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Optimized Gain Control for Single-Frequency Relaying with Loop Interference Taneli Riihonen, Student Member, IEEE, Stefan Werner, Senior Member, IEEE, and Risto Wichman

Abstract—This letter derives new gain control schemes for an amplify-and-forward single-frequency relay link in which loop interference from the relay transmit antenna to the relay receive antenna has to be tolerated. The proposed gain control schemes take into account the effect of residual loop interference that remains after imperfect loop interference cancellation. As a result of our gain control strategy, the signal-to-interference and noise ratio can be maximized while, at the same time, transmit power is decreased. Finally, we evaluate system performance by deriving closed-form outage probability expressions for the gain control schemes. Index Terms—Echo interference, echo suppression, gain control, land mobile radio cellular systems, radio repeaters.

I. I NTRODUCTION

W

IRELESS relays are transceivers that receive, process, and then retransmit radio signals. In cellular networks, relays offer a cost-effective solution for coverage extension or gap filling, and hotspot capacity enhancement. We study a twohop OFDM relay link that consists of a source, a relay and a destination. The source and the relay transmit simultaneously on the same frequency band, and the relay operates in an amplify-and-forward mode. Furthermore, we concentrate on the scenario of cell coverage extension, i.e., it is assumed that the direct source–destination link is weak compared to the two-hop transmission. Concurrent transmission and reception at the same frequency band in the relay requires appropriate avoidance of loop interference (LI) leakage from transmit signal to receive signal [1], [2]. In practice, single-frequency operation requires two separated antennas in the relay: one for receiving and the other for transmitting. Furthermore, high physical isolation between the antennas has to be guaranteed, e.g., by placing one antenna on rooftop and the other antenna on street level. Another possible setup is outdoor-to-indoor transmission where the relay backhaul antenna is placed outside of a building and the indoor service antenna fills a base station coverage area gap. Furthermore, directivity properties of the antennas can be exploited. Interference cancellation by subtracting an estimated loop interference signal from the relay input signal reduces further the need for physical isolation between the two antennas. Loop Manuscript received April 19, 2008; revised September 11, 2008 and December 12, 2008; accepted March 23, 2009. The associate editor coordinating the review of this paper and approving it for publication was Ying Jun (Angela) Zhang. The authors are with the Department of Signal Processing and Acoustics, Helsinki University of Technology, P.O. Box 3000, FI-02015 TKK, Finland (e-mail: {taneli.riihonen, stefan.werner, risto.wichman}@tkk.fi). This work was partially funded by the SMARAD Centre of Excellence and the Academy of Finland.

interference cancellation is usually facilitated by adaptive filtering techniques [3]–[5], or by embedding a low power pilot signal into relay transmission [6]. In this letter, the relay is assumed to perform loop interference cancellation and amplification on the OFDM subcarrier level similarly as in [7]. We, therefore, impose the standard assumptions: time and frequency synchronization is perfect, the multipath channels are shorter than the OFDM cyclic prefix (CP), and the channel coherence times are reasonably longer than duration of several OFDM symbols. In the frequency domain, the loop interference channel for each subcarrier is a single flat-fading tap and its cancellation can be performed with a simple single tap filter. However, in practice even after cancellation, some residual interference remains which needs to be taken into account in the relay gain control. We consider in total four different gain control schemes, of which two are novel to the best of our knowledge. The conventional gain control scheme [1], [2], [8] guarantees nonoscillating relay behavior by setting the gain to be smaller than the isolation between the relay antennas with a pre-defined gain margin. Loop interference cancellation techniques can then be employed for improving the isolation and, thereby, for increasing the maximum available gain. Alternatively, the gain can be simply set to the maximum value allowed by a transmit power constraint. The two new gain control schemes are inspired by the observation that desired signal power is linearly proportional to relay gain, but residual loop interference power is not. Thus, relay gain that is considerably lower than the limitation set by the transmit power constraint can actually result in better signal-to-interference and noise ratio (SINR) in the destination. Our first contribution is to derive an optimal relay gain control scheme that maximizes the end-to-end SINR and a nearly optimal target SINR based scheme; The latter avoids the need for relay–destination channel state information in the relay. Our second contribution is to evaluate the performance of the gain control schemes in a cellular downlink scenario by deriving new closed-form expressions for outage probability of the end-to-end SINR. The results show that optimized gain control can at the same time improve SINR and outage probability, and still reduce transmit power usage. The letter is organized as follows. Section II presents the system model for the single-frequency relay link along with an expression for the end-to-end SINR. Section III introduces the relay gain control methods and their performance is evaluated in Section IV. Finally, Section V contains concluding remarks.

