Open Access

Experimental Investigation of Cooperative Schemes on a Real-Time DSP-Based Testbed

  • Per Zetterberg1Email author,
  • Christos Mavrokefalidis2,
  • Aris S. Lalos2 and
  • Emmanouil Matigakis3
EURASIP Journal on Wireless Communications and Networking20092009:368752

DOI: 10.1155/2009/368752

Received: 9 November 2008

Accepted: 31 March 2009

Published: 19 May 2009

Abstract

Experimental results on the well-known cooperating relaying schemes, amplify-and-forward (AF), detect-and-forward (DF), cooperative maximum ratio combining (CMRC), and distributed space-time coding (DSTC), are presented in this paper. A novel relaying scheme named "selection relaying" (SR), in which one of two relays are selected base on path-loss, is also tested. For all schemes except AF receive antenna diversity is as an option which can be switched on or off. For DF and DSTC a feature "selective" where the relay only forwards frames with a receive SNR above 6 dB is introduced. In our measurements, all cooperative relaying schemes above increase the coverage area as compared with direct transmission. The features "antenna diversity" and "selective" improve the performance. Good performance is obtained with CMRC, DSTC, and SR.

1. Introduction

MULTIPATH fading is one of the major obstacles for the next generation wireless networks, which require high bandwidth efficiency services. Time, frequency, and spatial diversity techniques are used to mitigate the fading phenomenon [1]. Recently, cooperative communications for wireless networks have gained much interest due to its ability to mitigate fading in wireless networks through achieving spatial diversity, while resolving the difficulties of installing multiple antennas on small communication terminals. In cooperative communication, a number of relay nodes are assigned to help a source in forwarding its information to its destination, hence forming a virtual antenna array.

Various cooperative protocols have been proposed and analysed in the literature. In [2], Laneman et al. proposed two cooperative protocols: the amplify-and-forward (AF) protocol and the decode-and-forward (DF) protocol, where the relays would either purely amplify and retransmit the information to the destination, or decode the information first and then transmit these information bits to the destination. In [3], Anghel and Kaveh showed that the conventional maximum ratio combining (MRC) was the optimum detection scheme at the destination for the AF and it could achieve the full diversity order of , where is the number of relays. When it comes to the DF, the optimum maximum likelihood (ML) detector was proposed in [4, 5]. Furthermore, many suboptimum detection schemes have been proposed, including the -MRC [4, 6], the simple adaptive decode-and-forward scheme [7], the cooperative MRC (CMRC) [8], and the link-adaptive regeneration (LAR) [9]. Recently, many works have been devoted to improve the bandwidth efficiency of cooperative networks, including the distributed space-time codes [10] and the relay selection [11, 12]. Among those techniques, the relay selection is very attractive. The basic idea is to let the relay with the best channel condition relay the signals. Since only one relay is working at each time slot, a very strict time and carrier synchronisation among the relays is not needed. Furthermore, because the transmission of one information-bearing symbol is completed within two-time slots, the relay selection has higher bandwidth efficiency than the repetition-based cooperative strategy.

In [13] the authors implement a cooperative coding scheme [14]. The scheme is compared with a traditional noncooperative one while transmitting frames of a video clip. From the experiments, it is observed that cooperation increases the quality of the video clip. In [15], the authors perform detailed simulations of two variations of the decode-and-forward protocol [4, 16] using low-density parity check (LDPC) codes, and a direct transmission scheme. It is concluded that the cooperative schemes outperform the direct transmission. Most of the implementation work that has appeared in literature focus on implementing variations of a single protocol. Herein, we are presenting an experimental investigation of several cooperation schemes, some of which are sophisticated. We also put focus on presenting quantitative results and measurements in a relevant propagation environment.

Specifically, in this work we have implemented the well-known AF, DF, and CMRC protocols, where the signal received at the destination is combined according to the MRC detection rule. Furthermore we provide experimental results for some more techniques that have been recently proposed, including a DSTC scheme based on the Alamouti coding and a novel relay selection scheme. The implementations are made on a real-time DSP-based testbed. Finally, in the experiments, we compare the performance of the implemented schemes in terms of outage probability, complexity and a novel "implementation loss'' measure.

The paper is organised as follows. The implementation of the schemes is described in Section 2 of this paper. The experimental results are described in Section 3. The results show that, compared with direct transmission, the proposed cooperative schemes increase coverage. By means of "implementation loss'' analysis we show that the results are fairly close to the theoretical results. A more full discussion of the conclusions drawn are given in Section 4.

