On Diversity Combining

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Petri Isomäki | Jouni Isoaho

On Diversity Combining

TUCS Technical Report

No 884, April 2008





On Diversity Combining

Petri IsomäkiUniversity of Turku, Department of Information Technology

Joukahaisenkatu 3-5, 20520 Turku, Finland

[email protected]

Jouni IsoahoUniversity of Turku, Department of Information Technology

Joukahaisenkatu 3-5, 20520 Turku, Finland

[email protected]

TUCS Technical Report

No 884, April 2008



Abstract

Diversity is needed for mitigating the effects of multipath fading in wirelesscommunications. Diversity techniques are based on that receiver gets several sig-

nals bearing the same information, through independently fading channels.

Diversity can be introduced in three different domains: time, frequency and

space. The use of interleaving and coding provides time diversity. Frequency

diversity can be achieved by using spread spectrum signals. Of multi antenna

configurations for space diversity, receive diversity is the most widely utilized, for

instance at the base stations of mobile communication systems.

This report discusses techniques for receive diversity combining. Typical

methods are presented at first, and thereafter, various physical layer designs with

receive diversity are discussed. Space-time coding is a more advanced techniquethat can approach the capacity limit of the MIMO channel and give the diversity

and coding gains.

Keywords: Diversity, Diversity Combining, Selection Combining, Maximal Ra-

tio Combining (MRC), Space-Time Coding, MIMO

TUCS Laboratory

Communication Systems Laboratory



1 Introduction

In wireless communications, diversity is commonly used for compensating the ef-

fects of multipath fading. Large attenuation of wireless channel results in very

poor performance. Even short periods of deep fade cause large performance

penalty [1]. Diversity techniques are based on different structures where receiver

gets several signals bearing the same information, through independently fading

channels [1]. The probability that all the signals are simultaneously in deep fade

is much lower [3].

Diversity can be introduced in three different domains: time, frequency and

space. This report concentrates on diversity combining methods for receive diver-

sity that is achieved by using multiple receive antennas, although diversity tech-

niques are also discussed in general. The combining can be performed by using

several different methods, and depending on the application, at different stages of

the receiver chain. Typical methods include selection combining, equal gain com-bining and maximal ratio combining. Simpler implementation is the advantage of

combining after detection of each branch one by one, i.e. post-detection combin-

ing. Combining can also be performed, for example, before or after decoding or

DFT if there are such blocks in the physical layer design.

Receive diversity is widely utilized, e.g. at the base stations of cellular com-

munication systems. Since size and power consumption of mobile devices are

usually constrained, transmit diversity may also be considered, although it is more

difficult to exploit than receive diversity [3]. However, there is a more attractive

technique: the joint design of coding and transmit diversity. The radio spectrum

is also a limited resource. By using multiple-input multiple-output (MIMO) sys-tems, a significantly higher efficiency is achievable [3]. Space-time coding is a

technique that can approach the capacity limit of the MIMO channel and give

the diversity and coding gains. Due to this, and from the practical point of view,

thanks to the benefits like higher bitrates, increased range and lower power con-

sumption, the MIMO approach has become increasingly popular for wireless local

area networks, cellular systems etc. That topic has been extensively covered for

instance in [3].

The report1 is organized as follows: Section 2 presents diversity techniques.

Sections 3 and 4 present diversity combining methods in general and for various

physical layer designs. Existing and upcoming wireless communication systems

with diversity techniques are discussed in Section 5.

1This work is a part of project called Scalable Error-Tolerant Software-Defined Radio Plat-

forms, funded by the Academy of Finland.

1



2 Diversity Techniques

This section presents techniques that allow the receiver to get multiple signals

through independently fading channels, in order to obtain diversity gain. There

are three resources that are used in communications: time, frequency and space.

Accordingly, there are these three domains where diversity can be introduced,

resulting time, frequency or space diversity. There are certain conditions for each

domain that provide independently fading channels. The techniques for different

domains are listed in Table 1 and further described in the following subsections.

Table 1: Diversity Techniques

Domain Technique

frequency diversity same information on multiple frequency slots

spread spectrum signalstime diversity repetition

error correction coding and interleaving

space diversity receive diversity (multiple rx antennas)

transmit diversity (multiple tx antennas)

angle-of-arrival diversity

polarization diversity

macroscopic diversity

MIMO and space-time coding

2.1 Frequency Diversity

For frequency diversity, the same information is transmitted on multiple frequency

slots [2]. The separation between the slots has to be at least the coherence band-

width ∆ f c of the channel [1]. A shortcoming of the scheme is that multiple trans-

mitters are needed [1]. In practice, frequency diversity is usually achieved by

using spread spectrum signals, i.e. direct sequence, frequency hopping or multi-

carrier spread spectrum modulation [3].

