreases with the increasing @1 spatial separation. Similarly, the required spatial separation :` . can be decreased with the frequency separation. For this `:JI1 V` VHV10V` reason, this employment is especially promising for systems that require placement of multiple antennas in close distances Fig. 7. Troposcatter common volumes in the angle diversity system. by using both parameters to achieve higher gains in MIMO. In RSM method, scatterers are assumed to be located just within the ring to make simple theoretical analysis. However, F. Angle Diversity angle diversity system can be analyzed without this assumption Vertical angle diversity is also a promising method for with slight modification of the proposed model. For the angle the troposcatter communications because 2 × 2 vertical angle diversity, the shape of the common volume is modeled as diversity system can form four different troposcatter common parallelogram as in Figure 7. The only source of correlation IEEE TRANSACTIONS ON COMMUNICATIONS 7 is the intersection of the lower and upper common volumes. squint-loss in the angle diversity case. In [1], the beam-width The rays that are associated with the intersection point have of the antennas are divided into small parts, thus the delay the same path lengths because the receivers are mounted to and power calculations for each ray are performed separately. the same parabolic reflector, so that (∆DTj,q + ∆DRi,l ) = 0. In this way, each ray is subjected to different atmospheric Therefore, the correlation for the angle diversity is given as conditions according to its path. The ray powers are calculated with differential bistatic radar α +w10dB β +w10dB +∆w ∗ Z 0 t Z 0 r equation E[hbi,jhbl,q] = 2 α β PtGtGrσV λ % 0 0 Pr = W, (22) A 3dB A 3dB (4π)3R2R2 Gt (α − α0 − wt )Gr (β − β0 − wr − ∆w) t r 2 Bn(|Rt cos(α) − R/2|, |h − hC |) dαdβ, (19) where Pt is the transmit power in Watt (W), Gt,r are the antenna gains for transmitter/receiver. % is the polarization where ∆w is the angular spacing, GA are the Gaus- t,r mismatch factor. σV is differential scattering cross-section. A sian antenna gain functions which is given as Gt,r(Θ) = The atmospheric profiles are included via the scattering 2 3dB 2 exp(−Θ /(0.6 × w ) ) [15]. The middle of the scattering cross-section. We define the differential scattering cross- volume is assumed as the reference point for the correlation section by using Rayleigh scattering and Kolmogorov spec- function Bn. The scattering height h and the center height of trum [16]. In this way, our model can take the real world the troposcatter common volume hC is given as [14] water-vapor mixing ratio measurements [17] as input to model sin(β) sin(α) the non-homogeneities and fluctuations in the air turbulence. h = R , (20) sin(α + β) The differential scattering cross section is represented as [1] sin(β + w3dB/2) sin(α + w3dB/2) 4 2 2 h = R 0 t 0 t . (21) σV = 2πk cos(Ψ) dVcΦ(ks) m , (23) C 3dB 3dB sin(α0 + β0 + wt /2 + wr /2) where k is the wave-number, Ψ is the scatter angle, dVc is Figure 8 shows the angular fading correlation for different the differential scattering volume. In addition, Φ(ks) is the beam-widths for 250 km and 50 m vertical correlation values. Kolmogorov spectrum which is formulated as [16] As noticed, the fading correlation becomes very low when the 3 2 −11/3 3 angular separation is higher than the 3 dB beam-widths, as also Φ(ks) = 0.33π Cn(2k sin(Ψ/2)) m , (24) suggested in [2]. Since the intersecting region will be higher k = 2k sin(Ψ/2) C for higher beam-widths, the correlation for the higher beam- where s . n is the structure constant of the widths are higher in the same separation values. The similar refractive-index which is directly generated by using the water- results can be found in [8] for lower 3 dB beam-widths. vapor mixing ratio measurements [17] (For more details [1]). Since increase in the angle causes increase in the path lengths and scattering angle, the upper beam will have con- V. MAXIMUM DATE RATE siderably higher path-loss. This path-loss difference between In this section, we present the calculations for the achievable lower and upper common volumes is called as squint-loss. The data rates that can be provided by the b-LoS troposcatter results for the squint-loss are presented in Section VI-A. communication under the employment of different diversity techniques. To this end, we improve our ray-based channel