2. The Implementations

The testbed consists of four nodes, where each node has two antennas, two transmitters, and two receiver chains, a DSP board for processing, and a laptop PC for control. The symbol- and sample-rate used are 9600 Hz and 48 kHz, respectively. A picture of a node is shown in Figure 1 and a schematic is shown in Figure 2. As shown in Figure 2, the base-band processing is made on the DSK6713 board, which is a DSP board provided by Texas Instruments. The A/D and D/A converters receive and transmit a signal with 10 kHz carrier frequency. The up- and donwnconversion between RF (1766.6 MHz) and base-band is done in the transmitter (TXM) and receiver modules (RXM), respectively. More information about the hardware and software are given in [17, 18]. The system uses sharp crystal filters in both the transmitter and the receiver. This confines the transmit bandwidth to 9600 Hz with little leakage outside this bandwidth. However, these filers introduce intersymbol interference. The intersymbol interference is 15–20 dB weaker than the desired signal. This is negligible for QPSK but degrades the performance for higher-order constellations. In this paper only QPSK modulation is used.
Figure 1

Picture of a node.

Figure 2

Schematic of a node. The acronyms are RF-switch (SW), power amplifier (PA), transmitter module (TXM), receiver module (RXM), and general purpose input/output (GPIO).

The nodes act as source, relay, destination, base-station, or mobile-station in the implementations herein. One of the nodes is called the master. This node sends out a synchronisation signal which is detected by the other nodes. A sinusoid follows the synchronisation sequence enabling the other nodes to adjust their up- and downconversion frequencies. These synchronisation sequences are sent at a power level of 10 dBm while the actual data is sent at a power level of  dBm. The synchronisation is rough and gives a remaining error of one sample. The master can be any of the nodes. In our measurements the source is usually the master. However, in a few measurements the source could not be used since the path-loss to the destination was too high. In this case, relay 2 was instead used as the master.

The power level used for transmitting payload data is  dBm. This results in a transmitted power spectral density of  dBm/kHz. This is comparable to what can be expected to be the case in future wireless LAN-type applications which may use 20 dBm transmit power over a 100 MHz bandwidth, which also gives  dBm/kHz power spectral density. The higher power used for synchronisation can be motivated by the fact that when a wideband system is synchronized all the available power can be used for this purpose, while payload data would be transmitted on multiple subcarriers using only a fraction of the total available power used for a given subcarrier.

The residual synchronisation error of one sample has to be accounted for. This is done differently for different schemes and this is described in more details below.

There is a delay of typically 58 samples between the transmitter and the receiver. This delay is due to digital antialias filters in the D/A and A/D converters and (but to a less extent) delays in the analog hardware. This delay is taken into account by letting the transmitting frames be scheduled 12 symbols (which correspond to 60 samples) before the corresponding receive frames. These delays lead to a nonnegligible overhead when switching between transmit and receive mode. The delay could be brought down to 4 symbols if the antialias filters of the D/A and A/D converters were removed. Unfortunately, we were not able to do this. However, in the throughput figures, we account for this delay as 4 symbols instead of 12, to show a result that better reflects the performance if this small practical issue could be resolved.

There is also a problem when a node transmits and then starts to receive directly following the transmission. This leads to six symbols being interfered by transients from the powering down of the transmitter. This problem should be solvable with a better hardware design. Therefore, we do not take these six symbols into account when calculating the throughput.

2.1. Amplify-and-Forward (AF), Detect-and-Forward (DF), and Cooperative Maximum Ratio Combing (C-MRC)

Before transmitting the useful data a synchronisation phase is executed to reduce the residual synchronisation error of one sample as described above. In the synchronisation phase the source first sends a frame with training symbols only, a frame which is captured by the relay and destination and used to estimate the best sampling phase of the source signal. After receiving the training signal from the source, the relay sends a training signal so that the destination can be synchronised. Twelve symbols are used to achieve the synchronisation at the power level  dBm.

After the synchronisation phase, the frame structure used for transfer of payload data starts. The frame structure of the AF scheme is shown in Figure 3.
Figure 3

Frame structure of AF and DF schemes.

The notation TX48 means that the node is transmitting a buffer of 48 symbols, while RX48 means that the node is receiving a buffer of 48 symbols. Idle is a period of 12 symbols where the node does not receive or transmit. However, processing of previously received signals does occur during idle slots. The buffers which are marked with the number 6 are also idle buffers of length 6 symbols. Hardware considerations made these extra idle slots necessary, see the introduction aforementioned. Note also that the transmit frames and the corresponding receive frames are offset 12 symbols due to the delay of 58 samples between the transmitter and receiver, as mentioned previously. The arrow indicates where the frame structure is repeated. In the measurements, five repeats are executed but in principle any number of repeats is possible.

During the fourth and fifth frames (with reference to Figure 3) the relay does the processing of the signal that was captured during the previous frame. In the case of AF, the processing consists of downsampling the signal to symbol rate. This signal is then scaled so that the maximum sample has an amplitude which equals the maximum amplitude that the transmitter allows. This leads to a power back-off compared to the other schemes investigated herein, as they transmit all symbols at maximum power level.