2.2 Time Diversity

For time diversity, the same information is transmitted in different time slots. The

separation between the time slots has to be at least the coherence time ∆t c of the

channel. The basic form of time and frequency diversity, as described here, can

be seen as utilization of repetition block coding, where combining method is the

soft decision decoding of the repetition code [2]. There exist much more efficient

codes than the repetition code. Thus, in practice, diversity is often introduced by

adding error correction coding and interleaving.

2



2.3 Space Diversity

Space diversity is achieved by using multiple antennas that are separated by a

large enough distance to make signals uncorrelated [3]. The distance requirement

depends, for instance, of the propagation channel and frequency. According to [3],distance of a few wavelengths is usually enough, whereas in [35], it is cited that 10

to 30 wavelengths are required at a base station for correlation of 0.7 according to

measurements. In receive diversity, there are multiple receiving antennas, whereas

in transmit diversity, there are multiple transmitting antennas. In macroscopic

diversity, two or more base stations are used simultaneously [38]. Angle-of-arrival

diversity and polarization diversity are special cases of space diversity. Because

the required distance of tens of wavelengths corresponds to several meters, a four

antenna configuration with ±45opolarized components, of the same size as a dual

antenna configuration, has been proposed in [35].

Receive diversity is widely used, for example in cellular base stations. Trans-mit diversity is more difficult to take advantage of, because the transmitted signals

are mixed together, and the transmitter does not have instantaneous channel state

information [3]. On the other hand, it is difficult to put multiple receive anten-

nas to a mobile device, because of size and power consumption constraints. In

contrast, transmit diversity decreases the processing power needed by the receiver

[3]. However, the receiver also has to be modified: either feedback or some signal

processing at the receiver is needed for exploiting the diversity in the transmit-

ted signal. Thus, the use of transmit diversity has to be defined in the standard,

whereas receive diversity can be employed in any receiver design.

Transmit diversity can be combined with error control coding. A more optimal

scheme is the joint design of transmit diversity, error control coding and modula-

tion [3]. The technique is called Space-Time Coding (STC). With STC, diversity

and coding gain can be achieved without bandwidth expansion [3]. Large capac-

ity gains have been shown to be possible by using multiple-input multiple-output

(MIMO) systems, and STC is a way to approach the capacity limit. Channel ca-

pacity formulas for different combinations of transmit an receive antennas can be

found in [3].

In practice, multiple diversity schemes are usually used together [3].

3



3 Diversity Combining Methods

A classification of diversity schemes can be made based on combining methods.

In order to get the diversity gain, the signals from multiple channels have to be

combined, and the combining method affects the performance of the diversity

technique. There are methods with different levels of complexity and varying

need for channel state information.

The combining techniques have applications also in other contexts, such as

frequency diversity (RAKE receiver) [2] or packet retransmission protocols [25].

However, here they are discussed especially from the point of view of space (re-

ceive) diversity.

The methods with low complexity include equal gain combining (EGC) and

selection combining (SC). In selection combining, the signal with the largest in-

stantaneous SNR is chosen as the output. A receiver with selection combiner is

shown in Fig. 3.1. In practice, it is difficult to measure SNR directly. Therefore,the highest total power (signal and noise) is used as the selection metric [16]. An

analysis of these S + N selection systems is provided in [16] for various binary

modulation schemes. The performance of the S + N selection is actually better

ADC

1

2

L

RF

RF

RF

Select Detector

ADC

ADC

Figure 3.1: Selection Combining

4



compared to the traditional SNR based method. For many cases, the performance

is equal to the EGC, which needs co-phasing.

Equal gain combining and maximal ratio combining (MRC) are linear com-

bining methods, i.e. signals are weighted and added together [3]:

r = L

∑i=1

air i

In equal gain combining, the amplitudes of the weights are equal:

ai = e− jϕ i

where ϕ i is the phase of the received signal, i.e. the signals are co-phased and

added together.

In maximal ratio combining, the weights are proportional to the received SNR

at each antenna. If the noise powers are assumed equal, the weights are given by:

ai = Aie− jϕ i

where Ai is the amplitude and ϕ i is the phase of the received signal. Therefore,

MRC requires the estimates of the channel fading and the signal phase. Maximal

ratio combining is the optimal method in the sense that it can maximize received

SNR [3]. A receiver with maximal ratio combiner is shown in Fig. 3.2.

The bit error probability of BPSK signaling with MRC is given by [1]

Pb, MR, BPSK = 1

2

1−µ

L−1

∑k =0

2k k

1−µ 2

4

k

µ =

E b/ N 0

1+ E b/ N 0

and the bit error probability with selection combining given by [31]

Pb,SC , BPSK =L

2

L−1

∑k =0 L−1

k (−1)k 1−

1 1+(1+ k )α

1

1+ k

α =1

E b/ N 0

where E b/ N 0 is the signal to noise ratio and L is the number of diversity branches.

The theoretical bit error rates and results from a simulation for up to four diversity

branches are shown in Fig. 3.3.

