Evaluation device for providing a transceiver system with performance information thereof

An evaluation device is adapted for providing a transceiver system with performance information thereof. The transceiver system includes a transmitter and at least one receiver, and models a channel between the transmitter and the receiver using Nakagami distribution with a fading parameter. The evaluation device includes a signal-to-noise ratio (SNR) setting module, an error rate computing module, and an output module. The SNR setting module is operable to set an average SNR for the channel between the transmitter and the receiver of the transceiver system. The error rate computing module is operable, based upon the fading parameter, the average SNR and a number of the receiver, to compute a bit error rate over the channel between the transmitter and the receiver. The output module is operable to provide the transceiver system with the average SNR and the bit error rate as the performance information of the transceiver system.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an evaluation device for providing a transceiver system with performance information thereof, more particularly to an evaluation device for providing a transceiver system, which models a channel thereof using Nakagami distribution, with performance information thereof.

2. Description of the Related Art

Referring toFIG. 1, a transceiver system900under a multiuser diversity scheme includes a transmitter91and a plurality of receivers92. The transmitter91includes a plurality of transmit antennas93, and the receiver92includes a plurality of receive antennas94. Under the multiuser diversity scheme, the transmitter91, such as a base station, is capable of communication with the receivers92, such as cell phones of users.

Further, when the transceiver system900utilizes a transmit selective combining/receive maximum ratio combining (SC/MRC) scheme as an antenna scheme thereof, each of the receivers92is operable, in advance, to estimate the channels between the transmitter91and itself so as to determine which one of the transmit antennas93results in a channel that has relatively better performance. According to the evaluation results from the receivers92, the transmitter91is operable to communicate with a selected one of the receivers92, and to transmit signals to the selected one of the receivers92using one of the transmit antennas93corresponding to one of the channels that has relatively better performance. Then, the selected one of the receivers92is operable to weight the signals received by the receive antennas94thereof so as to optimize the performance of the transceiver system900.

In “Outage probability of transmitter antenna selection/receiver-MRC over spatially correlated Nakagami-fading channels,”IEEE ICCT'06, November 2006, pages 1-4, Wang B. Y. et al. proposed a method for evaluating performance of a transceiver system under the multiuser diversity scheme by using Nakagami channels associated with integer fading parameters to simulate an outage probability. However, when evaluations are conducted in a metropolis, the channels of the transceiver system usually fade in various levels. Therefore, the Nakagami channels only associated with integer fading parameters are inappropriate for simulation of masking, fading, or other interferences in a metropolis.

SUMMARY OF THE INVENTION

Therefore, an object of the present invention is to provide an evaluation device and method adapted for appropriately evaluating performance of a transceiver system by using Nakagami channels associated with fading parameters not limited to integers to compute an outage probability of the transceiver system.

Accordingly, an evaluation device of the present invention is adapted for providing a transceiver system with performance information thereof. The transceiver system includes a transmitter and at least one receiver, and models a channel between the transmitter and the receiver using Nakagami distribution with a fading parameter. The evaluation device includes a signal-to-noise ratio (SNR) setting module, an error rate computing module, and an output module.

The SNR setting module is operable to set an average SNR for the channel between the transmitter and the receiver of the transceiver system. The error rate computing module is operable, based upon the fading parameter, the average SNR and a number of the receiver, to compute a bit error rate over the channel between the transmitter and the receiver. The output module is operable to provide the transceiver system with the average SNR and the bit error rate as the performance information of the transceiver system.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring toFIG. 2, a first preferred embodiment of an evaluation device100of this invention is adapted for providing a transceiver system901with performance information thereof. In this embodiment, the transceiver system901is a single-input single-output transceiver system under a multiuser diversity scheme, and includes a transmitter (Tx) and a number K (K>1) of receivers (Rx). The transceiver system901utilizes a modulation scheme, such as a binary phase-shift keying (BPSK) scheme, for conveying data. In practice, the transmitter (Tx) is a base station, and each of the receivers (Rx) is a cell phone of a user. For illustrative purpose, the transceiver system901includes three (K=3) of the receivers (Rx) inFIG. 2.