The scaled signal is transmitted during the fifth and sixth frames (with reference to Figure 3). Then, an idle period of 18 symbols follows, so that the relay aligns itself with the next two bursts from the source. Optionally, the relay can decode the received symbol sequence for debugging purposes.

The destination also remains idle for a period of 12 symbols while the source transmits. During the next two frames, the destination captures the signal from the source. Then, it remains idle for a period of 12 symbols to compensate for the delay in the relay-to-destination chain. Then, during the next two frames, it receives the signal transmitted by the relay. During the seventh and eighth frame (with reference to Figure 3) the destination combines the signals received from the source and relay. The criterion for selecting the th symbol from the th sample of the source-to-destination and relay-to-destination channels, that is, and , respectively, is given by

(1)
where is modulation constellation, and are the source-to-destination and relay-to-destination channels, and and are the receiver weights. The combining is based on the maximum ratio combining principle, see [1], which means that the weights are given by
(2)

Every burst of symbols carrying payload data is 48-symbol long. Every eight symbols, a training symbol is inserted which is used for channel and noise estimation at the receiver. The modulation constellation used is QPSK.

The detect-and-forward (DF) scheme is similar to the AF scheme, with the difference that the relay detects the transmitted symbols and then retransmits the sequence of detected symbols. Thus, if there is no error in the detection, the transmitted signal will be perfect, which is not the case with AF.

The so-called cooperative maximum ratio combining (CMRC) scheme is similar to DF with the difference that the relay estimates its received SNR and encodes that information so that the destination learns the receive SNR at the relay. This enables the destination to (partially) compensate for erroneous decisions that may have been made at the relay, see [19]. The compensation is made by reducing the influence of the relay-to-destination channel in the criterion (1) by scaling the relay-to-destination weight as
(3)
where . The optimum choice of (in terms of BER) is derived in [19]. The optimum is a rather complex function of and . We chose to approximate this expression with
(4)

which is an approximation of the optimal at high SNR.

In our implementation of CMRC we used two symbols to encode the SNR. Of the four available bits, two are used for actually encoding the SNR and the other two constitute a redundancy check. The relay first estimates the SNR based on the training sequence. The encoding is then done so that if the SNR of signal received at the relay is below 3 (in linear scale) the two bits are set as "00". If the SNR is in the range 3–9, 9–27, or larger than 27, the SNR two bits are set as "01", "10" and "11", respectively. The two redundancy bits are set as the complement of the first two bits. At the destination, the SNR of the source-relay path is assumed to be zero if the redundancy check fails. Otherwise, the low-end value of the SNR range is assumed. We set to be the minimum of the source-relay and relay-destination SNRs, as is defined in (4).

In an attempt to improve on DF, primarily to prevent the forwarding of erroneously detected bits, a "selective" feature is introduced. Thus if the source-relay SNR is below 4 (in linear scale), the relay stays silent during the slots allocated for forwarding. This is a selectable feature. In Section 3 we will present results for both switched on and switched off mode.

Another selectable option, antenna diversity, was also introduced. When switched on, the received signal from two antennas is combined by means of MRC at the relay and at the destination. However, this approach was only implemented for the DF and CMRC schemes and not for AF.

Assuming that the frame-structure of Figure 3 is repeated many times, the overhead due to the extra frames needed for synchronisation is negligible. Assuming further that the idle frames can be shortened, as suggested previously, the "duty cycle" of AF and DF is 43%. This means that 43% of the symbols received at the destination contains useful unique data. This number includes overhead due to the training sequence.

The CMRC approach has a slightly lower duty cycle of 41% due to the overhead incurred by transmitting the source-relay SNR.

We have also implemented a "direct" transmission mode, where no relaying occurs. This mode uses the same air interface, that is, 48-symbol long frames with six training symbols and QPSK modulation. This scheme has a duty cycle of 87%, since the only overhead incurred comes from training symbols.

2.2. Distributed Space-Time Coding (DSTC)

In the synchronisation phase of the DSTC scheme the source node sends a frame with training symbols that is captured by the two relays and the destination, and used to estimate the best sampling offset of the source signal. After receiving the training signal from the source, the relays take turns sending a training signal to the destination. The destination estimates the best sampling offset for each relay from the training signal. At this stage something happens which does not occur in the other approaches. In the other approaches the sampling offset can be taken into account at the receiver. But in DSTC the two relays are transmitting simultaneously, and a single offset at the receiver may thus not fit both relays. Therefore, in the case of DSTC the compensation is instead done at the transmitter. Hence, the relays adjust the timing of their outgoing frames one sample backward or forward (or no adjustment). In order to let the relays know in which direction to adjust their timing, this information is fed back from the destination to the relays in a special frame.