Without the channel state information about fading, noiseless signal power

cannot be used as the weight. The effect of using S + N instead of SNR for

5



1a

2a

La

1

2

L

RF

RF

RF

ADC

ADC

ADC

Detector

Figure 3.2: Maximal Ratio Combining

−4 −2 0 2 4 6 8 1010

−3

10−2

10−1

100

SNR (dB)

B E R

no diversity

maximal ratio

theoretical

selection combining

theoretical

Figure 3.3: Combining Methods

6



−4 −2 0 2 4 6 8 10

10−4

10−3

10−2

10−1

B E R

theoretical BER (MRC)channel attenuation as weight

received power as weightequal gain combining

Figure 3.4: Maximal Ratio Combining with Incomplete Channel State Informa-tion

weighting in MRC is depicted in Fig. 3.4. Perfect co-phasing has been assumed.

Opposite to the results for SC, the use of S + N decreases performance of MRC.

Actually, simulations show that even EGC performs better, i.e. S + N should not

be used as the weight. If the carrier phase does not change significantly over the

duration of two symbols, differential PSK (DPSK) modulation can be used [2],

and combining can be done without co-phasing [8, 9]. According to [16], EGC

after differential detection2 is the optimal combining method for DPSK, while for

two branch binary DPSK, S + N selection combining gives equal performance.However, as seen in [8, 9], pre-detection MRC is the most optimal, even though

an unnecessarily complex method for DPSK.

In generalized selection combining (GSC), more than one branch are chosen

for combining. In selection 2 combining (SC2), the two best diversity branches

are chosen. Generalized selection combining has been discussed in [31, 33, 34].

In [31], SC2 and SC3 have been compared to MRC for a coherent receiver and to

2Sometimes also called post-detection MRC or product detector combiner. See Section 4.

7



EGC for a non-coherent receiver. The performance of GSC is particularly good

in the case of non-coherent detection. In [33], there has been proposed a better

selection method for GSC, based on log-likelihood ratio instead of SNR. As men-

tioned in the previous section, increased power consumption is a disadvantage

of receive diversity. A threshold-based adaptive GSC for decreasing processing

power requirements has been presented in [27].

Rayleigh fading channel is commonly used in the analysis of diversity tech-

niques. Various departures from the model have been investigated. The effect of

correlated diversity has been explored in [20]. An unexpected result is that, in case

of selection combining, correlation decreases error rate at low SNR and increases

error rate at high SNR. The influence of the power profile of the fading channel

has been analyzed in [26]. The effect of impulsive noise has been investigated

in [15]. It is shown that post-detection combining is much more effective against

highly impulsive noise than pre-detection SC, EGC or MRC when there are many

diversity branches. An adaptive receiver design for non-Gaussian noise has beenproposed in [7].

8



4 Combining Domains

This section presents combining schemes with combining at different stages of

the receiver, for various system and receiver designs.

The combining of the outputs the branches can be performed either before de-

tection (pre-detection diversity combining) or after detection (post-detection di-

versity combining). Post-detection combiners weight and combine the diversity

channels after detection and therefore, there is no need for co-phasing operation,

which has a high implementation cost [8]. A receiver with post-detection com-

biner is shown in Fig. 4.5.

Combining can also be done before, within, or after FEC decoding. In OFDM

systems, combining may be performed before or after FFT, and in spread spec-

trum systems, there may be chip level or symbol level combining. The following

subsections represent a view based on the referred papers, rather than being a

complete analysis of the topic.

4.1 Post-Detection Combining

For differential detection, the post-detection MRC, shown in Fig. 4.5, is actu-

ally equivalent to the equal gain combining without hard limiters after product

detectors [8]. In [9], this combining method is called the post-detection product

detector combiner.

ADC

1

2

L

RF

RF

RF ADC

ADC

Product

Product

Productdetector

detector

detectorDecision

Figure 4.5: Post-Detection Maximal Ratio Combiner for DPSK

9



For two branch QDPSK, post-detection MRC outperforms post-detection se-

lection combining by 1.5 dB [8], whereas for 2-DPSK, the performance is equal

[16]. For higher order diversity, post-detection MRC performs better than SC [16].

In correlated Nakagami fading channel, the post-detection MRC is only 1 - 3 dB

worse than pre-detection MRC, depending on the channel, the branch separation

and the number of branches [9].

The optimal combining for differential PSK has been analyzed in [8]. The

analysis covers multiplicative and very slow frequency selective Rayleigh fading

channels with co-channel interference (CCI). It is shown that post-detection max-

imal ratio combining is optimal only in the case of equal average power in each

branch. If the CCI is the only significant cause of errors, the weights should be

inverse proportional to the average CCI power, whereas in the AWGN limited

case, the post-detection MRC provides good, almost optimal performance even

for unequal powers [8].

An efficient implementation of post-detection MRC without any multipliershas been presented in [22].