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II. S YSTEM M ODEL In this section, we introduce the signal model of the singlefrequency OFDM relay link and derive an expression for the end-to-end SINR. The system consists of four physical slowly time-varying multipath channels, namely source–relay, loop interference, relay–destination and source–destination channels. The channels are assumed to be shorter than the OFDM cyclic prefix, and by assuming also perfect frequency and time synchronization all subcarriers are orthogonal and subject to flat fading. There is no inter-carrier interference and no other inter-symbol interference than that due to loop interference. However, frequency selectivity causes different channel coefficients for the subcarriers. A. Signal Model In the following, we consider an arbitrary OFDM subcarrier in the frequency domain, omit the subcarrier index, and study relay operation at time index i assuming that the channels remain approximately stationary during a relatively long observation period. The end-to-end signal model is illustrated in Fig. 1.

D

S x[i]

y[i]

hSD

hSR

nD

hRD c

nR

t[i]

r[i] β

−w

Fig. 1. Signal model for an arbitrary subcarrier in single-frequency relaying with the amplify-and-forward protocol and loop interference cancellation. This model is extended over the OFDM symbol bandwidth by repeatedly applying it for all parallel subcarriers.

The source (S) transmits n signal o x[i] to the relay with a con2 stant transmit power E |x[i]| = PS while the transmission is also overheard by the destination. The relay operates in a single-frequency mode, i.e., it concurrently receives signal r[i] and transmits signal t[i]. Thus, the relay receives a combination of the signal transmitted by the source, loop interference and receiver noise: r[i] = hSR x[i] + ct[i] + nR [i],

where w is the cancellation filter coefficient. Delay of τ ≥ 1 symbols is required for enabling operation on the subcarrier level, because each OFDM symbol must be fully received before the discrete Fourier transform can be calculated. We let PR denote n theomaximum allowed transmit power in the relay, 2 i.e., E |t[i]| ≤ PR . The corresponding relative maximum transmit power is ρR = PσR2 . R By recursive substitution of (1) and (2) we obtain ∞ X j−1 (hLI β) (hSR x[i − jτ ] + nR [i − jτ ]), t[i] = β

(3)

j=1

where hLI = c − w β is the residual loop interference channel. The loop interference cancellation coefficient w can be determined by any existing adaptive filtering, or pilot-based channel estimation method. The relay would ideally use w = cβ. In practice, however, some loop interference remains, because the relay applies w = c˜β, where c˜ = c + ∆c is an estimate of the loop intererence channel and ∆c is an estimation error. In the following, we evaluate the performance of the system in 2 2 terms of the residual loop interference power |hLI | = |∆c| . As each cancellation algorithm results in specific residual loop 2 interference power, parametrization with |hLI | allows general analysis without limitation to a certain setup or cancellation algorithm. Finally, the received signal in the destination (D) is given by y[i] = hRD t[i] + hSD x[i] + nD [i], (4) where hRD and hSD are the flat-fading relay–destination and source–destination channels, respectively, and the power of the o n 2 2 noise term nD [i] is E |nD [i]| = σD .

delay τ

R

the receive antenna n of the o relay, and the power of the noise 2 2 term nR [i] is E |nR [i]| = σR . The relay (R) subtracts an estimate of the loop interference from its input and then amplifies the result by factor β > 0. Thus, t[i] = βr[i − τ ] − wt[i − τ ], (2)

(1)

where hSR is the flat-fading source–relay channel, c is the loop interference channel between the transmit antenna and

B. End-to-End SINR We start studying the end-to-end signal power by deriving a condition to guarantee a non-oscillating relay. By assuming that all signal and noise samples are mutually independent, and the source–relay and the loop interference channels vary slowly, the relay transmit power is calculated from (3) as ∞  o j−1   n X 2 2 2 2 = β2 PS |hSR | + σR (5) E |t[i]| |hLI | β 2 j=1

2

= β

2 2 PS |hSR | + σR 2

1 − |hLI | β 2

,

where the relay gain must be limited by 1 β2 < 2. |hLI |

(6)

(7)

This condition prevents oscillation and guarantees finite relay transmit power, and it is ensured by design for all gain control methods considered in this letter.

