1. Field of the Invention
The present invention relates to an evaluation device and method for providing a transceiver system with performance information thereof, more particularly to an evaluation device and method for providing a transceiver system, which models a channel thereof using Nakagami distribution, with performance information thereof.
2. Description of the Related Art
Referring to
In “Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels,” IEEE Trans. Veh. Technol., Vol. 54, No. 4, pages 1312-1321, July 2005, Z. Chen et al. propose a method for evaluating performance of the conventional transceiver system 9 by using Rayleigh fading model (see Rayleigh distribution shown in
In “BER Performance of Transmitter Antenna Selection/Receiver-MRC over Arbitrarily Correlated Fading Channels,” IEEE Trans. Veh. Technol., Vol. 58, No. 6, pages 3088-3092, July 2009, B. Y. Wang and W. X. Zheng introduce a method for evaluating performance of the conventional transceiver system 9 by using Nakagami channel model (see Nakagami distribution shown in
Addressing the drawbacks of the method proposed by B. Y. Wang and W. X. Zheng, there is an improved method for evaluating the SER described in “Performance of Multichannel Reception with Transmit Antenna Selection in Arbitrarily Distributed Nakagami Fading Channels,” J. M. Romero-Jerez et al., IEEE Trans. Wireless Commun., Vol. 8, No. 4, pages 2006-2013, April 2009. The method proposed by J. M. Romero-Jerez et al. is suitable for the Nakagami channel model associated with arbitrary fading parameters, and is generally useful for M-PSK and M-QAM. However, in this method, the SER is computed based upon Lauricella hypergeometric function with a number (LT+1) of variables, where LT is the number of the transmit antennas 921, and thus, the computation of the SER is considerably large.
Further, Z. Chen et al. propose another improved method similar to the method proposed by J. M. Romero-Jerez et al. in “Error Performance of Maximal-Ratio Combining with Transmit Antenna Selection in Flat Nakagami-m Fading Channels,” IEEE Trans. Wireless Commun., Vol. 8, No. 1, pages 424-431, January 2009. In this method, an infinite polynomial with a power of (LT−1) is used for evaluating the conventional transceiver system 9, and thus, the computation of evaluation is also considerably large.
Therefore, an object of the present invention is to provide an evaluation device and method involved with relatively less computation for providing a transceiver system with performance information thereof.
Accordingly, an evaluation device of the present invention is configured to provide a transceiver system with performance information thereof. The transceiver system includes a transmitter and a receiver for receiving a signal from the transmitter, and models a channel between the transmitter and the receiver using Nakagami distribution with a fading parameter. The evaluation device comprises a setting module, a computing module, and an output module.
The setting module is operable to set an average signal-to-noise ratio (SNR) for the channel between the transmitter and the receiver of the transceiver system. The computing module is operable, based upon the fading parameter and the average SNR, to estimate a symbol error rate related to the signal received by the receiver of the transceiver system. The output module is operable to provide the transceiver system with the average SNR and the symbol error rate as the performance information of the transceiver system.
According to another aspect, an evaluation method of the present invention is for providing a transceiver system with performance information thereof. The transceiver system includes a transmitter and a receiver, and models a channel between the transmitter and the receiver using Nakagami distribution with a fading parameter. The evaluation method is to be implemented using an evaluation device, and comprises the steps of:
a) configuring the evaluation device to set an average signal-to-noise ratio (SNR) for the channel between the transmitter and the receiver of the transceiver system;
b) configuring the evaluation device to estimate a symbol error rate related to the signal received by the receiver of the transceiver system based upon the fading parameter and the average SNR; and
c) configuring the evaluation device to provide the transceiver system with the average SNR and the symbol error rate as the performance information of the transceiver system.
Other features and advantages of the present invention will become apparent in the following detailed description of the preferred embodiment with reference to the accompanying drawings, of which:
Referring to
In such a TAS/MRC scheme, there are a number LT×LR of possible channels, each of which is defined by one of the transmit antennas 12 and one of the receive antennas 22 and can be simulated using Nakagami channel model (see Nakagami distribution shown in
In “Concise Performance Analysis of Maximal Ratio Combining with Transmit Antenna Selection in Nakagami-m Fading Channels,” IEICE Transaction on Communications, Vol. E94-B, No. 2, pages 595-598, February 2011, Ching-Tai Chiang et al. disclose a method for estimating performance information of the transceiver system 100 under the TAS/MRC scheme by computing a symbol error rate (SER) or a bit error rate (BER). This method is suitable for the transceiver system 100 configured for M-ary phase-shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM).
When the transceiver system 100 is configured to perform signal modulation using M-PSK and the fading parameter (m) of Nakagami channel model is greater than or equal to ½, the SER (PSER) can be expressed as Equation (1).
In Equation (1),
for a positive integer n. It could be appreciated from the foregoing that α0, α1, α2, . . . , αn are a sequence of rapidly decreasing convergent numbers, that is to say, αn-1 is much greater than αn. Therefore, when the SNR (
It could be appreciated from the foregoing that it is only needed to compute the summation of the infinite series (αn) in Equation (1). Thus, the computation of the SER using Equation (1) is significantly less than the computation of the SER in D1 when the number (LT) of the transmit antennas 12 is relatively greater. Further, Equation (2) is simplified from Equation (1) without the summation of the infinite series (αn), and computation of the SER using Equation (2) is relatively less.
Further, when the transceiver system 100 is configured to perform signal modulation using binary phase-shift keying (BPSK) or binary frequency-shift keying (BFSK), Equations (1) and (2) can be also used for computing the SER with respect to BPSK and BFSK with (a,b)=(1,2) and (a,b)=(1,1), respectively.