4.2 Combining of Coded Waveforms

It is non-trivial to find the relationship between branch weights and error rate after

decoding [23]. The conventional selection diversity combiners try to minimize

the probability of hard decision error [10]. They do not necessarily minimize the

post-decoding error probability. In [10], multiple generalized selection combining

methods based on the log-likelihood ratio have been presented. Simulations have

been performed for low-density parity check and Turbo codes. The coding gain,compared to the traditional SNR based selection, is improved especially when

only a few diversity branches are selected for combining.

The combined effects of maximal ratio combining and hard decision Viterbi

decoding have been investigated in [11]. It is concluded that with two-branch

diversity, the tolerable rms delay spread and the spectrum efficiency are insensitive

to the code rate, whereas without diversity, the performance degrades while code

rate increases.

Soft decision Viterbi decoding with selection combining in or after decoder,

and pre-Viterbi maximal ratio combining in Rician fading channel have been com-

pared in [14]. The post-Viterbi selection combiner compares decoded signals us-ing the likelihood information given by the Viterbi decoder. The method that

makes the selection in the decoder computes first branch metrics for transitions in

all diversity channels, and then selects the survivor by comparing all the metrics

jointly. The pre-Viterbi MRC performed better than the two other combiners.

A method similar to [14] for combining within the Viterbi algorithm has been

compared to soft decision decoding with pre-decoding combining also in [13].

Binary PSK and (7,4) Hamming code were used. In this case, the simulations

show better performance for the pre-decoding combiner.

10



(a)

(c)

1

2

L

ADCRF

RF

RF ADC

1

2

L

ADCRF

RF

RF ADC

MRCViterbidecoder

decoder

decoder

decoderViterbi

Viterbi

Viterbi

Selector

(b)

1

2

L

ADCRF

RF

RF ADC

Viterbi decoder

memorypath

ADC

ADC ACS MLDADC

(d)

1

2

L

RF

RF

RF

Detector

Detector

Detector

Codecombiner

ADC

ADC

ADC decoderViterbi

Figure 4.6: Combining Methods with Viterbi Decoding [14, 19]

Interleaved code combining (ICC) interleaves outputs of diversity branches in

order to obtain a combined code word [19]. The combined code word can be

decoded by using the same trellis structure that would be used without diversity.

Interleaved code combining was originally used in packet retransmission proto-

cols [25]. For diversity combining in a system with trellis coded modulation, the

performances of EGC before decoding and ICC have been theoretically analyzed

in [25]. The case of 1/2 rate convolutional encoding with QPSK has also beensimulated. With large number of diversity branches, the ICC method gives about

1 dB gain compared to the pre-decoding combining, but demodulation complexity

increases significantly. For practical number of branches, the gain is minimal.

However, the analysis in [19] shows that ICC is effective for a wider range

a of conditions and gives much better performance in channels with frequency

selective fading or co-channel interference, compared to the conventional MRC.

The four different combining methods for coded waveforms are shown in Fig.

4.6. Post-Viterbi-decoding selection in Fig. 4.6(a) selects the best diversity branch

11



−4 −2 0 2 4 6 8 10

10−4

10−3

10−2

10−1

100

SNR (dB)

B E R

Binary PSK over Rayleigh Fading Channel

pre−detection MRC, (7,3) cyclic code

(7,3) cyclic code, post decoding combining

post detection combining, (7,3) cyclic code

MRC, no coding

Figure 4.7: Diversity and Coding

after Viterbi decoding. The method of Fig. 4.6(b) selects the survivor path among

all the diversity branches at add-compare-select (ACS) function of the Viterbi

algorithm. The pre-Viterbi-decoding maximal ratio combiner in Fig. 4.6(c) per-

forms the combining before the Viterbi decoder. Interleaved code combining is

shown in Fig. 4.6(d). In [19], the method (d) has been enhanced by using error-

and-erasure correction Viterbi decoding. Unreliable symbols are erased based on

the channel state information.

In Fig. 4.7, there are shown simulation results of BPSK over fading channel

with combining at three different stages. The post-decoding combining is basedon the detected errors, which is clearly a non-optimal method. As discussedabove,

if there is likelihood information available from the decoder, some performance

gain can be achieved.

4.3 Combining and OFDM

Orthogonal frequency division multiplexing (OFDM) can be used for communi-

cation over fading channels. However, there is still performance loss due to fading

12



ADC

1

2

L

MRC P/S decoderleaverdeinter−

RF ADC DFT

RF DFT

RF ADC DFT

Figure 4.8: COFDM diversity receiver with post-DFT combining [23]

even with OFDM, and therefore, combination of space diversity and OFDM has

been investigated.

In frequency selective fading, conventional combining methods are inefficient

for OFDM [23]. MRC before DFT amplifies noise if corresponding subcarrier

is in deep fade [18]. Post-DFT combining is the optimal method in sense that it

maximizes SNR after combining [23]. In [18], there has been proposed an optimal

combiner that integrates diversity combining, demodulation and equalization in

a maximum likelihood decoder of COFDM. Simulations show that the bit level

combiner can provide 2 - 4 dB gain over a conventional symbol level combiner.