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The notation in (3), (5) and (6) omits the time indices of the time-varying channel coefficients, which reflects the assumption that channels remain stationary during the observation period. Even if the channel states are different before the observation period, the effect on (3), (5) and (6) is negligible. This is because the corresponding sum terms are close to zero due to (7). Similarly, the formulation is also valid if the relay does not operate prior to the observation period, because the corresponding sum terms would then be exactly zero. At time index i, the destination employs any standard detection procedure to decode the desired signal x[i−τ ], and the rest of the signal components act as interference and noise. Again by requiring signal and noise independence, the received signal o n 2 power in the destination is calculated from (4) as E |y[i]| = n o n o 2 2 2 2 2 |hRD | E |t[i]| + |hSD | E |x[i]| + σD . This expression with substitution of (6) can be further reorganized into a sum of desired signal power, loop interference power, source– destination interference power, and noise power: o n 2 2 2 = PS |hSR | β 2 |hRD | E |y[i]| 2   |hLI | β 2 2 2 2 + PS |hSR | + σR β 2 |hRD | 2 1 − |hLI | β 2 2

2

2 2 + PS |hSD | + β 2 |hRD | σR + σD .

(8)

Finally, the end-to-end SINR can be expressed from (8) with simplification as γSR γRD , (9) γ= (γSR + 1) γRD ρR /βγ2LI−γLI + γRD + ρR /β 2 where the channel signal-to-noise ratios (SNRs) are defined as 2 2 |2 SR | LI | γSR = PS |h , and γLI = PR |h , γRD = P P|hR |hRD . As σ2 σ2 |2 +σ 2 2

S

R

SD

D

R

|hSD | is small, when the relay is employed for cell coverage extension, it is reasonable to embed the source–destination interference in the destination receiver noise. In a hotspot scenario, where the direct and two-hop transmissions are both strong, equalization or multi-antenna techniques could instead facilitate signal separation and two-branch diversity combining. This would allow the direct transmission to contribute (at least partly) to desired signal power. III. R ELAY G AIN C ONTROL In this section, we discuss the methods for selecting the relay amplification factor β. The instantaneous channel state information exploited in relay gain control is assumed to be ideal. A. Gain Control Methods The relay gain is conventionally determined by first measur2 ing the residual loop interference power |hLI | and then setting the relay gain to satisfy the non-oscillatory condition (7) with a fixed, pre-defined gain margin ∆gm > 1. Thus, the conventional relay gain is given by 2 βgm =

1 ρR 1 1 = . ∆gm |hLI |2 ∆gm γLI

(10)

However, this method is suboptimal in terms of the end-to-end SINR and it does not ensure desired transmit power usage. Another simple gain control method sets the gain in such a way that the maximum relay transmit power is always used. With zero or negligible loop interference, this method maximizes the end-to-end S(I)NR and n o it is often employed in 2 literature. The condition E |t[i]| = PR with substitution of (6) results in the maximum gain ρR 2 βmax = , (11) γSR + γLI + 1 which also guarantees that (7) holds. Note that this control method can be considered to exploit the conventional approach with an adaptive gain margin of ∆max = 1 + (γSR + 1)/γLI . By substitution of (11) into (9), the end-to-end SINR with maximum transmit power usage is given by γSR γRD . (12) γmax = γSR + (γRD + 1) (γLI + 1) It is somewhat simple to use the maximum gain, because the relay can adaptively adjust its transmit power to the constant level without knowing the actual channel SNRs in (11). 2 2 However, neither of the simple gains (βgm , βmax ) offers optimal end-to-end performance. From (8) we see that as a function of the relay gain β 2 , the desired signal power is linear, but the loop interference power is nonlinear. Consequently, increasing relay gain can increase the loop interference power faster than the desired signal power which leads to reduced end-to-end SINR. It can be shown that (9) has a single R maximum point for β 2 ∈ (0, γρLI ). Thus, by finding the correct root of the derivative of (9), the optimal gain becomes ρR 2 p = βopt , (13) γLI + (γSR + 1) γRD γLI which satisfies (7). The optimal gain is equivalent to the conventional gain whenpexploiting an adaptive gain margin given by ∆opt = 1 + (γSR + 1)γRD /γLI . By substitution of (13) into (9), the corresponding end-to-end SINR becomes γSR γRD p γopt = . (14) γRD + γLI + 2 (γSR + 1) γRD γLI  2 2 is employed to satisfy In practice, β 2 = min βopt , βmax 2 2 also the transmit power constraint. By solving βopt ≥ βmax , we see that the condition for residual loop interference is 2