The transmitter (Tx) includes a transmit antenna (T1). Each of the receivers (Rx) includes a receive antenna (R1) and a channel estimator (R2). In this embodiment, the evaluation device100is operable to model a channel between the transmit antenna (T1) and the receive antenna (R1) of each of the receivers (Rx) using Nakagami distribution with an arbitrary positive fading parameter m.

The channel estimator (R2) of each of the receivers (Rx) is operable to provide the transmitter (Tx) with a transmission quality of the channel corresponding to each of the receivers (Rx). Then, according to the transmission quality, the transmitter (Tx) is operable to determine which one of the receivers (Rx) will be selected as a communication target, and to transmit a signal through the transmit antenna (T1) for transmission of the signal to the communication target. Then, the communication target is operable to receive the signal as a received signal through the receive antenna (R1) thereof. It should be noted that the communication target is one of the receivers (Rx) that demonstrates the greatest transmission quality with the transmitter (Tx).

When the fading parameter m of Nakagami distribution is greater than or equal to ½, a bit error rate of BPSK in the received signal may be calculated based upon Equation (1).

In Equation (1),Qis an average signal-to-noise ration (SNR) of the channel, Γ(z) is a Gamma function

(Γ⁡(z)=∫0∞⁢tz-1⁢ⅇ-t⁢⁢ⅆt)
for an arbitrary positive number z,

It could be appreciated from the foregoing that αnare a sequence of rapidly decreasing convergent numbers, that is to say, αn-1is much greater than αn. Therefore, when the average SNRQis much greater than 1, i.e., greater than a predetermined value, Equation (1) can be simplified as Equation (2). For the procedure of this simplification, one may refer to “A simple and general parameterization quantifying performance in fading channels,” Wang Z. et al.,IEEE Trans. Commun., August 2003, 51(8), pages 1389-1398.

When the fading parameter m of Nakagami distribution is a positive integer, the bit error rate of BPSK in the received signal may be calculated based upon Equation (3).

βn=1n⁢∑j=1min⁡(n,m-1)⁢[j⁡(i+1)-nj!·βn-j]
for a positive integer n, and

As shown inFIG. 2, in this embodiment, the evaluation device100is adapted for analyzing the received signal in the transceiver system901modeling the channels using the Nakagami distribution, and each of the channels has the same average SNRQ.

Referring toFIG. 3, the evaluation device100includes an SNR setting module1, an error rate computing module2coupled to the SNR setting module1, a threshold value computing module4, an outage probability computing module5coupled to the SNR setting module1and the threshold value computing module4, and an output module3coupled to the error rate computing module2and the outage probability computing module5.

The SNR setting module1is operable to set the average SNRQfor each of the channels between the transmitter (Tx) and the receivers (Rx) of the transceiver system901. The threshold value computing module4is operable to compute a threshold value λ based upon a given capacity R. The error rate computing module2is operable to compute the bit error rate PBERof the received signal based upon the fading parameter m, the average SNRQand the number K of the receivers (Rx). The outage probability computing module5is operable, based upon the fading parameter m, the number K of the receivers (Rx), the average SNRQand the threshold value λ, to compute an outage probability of the transceiver system901corresponding to the given capacity R. Then, the output module3is operable to provide the transceiver system901with the average SNRQ, the bit error rate PBERand the outage probability as the performance information of the transceiver system901.

FIG. 4shows a flow chart of an evaluation method implemented by the evaluation device100. The evaluation method includes the following steps.

In step71, the threshold value computing module4is operable to compute the threshold value λ based upon the given capacity R (λ=2R−1).

In step72, the SNR setting module1is operable to set each of the channels with the same average SNRQ.

In step73, the error rate computing module2is operable to compute the bit error rate PBERbased upon the fading parameter m, the average SNRQand the number K of the receivers (Rx).

In practice, the error rate computing module2is operable in advance to determine whether the fading parameter m is a positive integer. The error rate computing module2is operable to compute the bit error rate PBERbased upon Equation (3) when the determination is affirmative, and to compute the bit error rate PBERbased upon Equation (1) or (2) when otherwise. In particular, when the fading parameter m is not a positive integer, the error rate computing module2is operable to compute the bit error rate PBERbased upon Equation (2) if the average SNRQis greater than a predetermined value, and to compute the bit error rate PBERbased upon Equation (1) if the average SNRQis not greater than the predetermined value. Further, in practice, it is impractical to calculate the summation of the infinite series

(∑n=0∞)
in Equation (1). Therefore, the error rate computing module2is operable to compute a limited number of the series. In this embodiment, the error rate computing module2is operable to compute the series for n=0˜50 when computing the summation.