A post-DFT combining coded OFDM (COFDM) diversity receiver is shown

in Fig. 4.8.

Post-DFT combining requires FFT processor for each branch. In [5], a joint

antenna and post-DFT combining has been proposed. The antenna combining is

based on an electromagnetic coupled array antenna, which has limitation on the

number of diversity branches. Simulation results show that the joint antenna andpost-DFT combiner can achieve the same performance as four branch post-DFT

combiner while using only two sets of receiver components.

A Pre-DFT combining scheme is proposed in [23], in order to reduce com-

putational complexity. Only one FFT processor is needed. For calculating the

weights, time domain correlation between the signals is used, instead of estimat-

ing frequency response directly, in order to avoid the need for FFT processors. It

is shown that the optimum weights can be obtained from the covariance matrix

that is built using the impulse responses of all branches.

13



4.4 Combining and Spread Spectrum

Combining for multipath diversity gain in RAKE receiver of direct sequence

CDMA (DS-CDMA) systems has been presented for instance in [2].

In spread spectrum systems, space diversity combining can be performed ei-

ther at chip level or at symbol level. For spread spectrum OFDM (SS-OFDM),

symbol level combining after despreading has been compared to chip level maxi-

mal ratio combining in [17]. The chip level combining is shown to be better if the

diversity branches are uncorrelated. The chip level combining can compensate the

effect of inter code interference caused by frequency selective fading.

The SS-OFDM system in [17] is actually commonly known as a multicarrier

CDMA (MC-CDMA) system. In [40], there has been presented a post-detection

symbol level combiner for multi tone CDMA (MT-CDMA). In the receiver of this

scheme, the despreading is performed first, followed by detection of each tone

and combining with other branches. The scheme differs from MC-CDMA in thatthe transmitter spreads the signal in the time domain and the signal is serial-to-

parallel converted for transmission using multiple tones, whereas in MC-CDMA,

the spreading is performed in the frequency domain and the same information

is transmitted at each subcarrier [41]. In MC-CDMA, the subcarriers have to

be combined, e.g. by using minimum mean square error combiner (MMSEC).

Combiners like EGC and MRC are insufficient due to interference and loss of or-

thogonality. The space diversity combiner can be included in the same operation,

i.e. the chip level combiner in [17].

The MT-CDMA diversity receiver is similar to Fig. 4.8. In addition, there is

a despreading block before the DFTs. The MC-CDMA diversity receivers withchip level and symbol level combining are shown in Fig. 4.9. There are MMSE

equalization and despreading blocks after the DFTs. The chip level combining is

performed before despreading together with an appropriate MMSE equalization,

whereas the symbol level combing is performed after despreading.

A recurrent neural network (RNN) based symbol level combiner for multi-

carrier direct sequence CDMA (MC-DS-CDMA) has been proposed in [36]. MT-

CDMA is a special case of MC-DS-CDMA and from the point of view of diversity

combining, they are equal. The performance of the RNN combiner is compared to

a square root Kalman combiner in Rayleigh and Rician channels. The RNN com-

biner uses a real time training algorithm. Chip level combining has been discardedbecause it needs longer training sequences and more processing power. With high

Rician factor, the RNN combiner has better performance only with a low number

of diversity branches, in which case the Kalman system has an error floor. With

lower Rician factors, the Kalman system is unable to track the changing channel

and the RNN combiner becomes the only usable choice.

In [39], there has been proposed a combination of space diversity with MRC

and adaptive antenna array beam forming for uplink of WCDMA, i.e. for DS-

CDMA. The adaptive antenna array gives better performance than space diversity

14



c L−1

c 0

c 1

ADC

1

2

L

&MMSE

Combining

RF ADC DFT

DFTRF

RF ADC DFT

(a)

c L−1

c 0

c 1

c L−1

c 0

c 1

c L−1

c 0

c 1

ADC

1

2

L

C om b i ni n g

MMSE

MMSE

DFT

DFT

MMSEDFTRF ADC

RF

RF ADC

(b)

Figure 4.9: MC-CDMA diversity receiver (a) with chip level combining; (b) with

symbol level combining [17]

15



receiver with the same number of antennas [39]. Simulations show that combina-

tion where two branches contain four antennas in each branch gives a significant

amount of diversity gain, while interference suppression capability is slightly de-

creased. Therefore, the combination is suitable for a wider range of environments,

including the interference limited case and channels with only few resolved paths.