|hLI | ≤

1 γSR + 1 ρR γRD

(15)

for determining whether the transmit power limitation constraints the relay to use the maximum gain instead of the optimal gain. 2 is that it exploits knowledge of γRD that A drawback of βopt can be estimated only at the destination. A feedback channel is then required. Therefore, we propose a simplified relay gain 2 βtar that results in consuming a constant fraction pˆ of the maximum allowed power (ˆ p ∈ [0, 1]), i.e., relative power ρˆR = pˆρR . The corresponding channel SNRs with this approach are 2 given by γˆRD = pˆγRD and γˆLI = pˆγLI . Expressions for βtar and the end-to-end SINR γtar are obtained from (11) and (12),

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respectively, by replacing ρR , γRD , and γLI with ρˆR , γˆRD , and γˆLI , respectively: (16)

γtar =

γSR pˆγRD . γSR + (ˆ pγRD + 1) (ˆ pγLI + 1)

(17)

To avoid using knowledge of γRD , target end-to-end SINR 2 γˆ < γSR is defined and βtar is designed to result in optimal performance only when γtar ≈ γˆ . The fraction pˆ is selected in such a way that the SINR is maximized at the target SINR γˆ . Thus, by eliminating γRD from the equation pair γˆ = γtar , γˆ = γopt , the desired power fraction can be shown to admit the form p γSR (γSR + 1)ˆ γ (ˆ γ + 1) γSR + 1 − (18) pˆ = γˆ γLI γLI when the target SINR satisfies γˆ >

γSR (γSR + 1) γSR + 2γSR γLI + (γLI + 1)2

20

γ [linear]

pˆρR , γSR + pˆγLI + 1

2 βtar =

Varying β 2 , fixed |hLI |2 2 , varying |h |2 With βopt LI 2 With βtar , varying |hLI |2 2 With βmax , varying |hLI |2

25

|hLI |2 = 0 |hLI |2 ≈ −29.86dB

|hLI |2 = −25dB

15

10

|hLI |2 = −20dB

|hLI |2 = −15dB

5

|hLI |2 = −10dB 0 0

1

2

3

4

5

6

7

8

9

10

β 2 [linear] Fig. 2. The end-to-end SINR with different relay gain control methods. The example parameter values are ρR = 25dB, γSR = 15dB and γRD = 20dB. 2 is γ The target SINR for βtar ˆ = 12. 1.4

(19)

|hLI |2 = −10dB, γ ˆ = 3dB |hLI |2 = −15dB, γ ˆ = 6dB

1.2

|hLI |2 = −20dB, γ ˆ = 9dB

and otherwise pˆ = 1 due to the transmit power constraint.

|hLI |2 = −25dB, γ ˆ = 12dB

B. SINR Comparison To illustrate the differences of the gain control schemes, SINRs are plotted in Fig. 2 in a fixed example link setup where ρR = 25dB, γSR = 15dB, γRD = 20dB, and γˆ = 12 2 . Only the achievable SINR area bounded by the case for βtar of no residual loop interference and the case of maximum transmit power usage is shown. The figure displays SINRs of the different gain control methods in terms of the residual 2 2 loop interference power |hLI | . For each fixed value of |hLI | , the SINR in terms of the relay gain β 2 has a distinct global maximum which is reached with optimal gain control. 2 2 For reasonably large |hLI | , optimal gain control with βopt provides both significant SINR improvement and transmit power reduction compared to maximum power usage with 2 2 results in only small βmax . On the other hand, using βmax 2 performance degradation when |hLI | = −25dB, but power 2 savings are still significant with βopt . The target SINR scheme 2 2 with βtar is optimal only when |hLI | ≈ −21.99dB, but 2 except when performance is always improved over βmax 2 |hLI | ≤ −25.93dB and pˆ = 1. From (15) we see that 2 is optimal due to the transmit power constraint when βmax 2 |hLI | ≤ −29.86dB. The gain loss of using the target SINR scheme instead of γ with substitution of the optimal scheme is expressed as γopt tar (14) and (17). This measure is illustrated in Fig. 3 using a fixed example link setup, where ρR = 30dB and γSR = 20dB. The free design parameter γˆ defines the SINR operation area, 2 where the performance of βtar is nearly optimal. We can see that the gain loss is small in a range of several decibels around the value of relay–destination channel SNR γRD that results in the target end-to-end SINR γˆ .