After having achieved synchronisation, the signalling goes into the frame structure indicated in Figure 4 one that is identical to the frame-structure of AF, DF, and CMRC except that the two relays are transmitting at the same time.
Figure 4

Frame structure of DSTC scheme.

After capturing the signal from the source and storing it in a buffer, the relays downsample the sequence to get symbol-spaced samples. Then, the channel is estimated and the symbol sequence is detected. The next step is to create the Alamouti code sequence. Each relay plays the role of one antenna in the conventional Alamouti diversity, [20], so each relay creates a different sequence.

The destination does not use the signal which comes directly from the source. During the sixth and seventh frame (with respect to Figure 4), the destination captures the signal from the relays.

In Alamouti coding every pair of symbols , is mapped onto two consecutive outgoing symbols as , at relay 1 and , at relay 2. The signal received at the destination in two consecutive symbols, and , then becomes
(5)

where and are the channel coefficients associated with relay 1 and 2, respectively, and and are noise samples.

With and known, and are detected based on and which are obtained as
(6)
(7)

respectively. In order to obtain and , symbols with number 7, 8, 15, 16, 23, 24, 31, 32, 39, 40, 47, 48 are used for channel estimation (the frames have 48 symbols). The equations for obtaining a channel estimate from two consecutive training symbols are given in Appendix A.

As in the case of DF, the two options "selective" and "antenna diversity" exist. When the selective option is switched on the relays are silent if the SNR is less than 4. When the antenna diversity option is switched on the signals received from both antenna branches are combined in the relays as well as in the destination. The combining scheme used is maximum ratio combining.

The duty cycle of DSTC is 36% which is somewhat lower than for DF, as more symbols are used for channel estimation.

2.3. Selection Relaying (SR)

As in the DSTC case, two relays are used. The frame structure has three phases which are illustrated in Figures 5 and 6.
Figure 5

The three-phase transmission of the cooperative system. In Phase 1, S transmits to the other nodes. In Phase 2, the best relay is decided. Finally, in Phase 3, the best relay (e.g., R1) transmits to D.Phase 1 Phase 2 Phase 3

Figure 6

Frame definition.

In the first phase the source sends information to the two relays and the destination. The relays calculate the average signal to noise ratio ( , where ) over all the payload frames of the first phase. In the second phase, the relays send their ASNR values to the destination in signalling frames. The destination estimates the signal to noise ratios of the two relay-to-destination links directly from the signalling frames ( , where ). Using this information, the destination decides which relay has a better overall source-relay-destination channel. The destination informs the relays about which relay is going to be active in the third phase. The format of the frames used in Phase 2 are shown in Figures 7(a) and 7(b). In the third phase the selected relay retransmits the information detected from the source in the first phase. Note that while Figure 6 shows five payload frames being transmitted in the first and third phase. This number is actually increased to ten during the measurements presented in Section 3.
Figure 7

The transmit frame structures used in phase 2. Frame structure 1Frame structure 2

During the second phase, the integrity of the frames used for signalling is checked by estimating the SNR of the frames based on their training sequences. If the SNR is lower than 4 (in linear scale), then the frame is assumed to be in error. The corresponding relay will then not be eligible for transmission in the third phase. Likewise, the relays will not transmit if the frame sent from the destination to the relays during the second phase has an SNR of less than 4. The destination will not use either of the two relays if the frames received from both relays in the second phase are in error. If both frames are received correctly, then the following criterion is used for relay selection
(8)

The ASNR and SNR values used in the criterion (8) for selection of the best relay are estimated differently from all other SNR values used in the cooperative schemes. The difference lies in the way the noise is estimated. In the case of the ASNR and SNR values in (8) the noise is estimated in an initial frame which is sent before the execution of Phase 1, Phase 2, and Phase 3, and where there is no other transmission. In the other cases, the noise is estimated as the difference between the received signal samples and the signal obtained by multiplying the estimated channel with the training symbols. A detailed description of the procedure used for estimating and sending the SNR and ASNR values of (8) is given in Appendix B.

The relay usage is reduced by 50% compared with DSTC as only one relay out of two is chosen. The idea behind the scheme is that channel variations are composed of short-term variations, due to Doppler fading, and long-term variations, due to obstacles between the nodes and obstructions, for example, walls. With the proposed scheme we should be able to select the best relay when the difference in channel conditions between the two relays is large because of the long-term properties, even though time delays may somewhat alter the propagation conditions between the moment of selection and use.

The careful reader may have noticed that we have not started with a synchronisation phase as in the other approaches described above. Instead, synchronisation is done by embedding known training symbols in the first frame of Phase 1, in all the frames sent during Phase 2, and in the first frame sent during Phase 3 (in the last case indirectly since it relays the data sent from the source). Regarding the first frame in Phase 1 and Phase 3, we treat it as known data when we synchronise, while we assume the data to be unknown during the detection (the data is not used for channel estimation though), and therefore we can calculate the BER also based on this data. When we calculate the duty cycle we assume that these symbols were actually carrying payload data. The results should be the same as in a case where synchronisation had occurred in a dedicated synchronisation phase.