From Equations (1) to (3), it can be appreciated that the error rate computing module2computes the bit error rate PBERbased upon the average SNRQ, the fading parameter m, and the number K of the receivers (Rx). Certainly, in other embodiments, the error rate computing module2may be operable in advance to determine whether the fading parameter m is greater than or equal to ½, and to compute the bit error rate PBERbased upon Equation (1) or (2) when affirmative.

In step74, the outage probability computing module5is operable, based upon the fading parameter m, the number K of the receivers (Rx), the average SNRQand the threshold value λ, to compute the outage probability of the transceiver system901corresponding to the given capacity R.

For the procedure of the computation of the outage probability, one may refer to “Outage analysis of MIMO systems with multiuser diversity over Nakagami-m fading channels,” 2009Fundamental Academic Conference of R.O.C. Military Academy, pages EE.115-EE.124. Therefore, details of this computation will be omitted herein for the sake of brevity.

It should be noted that step74could be implemented before or simultaneously with step73in other embodiments.

In step75, the output module3is operable to determine whether there is an instruction of setting another average SNR. The flow goes back step72when the determination is affirmative, and goes to step75when otherwise.

In step76, the output module3is operable to provide the transceiver system901with the bit error rate PBERand the outage probability corresponding to each of the average SNRsQset in step72as the performance information of the transceiver system901.

TakingFIG. 5as an example, it is assumed that K=2 and m=0.7, and the bit error rates PBERcorresponding to the respective average SNRsQare computed based upon Equation (1). The symbols ◯ inFIG. 5represent the bit error rates PBERcomputed using the evaluation device100of this embodiment. It can be appreciated that the bit error rates PBERincrease with the average SNRsQ, that is to say, transmission error of the transceiver system901decreases and the performance thereof is relatively better.

Referring toFIG. 6, a second preferred embodiment of an evaluation device200of this invention is adapted for providing a transceiver system902with performance information thereof. The transceiver system902is a multiple-input multiple-output (MIMO) transceiver system under a multiuser diversity scheme, and includes a transmitter (Tx) and a number K (K>1) of receivers (Rx). The transceiver system902utilizes a modulation scheme similar to that of the first preferred embodiment (e.g., the BPSK scheme) for conveying data. In this embodiment, the transceiver system902utilizes a transmit selective combining/receive selective combining (SC/SC) scheme as an antenna scheme thereof. In practice, the transmitter (Tx) is a base station, and each of the receivers (Rx) is a cell phone of a user. For illustrative purpose, the transceiver system902includes three (K=3) of the receivers (Rx) inFIG. 6.

The transmitter (Tx) includes a number LT(LT>1) of transmit antennas (T1), and a diversity unit (T2). Each of the receivers (Rx) includes a number LR(LR>1) of receive antennas (R1), a synthesis unit (R3), and a channel estimator (R2). In this embodiment, the evaluation device200is operable to model channels between the transmit antennas (T1) and the receive antennas (R1) using Nakagami distribution with an arbitrary positive fading parameter m.

In such a SC/SC scheme, there are a number LT×LRof possible channels for each of the receivers (Rx), and each of the channels is defined by one of the transmit antennas (T1) and one of the receive antennas (R1). The channel estimator (R2) of each of the receivers (Rx) is operable to provide the transmitter (Tx) with transmission qualities of the possible channels corresponding to each of the receivers (Rx). Then, according to the transmission qualities, the diversity unit (T2) of the transmitter (Tx) is operable to determine which one of the receivers (Rx) will be selected as a communication target, and to determine which one of the transmit antennas (T1) will be used to transmit signals. The diversity unit (T2) is further operable to transmit the signals to a selected one of the transmit antennas (T1) for transmission of the signals to the communication target. It should be noted that the communication target is one of the receivers (Rx) that demonstrates the greatest transmission quality with the transmitter (Tx), and the selected one of the transmit antennas (T1) is capable of reaching such transmission quality.