1 modeling approach [1] to implement the diversity techniques ° w3dB =0.6 in the troposcatter channel with MIMO-OFDM. ° w3dB =1 0.8 ° w3dB =1.5 A. System Model for Maximum Date Rate 0.6 The block diagram of MIMO-OFDM troposcatter system is in Figure 9. In this work, only single-user to single-user 0.4 Correlation link is considered to show the performance of the troposcatter channel, and the channel is assumed to have slow fading. Full 0.2 CSI is assumed at both sides of the communication. Therefore, the maximum ratio transmission technique [18] is utilized. In 0 0 0.5 1 1.5 this technique, the transmitter beam-forming is implemented ∆ w (in Beam−widths) with maximum-ratio-combining (MRC). Transmitter beam- Fig. 8. Fading correlation vs. angular separations. forming with MRC reception is also called as MIMO-MRC. In frequency domain, the Mr × 1 received signal vector for kth OFDM tone (y[k]) is given as IV. RAY-BASED TROPOSCATTER CHANNEL MODELING y[k] = H ej2πk/N w s + n, (25) APPROACH t

In this work, we utilize our previously developed ray-based where s is the transmitted symbol with average power Ps, wt method [1] to compare different diversity techniques in terms is the transmitter beam-forming vector, n represents AWGN of data rate. In addition, we present simulation results for the vector, and N is the number of OFDM tones. IEEE TRANSACTIONS ON COMMUNICATIONS 8

J QIIQJ QC%IV 1 1 J]% ` % ]% 1 ` 1``

V:I`Q`I1J$VH Q` V:I`Q`I1J$VH Q`

Fig. 9. OFDM antenna array block diagram.

The estimated output signal (y˜[k]) is given by B. Channel Gain Matrix for Diversity Techniques To generate H ej2πk/N , we ﬁrst use the channel matrix H j2πk/N H y˜[k] = wr H e wts + wr n, (26) normalization to exclude the effects of large-scale path loss which is calculated by the ray-based technique [1]. The large- H where (.) represents the conjugate transpose operation, wr scale path loss is derived by using real world measurements is the receiver beam-forming vector. as described in Section IV. The small-scale fading is assumed 2 By using the following property ||wr|| = 1, the SNR for as Rayleigh fading as suggested in [3], [7], [15], [22], [23]. kth tone can be found with the following expression [19] Normalized channel gain matrix H˜ ej2πk/N is found as [24]