4.5 Combining and Multiuser Communications

Combined multiuser detection and diversity reception has been investigated in

[37]. For a DS-CDMA system, both MRC for coherent RAKE receiver and EGC

for differentially coherent RAKE receiver have been presented. Instead of using

pre-detection combining, the decorrelating operation of the multiuser detection

may be performed first. The method has a significant advantage: the estimation

of channel fading and diversity combining can be performed on multiple access

interference free signals [37].In [38], it has been shown that by using both multiuser detection and macro-

scopic diversity in a DS-CDMA system, a significant performance gain can be

achieved, compared to employing another of the techniques alone.

In the wide band multiuser communications, there is no loss of diversity order

due to linear detection, assuming that the waveforms of different users are linearly

independent [30]. In contrast to the wide band case, in narrow band multiuser

communications with linear detectors, there is a decrease of achieved diversity

with increased number of interfering users. Therefore, pre-combining multiuser

detection is even more useful in the narrow band case. In [30], there has been

presented a pre-combining group detector, which gives performance gain over thelinear ones. The receiver complexity, in addition to the number of antennas, is a

new parameter for controlling the diversity order.

16



5 Applications

Time diversity is widely exploited in the form of error control coding. Frequency

diversity is also achieved in any spread spectrum system. In present wireless

communication systems, receive diversity is the type of spacediversity that is most

widely used, though MIMO systems have become increasingly common. Some

applications in which space diversity techniques have been utilized are listed in

Table 2.

Table 2: Applications of Space Diversity

Receive Diversity Transmit Diversity MIMO

uplink: GSM, IS-136,

UMTS etc

UMTS/WCDMA 3GPP LTE

downlink:cdma-2000 1xEV-DO,

UMTS/HSDPA

802.16 (WiMAX)802.16e (mobile WiMAX)

DVB-T 802.11n (WLAN)

Receive diversity can be used for enhancing performance in fading environ-

ments and for suppressing co-channel interference, with existing standards and

systems (although, it may be useful to define the use of receive diversity also

within standardization, e.g. measurements when there is receive diversity [50]

and the impact of diversity on control channels [51].) Therefore, receive diver-

sity is commonly utilized in mobile cellular communications: multiple antennasare employed at base stations, for example in GSM and IS-136 [3]. Even though

more common at the uplink, receive diversity is used in the downlink of some

3G cellular systems, i.e. at the mobile device side in cdma-2000 1xEV-DO and

UMTS/HSDPA high-speed data chipsets [42, 43]. Macroscopic diversity [38] and

polarization diversity [35] are also utilized in 3G systems.

There are also DVB-T digital television receivers with receive diversity, de-

signed for mobile reception. In [44], MRC has been used for combining the

COFDM signal of DVB-T. The tests show the receive diversity allows signifi-

cantly higher speeds for receivers in motion, making DVB-T reception possible at

vehicle speeds typical in urban area.Due to the size and power consumption limits of mobile devices, transmit

diversity is also gaining more interest. Space-time coding is an efficient way to

exploit transmit diversity and reach the capacity limit of MIMO channels. Space-

time coding and multiple antennas are the key additions of the wireless local area

network standard draft 802.11n [45]. Marketing claims often suggest very high

ratings, such as 270 Mbps throughput, while actual tests show bit rates around

80 Mbps even at good conditions [52]. Nevertheless, the actual bit rates are far

higher than without diversity, i.e. 802.11g, and the operating range is greater. The

17



WiMAX fixed (802.16) and mobile (802.16e) broadband standards also include

MIMO in the definition of the physical layer [46, 47].

In the WCDMA air interface standard for 3G mobile phone networks, transmit

diversity with two transmit antennas has been included since 3GPP WCDMA

Release 4 [48]. MIMO with up to four transmitting and four receiving antennas

will be included in high speed packet access networks [49].

18



6 Conclusions

Because of the effects of multipath fading, some form of diversity is needed in

order to reach reliable transmission.

This report discussed the diversity techniques at first in general. Diversity can

be introduced in three different domains: time, frequency and space. Time di-

versity is often achieved by using error correction codes and interleaving. Spread

spectrum systems make use of frequency diversity. Space diversity can be based

on multiple receive or transmit antennas and signal processing for combining. In

practice, multiple diversity schemes are usually used together.

The report concentrated on space diversity, more specifically, on diversity

combining for receive diversity. Receive diversity is commonly utilized, e.g. in

cellular base stations for uplink. There are various techniques for combining the

signals from the antennas, with different trade-offs between complexity and effi-

ciency. Different physical layer designs have also variable choices of the combin-

ing methods. For instance, encoded waveforms may be combined before, within

or after the decoder.

Pre-detection maximal ratio combining is an optimal method in the sense that

it can maximize the signal-to-noise ratio of the received signal. However, there

are various rationales to use other combining methods. For instance, generalized

selection combining may provide the required trade-off between complexity (or

power consumption) and performance. Post-detection combining may be used for

the same reason as non-coherent modulation in general, i.e. significantly lower

complexity with a reasonable performance loss. Variations from the Rayleigh

channel model may also affect the choice of the combining method. In the pres-ence of impulsive noise, post-detection combining may actually perform better.