After the selected one of the receivers (Rx), which is selected as the communication target, receives the signals from the transmitter (Tx) through the receive antennas (R1) thereof, the signals are transmitted to the synthesis unit (R3) of the selected one of the receivers (Rx). The synthesis unit (R3) is operable to select one of the signals received by the receive antennas (R1) for analysis.

When the fading parameter m of Nakagami distribution is greater than or equal to ½, the bit error rate of BPSK in the selected one of the signals received by the receive antennas (R1) may be calculated based upon Equation (4).

In Equation (4),

It could be appreciated from the foregoing that αnare a sequence of rapidly decreasing convergent numbers, that is to say, αn-1is much greater than αn. Therefore, when the average SNRQis much greater than 1, i.e., greater than a predetermined value, Equation (4) can be simplified as Equation (5). For the procedure of this simplification, one may refer to “A simple and general parameterization quantifying performance in fading channels,” Wang Z. et al.,IEEE Trans. Commun., August 2003, 51(8), pages 1389-1398.

When the fading parameter m of Nakagami distribution is a positive integer, the bit error rate of BPSK in the selected one of the signals received by the receive antennas (R1) may be calculated based upon Equation (6).

βn=1n⁢∑j=1min⁡(n,m-1)⁢[j⁡(i+1)-nj!·βn-j]
for a positive integer n, and

The second preferred embodiment of the evaluation device200of this invention has a configuration similar to that of the first preferred embodiment, and also includes the SNR setting module1, the error rate computing module2, the output module3, the threshold value computing module4and the outage probability computing module5shown inFIG. 3. Operations of the modules of the evaluation device200in this embodiment are also similar to those of the first preferred embodiment.

In this embodiment, the error rate computing module2is operable, in step73of the flow chart shown inFIG. 4, to compute the bit error rate PBERbased upon the fading parameter m, the average SNRQ, the number LTof the transmit antennas (T1), the number LRof the receive antennas (R1), and the number K of the receivers (Rx).

In practice, the error rate computing module2is operable in advance to determine whether the fading parameter m is a positive integer. The error rate computing module2is operable to compute the bit error rate PBERbased upon Equation (6) when the determination is affirmative, and to compute the bit error rate PBERbased upon Equation (4) or (5) when otherwise.

Certainly, in other embodiments, the error rate computing module2may be operable in advance to determine whether the fading parameter m is greater than or equal to ½, and to compute the bit error rate PBERbased upon Equation (4) or (5) when affirmative.

In particular, when the fading parameter m is not a positive integer, the error rate computing module2is operable to compute the bit error rate PBERbased upon Equation (5) if the average SNRQis greater than a predetermined value, and to compute the bit error rate PBERbased upon Equation (4) if the average SNRQis not greater than the predetermined value. Further, in practice, it is impractical to calculate the summation of the infinite series

(∑n=0∞)
in Equation (4). Therefore, the error rate computing module2is operable to compute a limited number of the series. In this embodiment, the error rate computing module2is operable to compute the series for n=0˜50 when computing the summation.

As an example, when it is assumed that LT=1, LR=4, K=2 and m=0.7, the bit error rates PBERcorresponding to the respective average SNRsQmay be computed based upon Equation (4) represented by the symbols □ inFIG. 5. The information of the symbols □ could serve as the performance information of the transceiver system902in step76of the flow chart shown inFIG. 4.

Referring once again toFIG. 6, a third preferred embodiment of an evaluation device300of this invention has a configuration similar to that of the second preferred embodiment, and is adapted for providing the MIMO transceiver system902with the performance information thereof. In this embodiment, the transceiver system902utilizes a transmit selective combining/receive maximum ratio combining (SC/MRC) scheme as an antenna scheme thereof.

In such a SC/MRC scheme, the channel estimator (R2) of each of the receivers (Rx) is operable to provide the transmitter (Tx) with transmission qualities of the possible channels corresponding to each of the receivers (Rx). Then, according to the transmission qualities, the diversity unit (T2) of the transmitter (Tx) is operable to determine which one of the receivers (Rx) will be selected as the communication target, and to determine which one of the transmit antennas (T1) will be used to transmit signals. The diversity unit (T2) is further operable to transmit the signals to a selected one of the transmit antennas (T1) for transmission of the signals to the communication target.