j2πk/N H j2πk/N H H j2πk/N H e w H e wrw H e wt ˜ j2πk/N γ[k] = γ t r , H e = q , (31) wH w 1 ||H ej2πk/N ||2 r r MtMr F H H j2πk/N j2πk/N = γwt H e H e wt, (27) where ||.||F is the Frobenius norm. Thus, the average SNR on the channel is found as [24], [25] where γ = Ps/N0 is the average SNR per receive antenna. 2 j2πk/N 2 2 SNRav = Pt/(σnMtMr)||H e ||F , (32) Since we have the ||wt|| = 1 constraint for the transmit H j2πk/N H j2πk/N beam-forming vector, wt H e H e wt is on where SNRav is the average receive SNR that is calcu- the unit sphere. This expression is maximized by the λmax, the lated with the ray-based method. As described in Section H largest eigenvalue of H ej2πk/N H ej2πk/N (For more IV, the water-vapor mixing ratio measurements are utilized detail, see [18]–[20]). Therefore, the maximum achievable data for atmospheric modeling, and the data set includes 1000 rate, capacity, is given by measurements that are measured in August near Cape Verde Islands [17]. Therefore, the average SNR is calculated for each N−1 k X λmaxPk measurement instant to model the atmospheric fluctuations. C = max BN log 1 + 2 , (28) P :P P =P σ BN With the channel normalization, (27) can be represented as k k t k=0 n H wH H ej2πk/N H ej2πk/N w = where Pt is the total power constraint, BN is the bandwidth of t t the each sub-channel (B/N), λk is the largest eigenvalue H max H ˜ j2πk/N ˜ j2πk/N j2πk/N H j2πk/N 2 SNRavwt H e H e wt. (33) for H e H e . σn is the noise power in W/Hz which is modeled as thermal noise. In addition, Pk is This expression is maximized by the largest eigenvalue of th H the allocated power for k OFDM sub-channel and they are H˜ ej2πk/N H˜ ej2πk/N , and H˜ is generated for each di- calculated by the well-known water-filling algorithm [21] versity technique differently. ( 1) Space diversity: With the correlation results that are P 1/γ − 1/γ , γ ≥ γ k = 0 k k 0 (29) generated in Section III-C, the normalized channel gain matrix Pt 0, γk < γ0 is modeled as [26] k 2 H˜ ej2πk/N = (RRX )1/2G(RTX )1/2, (34) where γ0 is the cutoff value and γk = λmaxPt/σnBN . By H H using (28) and (29), the capacity is simplified into [21] RX 1/2 where G is the complex Gaussian iid matrix. (RH ) X C = B log(γ /γ ). (30) is the root of the receiver antenna correlation matrix N k 0 RX 1/2 RX 1/2 H RX k:γ ≥γ (RH ) [(RH ) ] = RH which is found by Cholesky k 0 TX factorization. (RH ) is the transmitter correlation matrix. Up to now, the framework for the capacity calculations is 2) Frequency diversity: Since the frequency separation formed. The remaining of the section includes how to generate between antennas nulls the cross components, there are Mt = j2πk/N H e matrix with our previously proposed ray-based Mr parallel channels in frequency diversity. Therefore, G in method and RSM for fading correlation. (34) is generated as diagonal matrix for frequency diversity. IEEE TRANSACTIONS ON COMMUNICATIONS 9

3) Space-frequency diversity: Since the frequency diversity 20 ° is provided with only one parabolic reﬂector, we can use w=0.6 ° w=1 horizontally placed antennas with frequency diversity, and ° 15 w=1.5 achieve quad-diversity. Suppose that NSFD represents the number of parabolic reﬂectors in one side and there are equal number of them in each side, G matrix in (34) for the space- 10 frequency diversity becomes Squint−Loss

5 GMF NSFD ×MF NSFD = diag (G1,..., GNSFD ) . (35) where G1,...,NSFD represents the complex Gaussian iid chan- 0 nel matrix with MF × MF , where MF is the number of 0 0.5 1 1.5 2 frequency used for the frequency diversity. The function diag ∆ w (in Beam−widths) forms a block diagonal matrix from its input arguments. Fig. 10. Squint-loss results for angle diversity. 4) Angle diversity: In angle diversity, the increase in the elevation angles cause signiﬁcant decrease in the average SNR. Instead of channel matrix normalization, the average SNR lower beams show 5 − 10 dB squint-loss for 0.6◦ 3 dB beam- for each antenna pair is calculated separately for Mt = Mr width and 1◦ beam separation (∆w ≈ 1.6 in beam-width). As case. (27) is represented as (36) for Mt = Mr angle diver- noticed in Figure 10, the average squint-loss calculated with sity system where ◦ is Hadamard product that is element [1] is also in the experimentally measured range. by element matrix multiplication. Therefore, (36) is maxi- [SNR ] ◦ mized with the largest eigenvalue of avi,j i = 1, ··· ,Mr B. Maximum Data Rate Results j = 1, ··· ,Mt H H˜ ej2πk/N H˜ ej2πk/N . (36) is calculated with the ray- We present the achievable data rate simulation results by based technique for each antenna pair for the angle diversity. using the RSM to estimate the required separations for the H˜ ej2πk/N term in (36) is also modeled as in (34). partial correlation between antennas. The required separations for partial correlations (for ρ = 0.5) can be found in Table I.