It is also non-trivial to predict error rates after combining and decoding of

coded waveforms, i.e. the optimal combining has to be designed for the post-

decoding error rate. Again, the relative performance of the methods also depends

on the type of the channel: interleaved code combining has been shown to be ro-

bust for variable conditions, while pre-decoding MRC may be a good choice in

some cases. In OFDM systems, pre-DFT combining may amplify noise, and in

MC-CDMA, a more complex MMSE combiner is needed due to interference and

loss of orthogonality. In multiuser communications, it is preferable to combine

the branches after detection, in order to be able to remove the interfering signals.In conclusion, the choice of combing method depends on the physical layer design

and the operating conditions, i.e. there is no “one fits all” strategy for diversity

combining. The method has to be fixed in the design phase according to the appli-

cation or, in systems like software defined radio, the method may be reconfigured

as the need arises.

Finally, some applications that exploit space diversity were discussed. The

processing power and size of mobile devices limit the use of receive diversity for

downlink of mobile cellular communication systems. Nevertheless, two receive

19



antenna configurations are sometimes used also at the mobile station. For transmit

diversity, the receiver also has to be modified: either feedback or some signal

processing at the receiver is needed. Thus, the use of transmit diversity is more

difficult to exploit and has to be defined in the standard, whereas receive diversity

can be employed in any receiver design.

Due to the limited feasibility of receive diversity in mobile devices, the use

of multiple transmit antennas is gaining more interest. In addition to combating

multipath fading, MIMO channel combined with space-time coding can give a

large capacity gain. Thus, the MIMO systems have become one of the most active

research topics in wireless communications, and the scheme has been introduced

into a number of the state of the art commercial applications, such as high speed

WLANs and upcoming 3G cellular networks.

20



References

[1] R. E. Ziemer, R. L. Petterson: Introduction to Digital Communication, 2nd

edition, Prentice Hall, 2000

[2] J. G. Proakis: Digital Communications, McGraw-Hill, 1995

[3] B. Vucetic, J. Yuan: Space-Time Coding Wiley, 2003

[4] D. G. Brennan: Linear Diversity Combining Techniques, Proceedings of the

IRE, 1959

[5] T. Noritomo, M. Okada, H. Yamamoto: A Joint Antenna and Post-DFT Com-

bining Diversity Scheme in OFDM Receiver, 1st International Symposium on

Wireless Communication Systems, 2004

[6] E. Conte, M. Di Bisceglie, M. Lops: Optimum Detection of Fading Signals in

Impulsive Noise, IEEE Transactions on Communications, Volume 43, Issue

234, Feb-Mar-Apr 1995

[7] R. S. Blum, R. J. Kozick, B. M. Sadler: An Adaptive Spatial Diversity Re-

ceiver for Non-Gaussian Interference and Noise, IEEE Transactions on Sig-

nal Processing, Volume 47, Issue 8, Aug. 1999

[8] F. Adachi: Postdetection Optimal Diversity Combiner for DPSK Differential

Detection, IEEE Transactions on Vehicular Technology, Volume 42, Issue 3,

Aug. 1993

[9] P. Lombardo, G. Fedele: Post-Detection Diversity in Nakagami Fading

Channels with Correlated Branches, IEEE Communications Letters, Vol-

ume 3, Issue 5, May 1999

[10] S. W. Kim, S.-J. Park, W. Chang: Diversity Selection Combining To Enhance

The Coding Gain, IEEE 60th Vehicular Technology Conference, 2004

[11] H. Zhou, R. H. Deng: Combined Effects of Convolutional Coding and

Diversity Reception for QDPSK Cellular and Mobile Radio, Singapore

ICCS/ISITA ’92. ’Communications on the Move’, 1992

[12] K. Kobayashi, Y. Murakami, et al: Soft-Decision Decoder Employing Eigen-

value of Channel Matrix in MIMO Systems, 14th IEEE Proceedings on Per-

sonal, Indoor and Mobile Radio Communications, 2003

[13] K. Mohamed-Pour, P. G. Farrell: Trellis decoding of combined diversity cod-

ing scheme (MLSD) for fading channels, Electronics Letters Volume 32, Is-

sue 10, May 1996

21



[14] T. Sakai, K. Kobayashi et al: Soft-Decision Viterbi Decoding with Diversity

Combining for Multi-Beam mobile Satellite Communication Systems, IEEE

Journal on Selected Areas in Communications, Volume 13, Issue 2, Feb.