After the selected one of the receivers (Rx), which is selected as the communication target, receives the signals from the transmitter (Tx) through the receive antennas (R1) thereof, the signals are transmitted to the synthesis unit (R3) of the selected one of the receivers (Rx). According to the transmission qualities of the channels between the selected one of the transmit antennas (T1) and the receive antennas (R1), the synthesis unit (R3) is operable to weight the signals received by the receive antennas (R1) so as to obtain a synthesized signal.

When the fading parameter m of Nakagami distribution is greater than or equal to ½, the bit error rate of BPSK in the synthesized signal may be calculated based upon Equation (7).

In Equation (7),

Similar to the foregoing description in connection with the second preferred embodiment, Equation (7) can be simplified as Equation (8) when the average SNRQis much greater than 1, i.e., greater than a predetermined value.

When the fading parameter m of Nakagami distribution is a positive integer, the bit error rate of BPSK in the synthesized signal may be calculated based upon Equation (9).

βn=1n⁢∑j=1min⁡(n,m⁢⁢LR-1)⁢[j⁡(i+1)-nj!·βn-j]
for a positive integer n, and

The third preferred embodiment of the evaluation device300of this invention has a configuration similar to that of the first preferred embodiment, and also includes the SNR setting module1, the error rate computing module2, the output module3, the threshold value computing module4and the outage probability computing module5shown inFIG. 3. Operations of the modules of the evaluation device300in this embodiment are also similar to those the first preferred embodiment.

In this embodiment, the error rate computing module2is operable, in step73of the flow chart shown inFIG. 4, to compute the bit error rate PBERbased upon the fading parameter m, the average SNRQ, the number LTof the transmit antennas (T1), the number LRof the receive antennas (R1), and the number K of the receivers (Rx).

In practice, the error rate computing module2is operable in advance to determine whether the fading parameter m is a positive integer. The error rate computing module2is operable to compute the bit error rate PBERbased upon Equation (9) when the determination is affirmative, and to compute the bit error rate PBERbased upon Equation (7) or (8) when otherwise.

Certainly, in other embodiments, the error rate computing module2may be operable in advance to determine whether the fading parameter m is greater than or equal to ½, and to compute the bit error rate PBERbased upon Equation (7) or (8) when affirmative.

In particular, when the fading parameter m is not a positive integer, the error rate computing module2is operable to compute the bit error rate PBERbased upon Equation (8) if the average SNRQis greater than a predetermined value, and to compute the bit error rate PBERbased upon Equation (7) if the average SNRQis not greater than the predetermined value. Further, in practice, it is impractical to calculate the summation of the infinite series

(∑n=0∞)
in Equation (7). Therefore, the error rate computing module2is operable to compute a limited number of the series. In this embodiment, the error rate computing module2is operable to compute the series for n=0˜50 when computing the summation.

As an example, when it is assumed that LT=1, LR=4, K=2 and m=0.7, the bit error rates PBERcorresponding to the respective average SNRsQmay be computed based upon Equation (7) represented by the symbols ∇ inFIG. 5. The information of the symbols ∇ could serve as the performance information of the transceiver system902in step76of the flow chart shown inFIG. 4.

Referring again toFIG. 6, a fourth preferred embodiment of an evaluation device400of this invention has a configuration similar to that of the second preferred embodiment, and is adapted for providing the MIMO transceiver system902with the performance information thereof. In this embodiment, the transceiver system902utilizes a space-time block codes (STBC) scheme as an antenna scheme thereof.

In such a STBC scheme, the channel estimator (R2) of each of the receivers (Rx) is operable to provide the transmitter (Tx) with transmission qualities of the possible channels corresponding to each of the receivers (Rx). Then, according to the transmission qualities, the diversity unit (T2) of the transmitter (Tx) is operable to determine which one of the receivers (Rx) will be selected as the communication target. The diversity unit (T2) is further operable to encode a to-be-transmitted signal using space-time block coding, and to transmit the coded signal to the communication target through each of the transmit antennas (T1).