VI.PERFORMANCE EVALUATION TABLE I TROPOSCATTER DIVERSITY SEPARATIONS. In this section, we compare the troposcatter diversity techniques by using maximum data rate simulations. In addition, Diversity technique Separations Correlation (ρ) we present the squint-loss results for the angle diversity. Space diversity (2 × 2) d = 65λ m 0.5 Frequency diversity (2 × 2) ∆f = 2 MHz 0.5 A. Squint-Loss Results Angle diversity (2 × 2) ∆w = 14 mrad 0.5 Squint-loss= 6 dB For space and frequency diversity cases, the antennas utilize Space-frequency diversity (4 × 4) d = 30λ m 0.5 the same vertical orientation. Therefore, different antenna pairs ∆f = 1.7 MHz in space and frequency diversity systems can maintain the same average received power levels. On the other hand, the The troposcatter simulation parameters can be found in angle diversity utilize angular separation and upper beam is Table II. In addition, there are 1000 atmospheric measurements subjected to signiﬁcantly higher path-loss because both the in the used data sets [17]. We perform 1000 realization for the path lengths and the scattering angle increase. For this reason, random G matrix as in Section V-B. Therefore, the maximum we analyze the additional path-loss caused by the angular data rate results are generated with the total of 1 million separation which is also known as squint-loss. realization by using the ray-based model [1] in MATLAB. We utilize the ray-based channel model [1] as in Section IV Figure 11 presents the cumulative distribution function for the following channel parameters: 250 km, 4.7 GHz carrier (CDF) of the data rate for different diversity techniques. As frequency, 41.5 dB antenna gains in each side. Figure 10 expected, 2 × 2 space diversity provides signiﬁcantly higher includes the squint-loss results for different beam-widths. As data rates compared to frequency and angle diversity. In noticed, the squint loss increases with increasing beam-width addition, the span of achievable data rates decreases with because the separations are given in beam-widths. Similar the space diversity, thus the additional antenna makes the results for the squint-loss is presented in [9] for the angle channel more reliable. However, 2 × 2 frequency diversity diversity. According to the experimental results, the upper and provides the lowest data rate gains because the frequency

  SNRav1,1 ··· SNRav1,M H 1 t H H j2πk/N j2πk/N H  . . .  ˜ j2πk/N ˜ j2πk/N wt H e H e wt = wt . .. . ◦ H e H e wt. Mt   SNRavMr ,1 ··· SNRavMr ,Mt (36) IEEE TRANSACTIONS ON COMMUNICATIONS 10

1 SISO Space Div. 0.8 Frequency Div. Angle Div. Space−frequency Div. 0.6 CDF 0.4

0.2

0 4 5 6 7 8 9 10 11 12 13 Capacity (bps) 7 x 1 0

Fig. 11. The distribution of the achievable data rates for different diversity techniques.

TABLE II TROPOSCATTER COMMUNICATION PARAMETERS. troposcatter communication can provide more than 8 Mbps at all times. Therefore, the troposcatter communication is a Parameter Value Unit promising candidate for high data rate b-LoS communications Horizontal distance (d) 250 km with the employment of diversity techniques. Carrier frequency (f) 4.7 GHz Transmit power (P ) 1000 W t PPENDIX Bandwidth (B) 10 MHz A A Average Transmission-loss (Pr/Pt) −138 dB INTEGRAL BOUNDS # of OFDM symbols N 64 ( ) - In (8), the integral bound is given as the whole ring deﬁned Beam-widths (wt,r) 26 mrad Beam-elevations (α0, β0) 14.7 mrad by the 10 dB beam-width. However, the lower part of the ring Antenna gains (Gt,r) 41.5 dBi should be excluded from the integral as also shown in Figure Antenna diameters (Dant) 3 m 12. To this end, we deﬁne a function ζ(r, θ) to exclude this area from the integral, and it is given as