The air interface employed for payload data is the same as for AF and DF, that is, 48 symbols, where every eight symbol is training. The duty cycle is 40% where the overhead of Phase 2 is included, but where we have assumed that the delay from the transmitter to the receiver is reduced from the actual value of 12 symbols down to 4 symbols. There is room for reducing the overhead of phase 2 by shortening the control frames and by slight modifications of the scheme. Since there is a possibility for the destination to select neither of the two relays, it would be possible to skip phase 3 if this information can be relayed to the source. This was however never implemented.

As in all the other approaches (except AF) there is an antenna diversity option where the signals from the two antenna branches are combined by MRC at the relay and the destination.

3. Measurement Results

A measurement campaign was conducted in an indoor office environment (see Figures 10 and 11). In the campaign a source (S), two relays (R1, R2), and a destination (D) were used, although relay R2 is only in DSTC and SR. Some of the positions of these nodes during the measurements are illustrated in Figure 12.

In order to be able to compare all five schemes with different options, a measurement procedure consisting of "measurement runs" was developed. Within each measurement run twenty-four different configurations were run in sequence. In Table 1 below we list the sequence of configurations in one measurement run. The reader may note that some configurations are identical. Each measurement run was conducted under stationary conditions, that is, there were no people moving on the floor plan and the source, the relays and the destination were all standing still. This is not a requirement for the schemes to work but it makes it more likely that the schemes see the same propagation channels. The fact that some configurations in one measurement run are identical can be used to verify the similarity of the channel conditions under which the different configurations are tested. A total of 47 measurement runs were conducted. The positions of the two relays and the destination were changed before every run.
Table 1

List of configurations in one measurement run.

Configuration

Scheme

Antenna diversity

Selective option

1

Direct

No

No

2

AF

No

No

3

DF

No

No

4

CMRC

No

No

5

DSTC

No

No

6

SR

No

No

7

Direct

Yes

No

8

AF

No

No

9

DF

Yes

No

10

CMRC

Yes

No

11

DSTC

Yes

No

12

SR

Yes

No

13

Direct

No

No

14

AF

No

No

15

DF

No

Yes

16

CMRC

No

No

17

DSTC

No

Yes

18

SR

No

No

19

Direct

Yes

No

20

AF

No

No

21

DF

Yes

Yes

22

CMRC

Yes

No

23

DSTC

Yes

Yes

24

SR

Yes

No

Each scheme transmitted ten payload frames of 48 symbols. The channel estimates obtained during these frames were saved and made available for postprocessing. We also calculate the bit error rate (BER) and the number of clock-cycles used by the DSPs. In addition to these metrics, some scheme specific results are also measured. The noise level was measured and found to be very similar on all antenna branches of all the nodes. In Figures 8 and 9 the cumulative distribution of the SNR of all propagation paths that are involved in the schemes is shown (the SNR is calculated by dividing the channel estimate level with the noise level of the receiver in question). The curves show that the relay 2 generally has a better channel to the source while relay 1 has better channel to the destination. The worst channel is that between the source and the destination. It can also be noted that the SNRs are very low which represents challenging conditions.
Figure 8

Cumulative distribution of the SNR of the channel between the source and the relays.

Figure 9

Cumulative distribution of the SNR of the channels to the destination.

Figure 10

Node inside office.

Figure 11

Node in corridor.

Figure 12

Some of the positions of the nodes used during the measurements. S = source, R1 = relay 1, R2 = relay 2, D = destination.

In Section 3.1 we do a straightforward analysis of the measurement results at hand while in Section 3.2 we do an analysis which provides more insight and is less dependent on the scenario chosen.

3.1. Straightforward Comparison

The most straightforward way of comparing the different schemes is to look at the bit error rate statistics over the 47-measurement runs. In Table 2 we show the "outage probability". We define this probability as the fraction of frames which have at least one bit in error. In order to make a fair comparison of the direct scheme, which has a duty cycle of about two times that of the other schemes, we assume that the direct scheme repeats every frame two times and that the receiver is able to determine which of the two copies of the same frame has the least number of bit errors (this reduces outage probability from 74% to 70%).
Table 2

Outage probability: the percentage of frames with one bit error or more. The notation (A) indicates that antenna diversity is switched on, while (S) indicates that the selective feature is used.