After the selected one of the receivers (Rx), which is selected as the communication target, receives the coded signals from the transmitter (Tx) through the receive antennas (R1) thereof, the coded signals are transmitted to the synthesis unit (R3) of the selected one of the receivers (Rx). Then, the synthesis unit (R3) is operable to decode the coded signals received by the receive antennas (R1) so as to obtain a decoded signal. Since the space-time block coding/decoding is well known to those skilled in the art, details thereof will be omitted herein for the sake of brevity.

When the fading parameter m of Nakagami distribution is greater than or equal to ½, the bit error rate of BPSK in the decoded signal may be calculated based upon Equation (10).

In Equation (10),

Similar to the foregoing description in connection with the second preferred embodiment, Equation (10) can be simplified as Equation (11) when the average SNRQis much greater than 1, i.e., greater than a predetermined value.

When the fading parameter m of Nakagami distribution is a positive integer, the bit error rate of BPSK in the decoded signal may be calculated based upon Equation (12).

In Equation (12),

βn=1n⁢∑j=1min⁡(n,mLT⁢LR-1)⁢⁢[j⁡(i+1)-nj!·βn-j]
for a positive integer n.

The fourth preferred embodiment of the evaluation device400of this invention has a configuration similar to that of the first preferred embodiment, and also includes the SNR setting module1, the error rate computing module2, the output module3, the threshold value computing module4and the outage probability computing module5shown inFIG. 3. Operations of the modules of the evaluation device400in this embodiment are also similar to those of the first preferred embodiment.

In this embodiment, the error rate computing module2is operable, in step73of the flow chart shown inFIG. 4, to compute the bit error rate PBERbased upon the fading parameter m, the average SNRQ, the number LTof the transmit antennas (T1), the number LRof the receive antennas (R1), and the number K of the receivers (Rx).

In practice, the error rate computing module2is operable in advance to determine whether the fading parameter m is a positive integer. The error rate computing module2is operable to compute the bit error rate PBERbased upon Equation (12) when the determination is affirmative, and to compute the bit error rate PBERbased upon Equation (10) or (11) when otherwise.

Certainly, in other embodiments, the error rate computing module2may be operable in advance to determine whether the fading parameter m is greater than or equal to ½, and to compute the bit error rate PBERbased upon Equation (10) or (11) when affirmative.

In particular, when the fading parameter m is not a positive integer, the error rate computing module2is operable to compute the bit error rate PBERbased upon Equation (11) if the average SNRQis greater than a predetermined value, and to compute the bit error rate PBERbased upon Equation (10) if the average SNRQis not greater than the predetermined value. Further, in practice, it is impractical to calculate the summation of the infinite series

(∑n=0∞⁢)
in Equation (10). Therefore, the error rate computing module2is operable to compute a limited number of the series. In this embodiment, the error rate computing module2is operable to compute the series for n=0˜50 when computing the summation.

As an example, when it is assumed that LT=1, LR=4, K=2 and m=0.7, the bit error rates PBERcorresponding to the respective average SNRsQmay be computed based upon Equation (10) represented by the symbols ⋄ inFIG. 5. The information of the symbols ⋄ could serve as the performance information of the transceiver system902in step76of the flow chart shown inFIG. 4.

In the disclosed embodiments, the output module3is operable to provide the transceiver system901,902with the bit error rate PBERand the outage probability corresponding to each of the average SNRsQset in step72as the performance information of the transceiver system901,902. However, in other embodiments, the output module3may be operable to provide only the bit error rate PBERcorresponding to each of the average SNRsQ, or only the outage probability corresponding to each of the average SNRsQas the performance information. Further, Equations (1) to (12) are still practical when the number of the receivers (Rx) is equal to 1 (K=1).

In conclusion, the fading parameter m of Nakagami channels is not limited to a positive integer in the present invention. The error rate computing module2is capable of computing the bit error rate PBERwith the fading parameter m that is an arbitrary positive integer, or that is equal to or greater than ½. Therefore, the evaluation device according to this invention is suitable for simulation of the channels of the transceiver system with various fading levels in a metropolis. Therefore, the evaluation device according to the present invention is suitable for simulating the performance of the transceiver system in a metropolis.