 10dB separation between antennas nulls the cross antenna signal 0, if r > r cos (π/2 − θ + α0), and  powers. On the other hand, 2 × 2 angle diversity, which can ζ(r, θ) = π − α0 + ϕ > θ > α0 + ϕ (37) be performed with only 2 parabolic reflectors, has significantly 1, otherwise higher performance compared to the frequency diversity. Since the increase in the elevation angle decreases the received where ϕ = arcsin(r3dB/r10dB). power of the additional troposcatter common volumes, the space diversity outperforms the angle diversity. % `R Although the frequency diversity has the worst achievable `R data rate performance, the space-frequency diversity can pro- ` vide quad diversity by using 2 parabolic reflectors in each side. In this case, there are 2 horizontally placed antennas, and each antenna mounted with 2 × 2 frequency diversity receivers. As seen in Figure 11, the achievable data rate performance of the Fig. 12. The integral boundaries. space-frequency diversity is higher than the space diversity, and its implementation is much more economical compared to adding additional parabolic reflector antennas. APPENDIX B ANTENNA GAINS VII.CONCLUSION Since RSM model utilize the 10 dB beam-width of the In this paper, RSM for fading correlation is proposed to antennas, we include the antenna gains in the correlation investigate the fading correlation between antennas for space, calculations. To this end, we utilize Gaussian antenna pattern frequency, angle and space-frequency diversity. In addition, [15]. For the RSM method, we also need to represent the we compare these diversity techniques with their distribution antenna gains as a function of r and θ. To this end, we utilize of achievable data rates. According to our results, space- Figure 2 and geometrical approximations that are introduced frequency diversity systems can provide more than 10% in- in Section III-C, thus the antenna gains is represented as crease in the achievable data rates. Since the implementation 2 w3dB of frequency diversity does not require additional parabolic re-  t r sin(θ)  α0+ −arctan 2 Rt−r cos(θ) flector, space-frequency diversity systems are much more eco- −  (0.6×w3dB )2  nomical compared to adding additional antennas. Furthermore, t the simulation results shows that the high powered b-LoS Gt(r, θ) = e (38) IEEE TRANSACTIONS ON COMMUNICATIONS 11