Direct

70

62 (A)

71

64 (A)

AF

57

56

57

57

DF

61

52 (A)

54 (S)

49 (A,S)

CMRC

53

42 (A)

52

43 (A)

DSTC

53

34 (A)

38 (S)

26 (A,S)

SR

34

23 (A)

36

26 (A)

As may be noticed, some of the configurations are actually identical. For instance, the second row of Table 2 shows the results for AF repeated four times. However, they correspond to different measurement time slots in the sequence of Table 1. The difference between multiple values for the same configuration is in the range 0–3%. This shows that the relative comparisons between the different configurations based on Table 2 are meaningful. We may immediately conclude that the features "selective" and "antenna diversity" consistently improve the performance. The performance of CMRC is better than that of AF. The performance of DF and CMRC is similar if the "selective" feature is switched on. Likewise, the performances of DSTC and SR are very similar, again assuming the "selective" feature is switched on. Table 3 shows the probability of a BER higher than 5%, that is, we allow a few bit errors in each frame. Under this criterion, the performance of AF is better than the performance of DF and CMRC.
Table 3

Outage probability: the percentage of frames with 5% bit errors or more. The notation (A) indicates that antenna diversity is switched on, while (S) indicates that the selective feature is used.

Direct

64

51 (A)

64

53 (A)

AF

39

37

35

36

DF

47

38 (A)

41 (S)

31 (A,S)

CMRC

46

32 (A)

43

29 (A)

DSTC

42

25 (A)

26 (S)

15 (A,S)

SR

25

14 (A)

28

15 (A)

The comparison in this section can be criticised for being highly dependent on the selection of positions for the source, relays, and destination. Therefore, we analyse the performance in terms of "implementation loss" in the next section.

3.2. Implementation Loss Analysis

As has been mentioned, we use QPSK modulation in our measurements. The bit-error rate (BER) versus SNR ( ) in an additive white Gaussian noise (AWGN) channel for this scheme is given by
(9)
where is defined by
(10)
This is a theoretical expression which assumes no imperfections such as frequency offset, synchronisation errors, and so forth. When a Rayleigh fading model is used, is assumed to be exponentially distributed with mean . The distribution function of is then given by
(11)
The mean BER average over fading can then be calculated as
(12)
This equation can be used as the basis for obtaining the mean BER under any propagation model by generating a lot of snapshots of the SNR (i.e., ) from the propagation model and then calculate the BER for each snapshot using the formula, and finally calculating the average. In the case of two-branch receive diversity in Rayleigh fading, with maximum ratio combining (MRC), the SNR of the combined channel can be simulated as
(13)

where and are the SNR of the two branches. If the two branches are independent Rayleigh fading the SNR of combined channel, , will be distributed. The combined channel will have a higher mean SNR and a lower variance than the two individual branches. This will concentrate the distribution of the resulting BER. This is often a desirable effect and is known as "channel hardening". The concept of channel hardening is also what is used in cooperative relaying. In cooperative relaying the hardening comes from gathering the energy from several distribution paths for the transmitted signal.

The question from an implementation point of view is whether in practise we are able to combine all the different channels so that (12) still applies. A straightforward ad hoc modification of (12) is
(14)

where is the "implementation loss". If we can characterise the implementation loss, the performance in any given environment can be obtained once the propagation scenario and user distribution is known.

In our reference scheme, "direct transmission", the SNR is that of the source-destination channel, and with diversity we add the SNRs of the two diversity branches, just as we did above. For AF, DF, and CMRC we combine the source to destination channel with the channel that passes through the relay. It may be argued that the relay in this case acts as two concatenated AWGN channels and therefore the channel through the relay can be seen as one AWGN by adding the noise of the source-to-relay and relay-to-destination links. Thus the SNR of the resulting channel is given by
(15)
When diversity is applied in DF or CMRC each SNR in the equation above should be the sum of the SNR of the two diversity branches. In the DSTC scheme there is no direct path but an attempt to combine the energy of both relays and therefore the resulting SNR is given by
(16)
In the SR scheme finally, we select the best of two relay paths and therefore (15) above generalises to
(17)
In Figures 13 to 25 we have marked the measured bit error rate (BER) and the combined SNR (as defined for each scheme by the equations above), for every received frame with an "x''. We have also plotted the BER as defined by (14) using different values for the implementation loss . The idea is to subjectively select a value of that seems to fit well with the measurement points. When we do this, it seems appropriate to put most focus on a range of SNRs where BER starts to approach zero.
Figure 13

Implementation loss plot for direct transmission. The "x'' are measurement points and the curves are theoretical BER curves for different implementation loss values.

Figure 14

Implementation loss plot for direct transmission with antenna diversity. The "x'' are measurement points and the curves are theoretical BER curves for different implementation loss values.

There is a problem with this analysis when it comes to AF. The symbols used for channel estimation are affected by the noise at the relay, and of the back-off. Thus we can not estimate the relay-to-destination propagation channel at the destination. For this reason we have used the SNRs estimated for DF instead of those actually estimated for AF. This introduces an error since the channel is not entirely constant.