Regarding the transceiver system 100 configured to perform signal modulation using M-PSK, the SER (PSER) can be expressed as Equation (3) when a product (m×LR) of the fading parameter (m) and the number (LR) of the receive antennas 22 is a positive integer.
In Equation (3), (a,b)=(2,2 sin2(π/M)), Γ(z)=∫o∞tz-1 e−tdt for an arbitrary positive number z,
for a positive integer n. It should be noted that the computation of the SER (PSER) in Equation (3) is only involved with two terms of summation of finite sequence. Similarly, Equation (3) can be used for computing the SER with respect to BPSK and BFSK with (a,b)=(1,2) and (a,b)=(1,1), respectively.
When the transceiver system 100 is configured to perform signal modulation using M-QAM and the fading parameter (m) of Nakagami channel model is greater than or equal to ½, the SER (PSER) can be expressed as Equation (4).
In Equation (4), 2F1(•,•;•;•) is the Gauss hypergeometric function, and (a,b,c)=(4(√{square root over (M)}−1)/√{square root over (M)},3/(M−1),4(√{square root over (M)}−1)2/M). Similarly, αn-1 is much greater than αn, and, Equation (4) can simplified as Equation (5) when the SNR (
Regarding the transceiver system 100 configured to perform signal modulation using M-QAM, the SER (PSER) can be expressed as Equation (6) when the product (m×LR) of the fading parameter (m) and the number (LR) of the receive antennas 22 is a positive integer. In Equation (6), (a,b,c)=(4(√{square root over (M)}−1)/√{square root over (M)},3/(M−1),4(√{square root over (M)}−1)2/M).
Referring to
The setting module 3 is operable to set the average signal-to-noise ratio (
In step 71, the setting module 3 is operable to set each of the possible channels with the same average SNR (
In step 72, the computing module 4 is operable to compute the SER (PSER) of the transceiver system 100. In this embodiment, the computing module 4 is operable in advance to determine whether the product (m×LR) of the fading parameter (m) and the number (LR) is a positive integer.
Then, when the product (m×LR) of the fading parameter (m) and the number (LR) is a positive integer, the computing module 4 is operable to compute the SER (PSER) based upon Equation (3) for M-PSK and based upon Equation (6) for M-QAM. When it is determined that the product (m×LR) is not a positive integer, the computing module 4 is operable to compute the SER (PSER) based upon Equation (1) or (2) for M-PSK and based upon Equation (4) or (5) for M-QAM. In particular, when the product (m×LR) is not a positive integer, the computing module 4 is operable to compute the SER (PSER) based upon Equation (2) for M-PSK and based upon Equation (5) for M-QAM while the average SNR (
Certainly, in other embodiments, the computing module 4 may be operable in advance to determine whether the fading parameter (m) is greater than or equal to ½, to compute the SER (PSER) based upon Equation (1) or (2) for M-PSK and based upon Equation (4) or (5) for M-QAM when affirmative, and to compute the SER (PSER) based upon Equation (3) for M-PSK and based upon Equation (6) for M-QAM when otherwise.
Since it is impractical to calculate the summation of the infinite series
in Equations (1) and (4) in practice, the computing module 4 is operable to count a limited number of the series. For example, in this embodiment, the computing module 4 is operable to count the series for n=0˜40 when computing the summation.
In step 73, the output module 6 is operable to determine whether there is an instruction of setting another average SNR (
In step 74, the output module 6 is operable to provide the transceiver system 100 with the SER (PSER) corresponding to each of the average SNRs (
It should be noted that, in other embodiments, the transmitter 1 may include only one transmit antenna 12 (i.e., LT=1), and thus, the diversity unit 11 could be omitted and the signal is transmitted through said only one transmit antenna 12. Similarly, the receiver 2 may include only one receive antenna 22 (i.e., LR=1), so that the synthesis unit 21 could be omitted and the evaluation device 300 directly analyzes the signal received from said only one receive antenna 22.
and the dashed lines “- - - ” are respective asymptotes of the SERs (PSER) based upon Equation (2). The symbols x represent the SERs (PSER) for the fading parameters (m=1, 2, 3) from Equation (3) with the product (m×LR) of the fading parameter (m) and the number (LR) of the receive antennas 22 being a positive integer. The symbols * represent the SERs (PSER) from Equation (1) with the summation of the series
for n=0˜40.
It could be appreciated from
for n=0˜40 are closely approximate to the results computed with the summation of the infinite series
so that truncation errors therebetween can be ignored.
when LR=1 to 4, respectively, and the dashed lines “- - - ” are respective asymptotes of the SERs (PSER) from Equation (2). The symbols * represent the SERs (PSER) computed according to Equation (1) with the summation of the series
for n=0˜40.
It could be appreciated from
for n=0˜40 and the results from Equation (1) with the summation of the infinite series
can be ignored.
Similarly,
for n=0˜40. In
for n=0˜40. The above-mentioned features can be also appreciated from
In conclusion, the evaluation device 300 according to the present invention is capable of computing the SER (PSER) for Nakagami distribution with arbitrary positive fading parameter (m) so that the evaluation device 300 is suitable for simulating the performance of the transceiver system 100 in a metropolis. In addition, Equations (1), (3), (4) and (6) for computing the SER (PSER) are relatively simple, and the simplified Equations (2) and (5) respectively from Equations (1) and (4) are practical when the average SNR (
While the present invention has been described in connection with what is considered the most practical and preferred embodiment, it is understood that this invention is not limited to the disclosed embodiment but is intended to cover various arrangements included within the spirit and scope of the broadest interpretation so as to encompass all such modifications and equivalent arrangements.