2 w3dB  t r sin(π−θ)  β0+ −arctan [15] P. Bello, “A Troposcatter Channel Model,” IEEE Trans. Commun. 2 Rt−r cos(π−θ) − Technol., vol. 17, no. 2, pp. 130-137, April 1969.  (0.6×w3dB )2  t [16] A. Ishimaru, Wave Propagation and Scattering in Random Media. IEEE Gr(r, θ) = e (39) Press Series on Electromagnetic Wave Theory, Wiley, 1999. [17] NAMMA LIDAR Atmospheric Sensing Experiment (LASE), NASA EOSDIS GHRC DAAC, [Online]. Available: APPENDIX C http://ghrc.msfc.nasa.gov/index.html. Accessed on Jan 30, 2013. ξ(r, θ) FUNCTION [18] T. K. Y. Lo, “Maximum ratio transmission,” Proc. IEEE ICC, vol. 2, pp. 1310-1314 vol. 2, 1999. To simplify the correlation equations, we define ξ(r, θ) to [19] A. Maaref, S. Aissa, “Closed-form expressions for the outage and er- represent the sine multiplication, and this function is given as godic Shannon capacity of MIMO MRC systems,” IEEE Trans. Commun., vol. 53, no. 7, pp. 1092-1095, July 2005. − 11 − 11 ξ(r, θ) = sin(Ψ1) 3 sin(Ψ2) 3 , [20] K. Ahn, “Performance analysis of MIMO-MRC system in the presence 11 of multiple interferers and noise over rayleigh fading channels,” IEEE !− 3 cos Ψ1+Ψ2 − cos Ψ1−Ψ2 Trans. Wireless Commun., vol. 8, no. 7, pp. 3727-3735, July 2009. = 2 2 , (40) [21] A. Goldsmith, Wireless Communications, Cambridge University Press, 2 2005. [22] Y. Zhao, X. Chen, “Research on MRC based on Rake receiver in Since the separation between antennas is very small in the troposcatter communication,” Proc. CECNet, pp. 4342-4345, 2011. troposcater communication between 70−100λ, there will be a [23] Y. Wang, Y. Fang, X. Da, W. Jin, “Study on Modeling of Troposcatter Communication and MRC in Correlated Channel by Matlab,” Proc. small difference between the scattering angles for the different WiCOM, pp. 1-4, 2008. antenna pairs in the space diversity. In frequency and angle [24] P. Kyritsi, D. C. Cox, “Effect of element polarization on the capacity of diversity, the antennas are mounted on the same parabolic a MIMO system,” Proc. IEEE WCNC, vol. 2, pp. 892-896, Mar. 2002. [25] Kai Yu, M. Bengtsson, B. Ottersten, D. McNamara, P. Karlsson, M. reflector therefore, the scattering angles will be same therefore, Beach, “Second order statistics of NLOS indoor MIMO channels based we assume Ψ1 = Ψ2. Thus, the ξ can be further simplified as on 5.2 GHz measurements,” Proc. IEEE GLOBECOM, pp. 156-160, 2001. [26] D. Gesbert, H. Bolcskei, D. Gore, A. Paulraj, “MIMO wireless channels: (−11/3) ξ(r, θ) = [(cos (Ψ1/2 + Ψ2/2) − 1)/2] . (41) capacity and performance prediction,” Proc. IEEE GLOBECOM, vol. 2, pp. 1083-1088, 2000. The scattering angles are calculated with the following equa- [27] A. Ishimaru, “Theory and application of wave propagation and scattering tion for both of the antennas, in random media,” Proc. IEEE, vol. 65, no. 7, pp. 1030-1061, July 1977. h − r sin(θ) Ψ(r, θ) = arctan + d/2 − r cos(θ) h − r sin(θ) + arctan . (42) d/2 + r cos(θ) Ergin Dinc [S’12] ([email protected]) received his REFERENCES B.Sc. degree in Electrical and Electronics Engineer- ing from Bogazici University, Istanbul, Turkey, in [1] E. Dinc, O. B. Akan, “A Ray-based Channel Model For MIMO Troposcat- 2012. He is currently a research assistant at Next- ter Communications,” Proc. IEEE PIMRC, London, UK, Sept. 2013. Generation and Wireless Communications Labora- [2] Comtech Systems, Technical Information, “Introduction to Tro- tory (NWCL) and pursuing his Ph.D. degree at poscatter Communications: a brief synopsis of over-the-horizon the Electrical and Electronics Engineering Depart- troposcatter” [Online]. Available: http://www.comtechsystems.com/wp- ment, Koc University, Istanbul, Turkey. His current content/uploads/2014/05/Troposcatter-Introduction-Nov-2013.pdf (URL). research interests include communication theory, [3] “ITU-R’s Rec. P. 617-2: Propagation prediction techniques and data beyond-Line-of-Sight (b-LoS) communications with required for the design of trans-horizon radio-relay systems,” ITU, 2012. troposcatter and atmospheric ducts. [4] W. S. Patrick, “Troposcatter for Tactical Communications,” IEEE Trans. Mil. Electron., vol. 9, no. 2, pp. 137-143, Apr. 1965. [5] D. Kennedy, “A Comparison of Measure and Calculated Frequency Correlation Functions over 4.6 and 7.6-GHz Troposcatter Paths,” IEEE Trans. Commun., vol. 20, no. 2, pp. 173-178, Apr. 1972. [6] G. C. Rider, “Some tropospheric scatter propagation measurements and tests of aerial siting conditions at 858 Mc/s,” Proceedings of the IEE, vol. 105, no. 8, pp. 143-152, 1958. [7] R. W. Meadows, “Tropospheric scatter observations at 3 480 Mc/s with Ozgur B. Akan [M00-SM07] ([email protected]) aerials of variable spacing,” Proceedings of the IEE, vol. 108, iss. 40, p. received his Ph.D. degree in electrical and com- 349-360, July 1961. puter engineering from the Broadband and Wireless [8] M. W. Gough, G. C. Rider, “Angle diversity in troposcatter communica- Networking Laboratory, School of Electrical and tions. Some confirmatory trials,” Proceedings of the IEE, vol. 122, no. 7, Computer Engineering, Georgia Institute of Tech- pp. 713-719, July 1975. nology in 2004. He is currently a full professor [9] P. Monsen, “Performance of an Experimental Angle-Diversity Troposcat- with the Department of Electrical and Electronics ter System,” IEEE Trans. Commun., vol. 20, pp. 242-247, Apr. 1972. Engineering, Koc University and the director of [10] S. B. Rhee and G. I. Zysman, “Results of suburban base-station spatial the Next-generation and Wireless Communications diversity measurements on the UHF band,” IEEE Trans. Commun., pp. Laboratory. 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