3.2.1. Direct Transmission

For the direct transmission the implementation loss is approximately 1 dB in the range of SNRs from 5 to 10 dB, both with and without diversity.

3.2.2. Amplify-and-Forward (AF)

Amplify and forward has a loss of approximately 2.5 dB in the range of SNRs from 5 to 10 dB.

3.2.3. Detect-and-Forward (DF)

Without the selective feature, DF gives implementation losses of up to 20 dB. With the feature switched on, the loss is about 4 dB without antenna diversity and 5 dB with antenna diversity.

3.2.4. Cooperative Maximum Ratio Combining (CMRC)

Cooperative maximum ratio combining gives an implementation loss of about 2.5 dB, both with and without antenna diversity. The results of the direct comparison in Section 3.1 showed a slight advantage for CMRC when aiming for zero bit error rate. This advantage is hard to find when comparing Figures 15 and 18. However, for SNRs above 10 dB the performances of both schemes are very similar.
Figure 15

Implementation loss plot for amplify-and-forward, the curves are theoretical BER curves for different implementation loss values.

Figure 16

Implementation loss plot for detect-and-forward (DF), the curves are theoretical BER curves for different implementation loss values.

Figure 17

Implementation loss plot for detect-and-forward (DF) with the selective feature, the curves are theoretical BER curves for different implementation loss values.

Figure 18

Implementation loss plot for cooperative maximum ratio combining (CARA), the curves are theoretical BER curves for different implementation loss values.

Figure 19

Implementation loss plot for cooperative maximum ratio combining (CMRC) with antenna diversity, the curves are theoretical BER curves for different implementation loss values.

Figure 20

Implementation loss plot for distributed space-time coding (STC), the curves are theoretical BER curves for different implementation loss values.

Figure 21

Implementation loss plot for distributed space-time coding with the selective feature (DSTC), the curves are theoretical BER curves for different implementation loss values.

Figure 22

Implementation loss plot for distributed space-time coding (DSTC) with antenna diversity, the curves are theoretical BER curves for different implementation loss values.

Figure 23

Implementation loss plot for distributed space-time coding (DSTC) with antenna diversity and the selective feature, the curves are theoretical BER curves for different implementation loss values.

Figure 24

Implementation loss plot for selection relaying (SR), the curves are theoretical BER curves for different implementation loss values.

Figure 25

Implementation loss plot for selection relaying (SR) with antenna diversity, the curves are theoretical BER curves for different implementation loss values.

3.2.5. Distributed Space-Time Coding (DSTC)

Without the selective feature, the performance is very poor with implementation losses of up to 20 dB. With the selective feature, the loss is 0–10 dB with some sort of typical value around 5 dB. This is true both with and without antenna diversity.

3.2.6. Selection Relaying (SR)

In selection relaying (without antenna diversity) the maximum implementation loss is 10 dB. However, if we disregard data with SNR less than 8 dB, we see an implementation loss of about 2 dB except for one outlier (  dB, %). When antenna diversity is switched on, the implementation loss is about 2.5 dB for SNRs above 8 dB, except for one outlier ( , %).

3.3. Complexity

All the processing was done on 6713 floating point processor from Texas Instruments which runs at a 225 MHz clock. The numbers of clock-cycles consumed per frame for the different configurations are listed in Tables 4 and 5 (using the same ordering as in Table 2). Table 4 is about the number of clock-cycles in the destination while Table 5 is about the number of clock-cycles in the relay.
Table 4

Number of clock-cycles used per frame at the destination.

Direct

2424

3864 (A)

2424

3864 (A)

AF

7400

7400

7392

7404

DF

2500

3996 (A)

2496 (S)

3996 (A,S)

CMRC

4496

6360 (A)

4492

6352 (A)

DSTC

2788

4860 (A)

2788 (S)

4860 (A,S)

SR

2500

3984 (A)

2504

3984 (A)

Table 5

Number of clock-cycles used per frame at the relay.

AF

2892

2888

2896

2892

DF

3016

4480 (A)

3432 (S)

5260 (A,S)

CMRC

3484

5340 (A)

3488

5340 (A)

DSTC

2864

4304 (A)

3276 (S)

5076 (A,S)

SR

2520

3976 (A)

2520

3976 (A)

The code was written in C and compiled using the compiler provided by Texas Instruments with all optimisations switched on, and set to minimise the number clock-cycles needed. The code was written so that all important loops are pipelined. We tried to keep the memory usage low to minimise the number of cache misses. All programs and data were located in the internal memory. The number of clock cycles shown below does not include up- and downconversion and channel filtering and pulse-shaping since these operations are implemented in FPGA or ASIC in a commercial implementation. The overhead for storing the bit error rate and SNR measurements is not included. The results for the complexity of the destination in AF may be surprisingly high. The reason is that this scheme was not as efficiently implemented as the other schemes. (The code of the AF implementation used some unnecessary buffers storing intermediate results in the destination which could be avoided. These buffers increase the number of cache-stalls and thereby the cycle-count.) So the actual value should be the same as for DF since the same processing is done in the destination.