γopt /γtar [dB]

1

0.8

0.6

0.4

0.2

0 6

8

10

12

14

16

18

20

γRD [dB] Fig. 3. The gain loss when the target SINR-based gain control method is used instead of the optimal method. The example parameter values are ρR = 30dB and γSR = 20dB.

IV. O UTAGE P ROBABILITY A NALYSIS In the following we concentrate on downlink operation of a cellular relay. The performance of the system with different gain control schemes is evaluated in terms of the outage probability Pout , i.e., the cumulative distribution function (CDF) of γ: Pout (γth ) = P (γ < γth ) = Fγ (γth ).

(20)

In other words, we consider the probability that the end-toend SINR falls below a pre-defined threshold SINR γth > 0. The outage probability is calculated for a single arbitrary subcarrier, while the performance over the whole OFDM symbol bandwidth can be determined by repeatedly applying the presented analysis.

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−

Pout (γth ) = FγRD (g −1 (γth )) = 1 − e

g −1 (γth ) γ ¯RD

This figure can also be interpreted to illustrate the sensitivity of the gain control schemes to the selection of a particular adaptation algorithm for loop interference cancellation. With 2 βmax , we see very steep transition to total outage around 2 |hLI | ≈ −15dB, which indicates high sensitivity. On the other 2 2 hand, the new proposed gain control schemes (βopt , βtar ) are rather insensitive. 1

(21)

(22)

with γlim,max = γSR /(γLI + 1) for relaying using maximum −1 (γ) can transmit power. With the target SINR approach, gtar also be expressed by (22) when γ¯RD , and γLI are replaced by pˆγ¯RD , and γˆLI , respectively, and the power fraction pˆ given in (18) is used. For relaying using the optimal gain, the inverse function is !2 p p γ (γSR + 1)γLI + γ(γ + 1)γSR γLI −1 (23) gopt (γ) = γSR − γ with γlim,opt = γSR . Finally, the outage probabilities are illustrated in Fig. 4 with an example link setup where ρR = 30dB, γSR = 20dB, 2 and γ¯RD = 25dB. With βmax , the end-to-end SINR is highly limited by loop interference. The maximum achievable SINR 2 γlim,max is only 4.86dB (13.81dB) when |hLI | is −15dB 2 (−25dB). Gain control with βopt minimizes the effect of loop interference. For example, the maximum SINR γlim,opt 2 is 20dB irrespective of |hLI | . For the median SINR value 2 2 is approximately (Pout = 0.5), the gain of βopt over βmax 2 5.8dB (1.3dB) when |hLI | is −15dB (−25dB). Gain control 2 with βtar is nearly optimal when SINR is close to the target 2 SINR γˆ . When |hLI | is −15dB (−25dB), γˆ is set to 10dB (15dB) resulting in transmit power fraction pˆ of 0.14 (0.34), i.e., power saving is also significant. Furthermore, outage probability is illustrated as a function of the residual loop interference power in Fig. 5 for an example link setup where ρR = 30dB, γSR = 20dB, and γ¯RD = 25dB. If the target SINR is selected to be equal to the outage threshold SINR (ˆ γ = γth ), then the performance 2 2 of βtar is equal to that of βopt in terms of outage probability.

2 , β2 With min{βopt max }

0.7 0.6

|hLI |2 = −25dB

|hLI |2 = −15dB 0.5 0.4 0.3 0.2

|hLI |2 = 0

0.1 0 0

2

4

6

8

10

12

14

16

18

20

γth [dB] Fig. 4. The outage probability with different relay gain control methods 2 when ρR = 30dB, γSR = 20dB, and γ ¯RD = 25dB. With βtar the target SINR γ ˆ is 10dB (15dB) when |hLI |2 is −15dB (−25dB).