The time available for doing the processing is 48 symbols. With the symbol rate of 9600 Hz the number of clock-cycles available per frame is 1.125e6. Thus, we are using less than 0.6% of the resources available in the DSP. There is a fixed-point version of the processor, called 6416, which has a clock frequency of 1.2 GHz. None of the processing done requires a large dynamic range and therefore a fixed point implementation could be made without increasing the number of clock-cycles.

It may seem that the amplify-and-forward technique would require much less computational power in the relay than the other schemes at the relay. However, note that in a TDD implementation the relay must still do synchronisation and subsample the signal (one sample per symbol instead of five samples per symbol). Moreover, we scale every burst to make optimum use of the available dynamic range of the D/A converter.

What should not be forgotten regarding the complexity of relaying schemes is the memory required for storing the signal to be relayed in the relays. In the DF, CMRC, and DSTC schemes the required amount of memory are two frames of 96 bits each. In the SR schemes, ten such frames are stored. In the AF technique we need to store the samples of the received signal, for example, using 16 bits for real and imaginary parts, respectively (in our implementation we have stored them as floats). Thus, these lead to a memory requirement in the relay of 24 bytes for DF, CMRC, and DSTC, 120 bytes for SR and 384 bytes for AF. These number will scale with the bandwidth if multiple subcarriers are introduced.

Other complexities that should be considered are the synchronisation requirements. Here, we have assumed that the transmission will go on for long enough for the overheads during the synchronisation phase to be neglected. This is also a question of the functionality of the upper layers, that is, how the source, relay, and destination are set up and how spectrum resources allocated. The DSTC scheme requires the relays to adjust the timing of the transmitted signal so that the signals from both relays to arrive aligned at the destination. This is probably not a very problematic issue in a commercial implementation as the destination will need to acknowledge packets, and therefore there will be signalling from the destination to the relays in any case.

4. Conclusion

We have implemented four well-known cooperative relaying schemes: amplify-and-forward (AF), detect-and-forward (DF), cooperative maximum-ratio combining (CMRC), and distributed space-time coding (DSTC), and one novel scheme selection relaying (SR), see Section 2.

In the novel scheme, SR, we select one out of two relays, on a "slow" basis, that is, we only aim to select the relay which has the best channel in average (taking into account both the source to relay and the relay to destination path), that is, we do not aim to track the fast fading but only the path loss.

For the DF and DSTC we introduced a feature "selective" where the relay only forwards a frame if its receive SNR is better than a threshold (4 dB), and otherwise stays silent. For all schemes except AF, we also introduced antenna diversity by means of maximum ratio combining.

We measured the performance of all five schemes plus direct transmission (which is a reference case), with and without antenna diversity and the "selective" options. The measurements were done in an indoor office environment under challenging conditions, that is, all links experienced low signal to noise ratios. As shown in Section 3.1, all schemes improved the coverage area over direct transmission. The feature "selective" helped improve the performance of DF and DSTC significantly. Using antenna diversity was also an effective means for improving performance. The greatest performance improvements were achieved using DSTC and SR which utilise two relays. We also analysed the implementation loss of our implementations. This was obtained by calculating the theoretical BER based on measured channels from the source to the relays, from the relays to destination, and the direct path from the source to the destination. The number obtained was compared with the actual BER. By doing so it was evident that DF and DSTC need the "selective" option to function properly. Doing so DF and DSTC have an implementation loss of around 5 dB, while CMRC, AF, and SR has an implementation loss of around 2.5 dB. Direct transmission has the smallest implementation loss of approximately 1 dB. It was noted that CMRC performs better than AF, when counting the number of frames with bit errors while AF performs better than CMRC when a few errors are allowed.

We implemented our system on a floating point DSP and used 0.6% of its resources for channel estimation and detection. When increasing the bandwidth of the system the load on the DSP should increase proportionally to the bandwidth expansions. Surprisingly, the implementation of the amplify and forward technique is not less computationally expensive than the other approaches. This is related to the fact that we are using a TDD system and therefore the relay needs to synchronise, store, and forward the received signal. Finally, the AF solution needs more memory than, for example, DF since it does not store decoded bits but rather signal samples.

Declarations

Acknowledgment

This work was performed in part within the framework of the EU funded IST-2002-2.3.4.1 COOPCOM Project.

Authors’ Affiliations

(1)
ACCESS Linnaeus Center, Royal Institute of Technology
(2)
Research Academic Computer Technology Institute
(3)
Department of Electronic and Computer Engineering, Technical University of Crete

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© Per Zetterberg et al. 2009

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