1

Pout (5dB)

γ (γSR + γLI + 1) γSR − γ(γLI + 1)

2 With βtar

0.8

for γth < γlim and Pout (γth ) = 1 otherwise. The boundary value γlim denotes the end-to-end SINR limit that is approached when γRD → ∞. The inverse functions for different gain control methods are obtained by straightforward algebraic computations that are omitted in this letter. The resulting inverse function is −1 gmax (γ) =

2 With βmax

0.9

Pout (γth )

Due to the single-frequency operation, the relay has to be a fixed infrastructure-based node. Thus, it is reasonable to assume that the source–relay channel is static, which is the closest approximation for Rice-fading with a high Kfactor that would be experienced in practice. The destination is assumed to be a mobile user equipment without lineof-sight connection to the relay. Thus, the relay–destination channel admits Rayleigh-fading statistics. If the average relay– destination link SNRγ is γ¯RD , the CDF of γRD is given by − th FγRD (γth ) = 1 − e γ¯RD for γth > 0. The outage probabilities can be derived by transforms of random variables. Depending on the gain control scheme, the end-to-end SINR is a function of the relay–destination link SNR, i.e., γ = g(γRD ) defined in (12), (14) or (17). After determining the inverse function γRD = g −1 (γ) for γ ∈ [0, γlim ), the outage probability can be calculated as

10−1

γ ˆ = 10dB

γ ˆ = 15dB

2 With βmax 2 , β2 With min{βtar max } 2 , β2 With min{βopt max }

10−2 0

−5

−10

−15

−20

−25

−30

|hLI |2 [dB] Fig. 5. The outage probability for threshold SINR γth = 5dB with varying residual loop interference power when ρR = 30dB, γSR = 20dB, and 2 γ ¯RD = 25dB. When γ ˆ = 5dB, the curve of βtar overlaps the curve of 2 . βopt

V. C ONCLUSION We studied the effect of loop interference in a singlefrequency relay link. Even with interference cancellation, the performance degradation due to residual loop interference cannot be completely avoided. However, adaptive gain control

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offers a win-win solution for alleviating the problem: With smart relay gain selection, less transmit power is consumed while the end-to-end link quality is improved. For gain control, we presented two conventional schemes and proposed two enhanced ones that improve the end-to-end signal-to-interference and noise ratio. Finally, the performance of the schemes was evaluated in terms of outage probability. R EFERENCES [1] W. T. Slingsby and J. P. McGeehan, “A high-gain cell enhancer,” in IEEE 42nd Vehicular Technology Conference (VTC’92), May 1992, vol. 2, pp. 756–758. [2] W. T. Slingsby and J. P. McGeehan, “Antenna isolation measurements for on-frequency radio repeaters,” in 9th International Conference on Antennas and Propagation, April 1995, vol. 1, pp. 239–243. [3] H. Suzuki, K. Itoh, Y. Ebine, and M. Sato, “A booster configuration with adaptive reduction of transmitter–receiver antenna coupling for pager systems,” in IEEE 50th Vehicular Technology Conference (VTC-Fall’99), September 1999, vol. 3, pp. 1516–1520. [4] H. Hamazumi, K. Imamura, N. Iai, K. Shibuya, and M. Sasaki, “A study of a loop interference canceller for the relay stations in an SFN for digital terrestrial broadcasting,” in IEEE Global Telecommunications Conference (GLOBECOM’00), November 2000, vol. 1, pp. 167–171. [5] H. Sakai, T. Oka, and K. Hayashi, “A simple adaptive filter method for cancellation of coupling wave in OFDM signals at SFN relay station,” in 14th European Signal Processing Conference (EUSIPCO’06), September 2006. [6] K. M. Nasr, J. P. Cosmas, M. Bard, and J. Gledhill, “Performance of an echo canceller and channel estimator for on-channel repeaters in DVBT/H networks,” IEEE Transactions on Broadcasting, vol. 53, no. 3, pp. 609–618, September 2007. [7] A. Hazmi, J. Rinne, and M. Renfors, “Diversity based DVB-T indoor repeater in slowly mobile loop interference environment,” in 10th International OFDM-Workshop (InOWo’05), August 2005. [8] C. R. Anderson, S. Krishnamoorthy, C. G. Ranson, T. J. Lemon, W. G. Newhall, T. Kummetz, and J. H. Reed, “Antenna isolation, wideband multipath propagation measurements, and interference mitigation for onfrequency repeaters,” in IEEE SoutheastCon, March 2004, pp. 110–114.

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