1995

[15] C. Tepedelenlioglu, P. Gao: On Diversity Reception over Fading Channels

with Impulsive Noise, IEEE Transactions on Vehicular Technology, Volume

54, Issue 6, Nov. 2005

[16] E. A. Neasmith, N. C. Beaulieu: New Results on Selection Diversity, IEEE

Transactions on Communications, May 1998

[17] R. Novak, W. A. Krzymie: Diversity Combining Options for Spread Spec-

trum OFDM Systems in Frequency Selective Channels, IEEE Wireless Com-

munications and Networking Conference, 2005

[18] X. Ouyang, M. Ghosh, J. P. Meehan: Optimal Antenna Diversity Combining

for IEEE 802.11 A System, IEEE Transactions on Consumer Electronics,

Volume 48, Issue 3, Aug. 2002

[19] H. Zhou and K. Okamoto: Comparison of Code Combining and MRC Diver-

sity Reception in Mobile Communications, IEEE Wireless Communications

and Networking Conference, 2004

[20] E. A. Jorswieck, T. J. Oechtering, H. Boche: Performance Analysis of Com-

bining Techniques with Correlated Diversity, IEEE Wireless Communica-

tions and Networking Conference, 2005

[21] J.-M. Chung, W.-C. Jeong, et al: Enhanced Robust Wireless Network QoS

Control Applying Adaptive Modulation and Macroscopic Diversity Com-

bining Techniques, First IEEE Consumer Communications and Networking

Conference, 2004

[22] T. Kumagai and K. Kobayashi: Postdetection Maximal Ratio Combining Di-

versity Receiver with Scalar Phase Signals, IEEE 6th International Confer-

ence on Universal Personal Communications, 1997

[23] M. Okada, S. Komaki: Pre-DFT Combining Space Diversity Assisted

COFDM , IEEE Transactions on Vehicular Technology, Volume 50, Issue

2, March 2001

[24] J. Sun, K. H. Li: Diversity Techniques for Reverse Link of Cellular

DS/CDMA, Proceedings of 1997 International Conference on Information,

Communications and Signal Processing, 1997

22



[25] L. K. Rasmussen, S. B. Wicker: A Comparison of Two Combining Tech-

niques for Equal Gain, Trellis Coded Diversity Receivers, IEEE Transactions

on Vehicular Technology, Volume 44, Issue 2, May 1995

[26] D. V. Djonin, V. K. Bhargava: On the Influence of the Power Profile on

Diversity Combining Schemes, IEEE Transactions on Wireless Communica-

tions, Volume 3, Issue 5, Sept. 2004

[27] H.-C. Yang, M.-S. Alouini: MRC and GSC Diversity Combining With an

Output Threshold , IEEE Transactions on Vehicular Technology, Volume 54,

Issue 3, May 2005

[28] S. Gollakota, R. Viswanathan: Order Statistics Based Diversity Combin-

ing for Fading Channels, Conference Record of the Thirty-Second Asilomar

Conference on Signals, Systems & Computers, 1998

[29] H. Sano, M. Miyake, T. Fujino: Performance of Diversity Combining

Scheme Using Simplified Weighting Factor , Universal Personal Communi-

cations. 1995. Record., 1995 Fourth IEEE International Conference on

[30] E. A. Fain, Mahesh K. Varanasi: Diversity Order Gain for Narrow-Band

Multiuser Communications with Pre-Combining Group Detection, IEEE

Transactions on Communications, Volume 48, Issue 4, April 2000

[31] T. Eng, N. Kong, L. B. Milstein: Comparison of Diversity Combining Tech-

niques for Rayleigh-Fading Channels, IEEE Transactions on Communica-

tions, Volume 44, Issue 9, Sept. 1996

[32] D. J. Love, R. W. Heath: Equal Gain Transmission in Multiple-Input

Multiple-Output Wireless Systems, IEEE Transactions on Communications,

Volume 51, Issue 7, July 2003

[33] Y. G. Kim, S. W. Kim: New Generalized Selection Combining for BPSK Sig-

nals in Rayleigh Fading Channels, IEEE Global Telecommunications Con-

ference, 2001

[34] A. I. Sulyman, M. Kousa: Bit Error Rate Performance Analysis of a

Threshold-Based Generalized Selection Combining Scheme in Nakagami

Fading Channels, EURASIP Journal on Wireless Communications and Net-

working, Volume 2005, Issue 2, April 2005

[35] L. Aydin, E. Esteves, R. Padovani: Reverse link capacity and coverage im-

provement for CDMA cellular systems using polarization and spatial diver-

sity, IEEE International Conference on Communications, 2002

23



[36] R. A. Carrasco, R. Uribeetxeberria: Neural network space diversity combi-

nation and ring coding for multicarrier CDMA over fast fading channels,

IEE Proceedings on Communications, April 2003

[37] Z. Zvonar: Combined multiuser detection and diversity reception for wire-

less CDMA systems, IEEE Transactions on Vehicular Technology, Feb 1996

[38] M. Juntti: Performance analysis of linear multiuser receivers for CDMA

in fading channels with base station diversity, IEEE VTS 50th Vehicular

Technology Conference, Sept 1999

[39] T. Ihara, S. Tanaka, M. Sawahashi: Performance of coherent adaptive an-

tenna array beamforming combined with MRC diversity techniques in W-

CDMA reverse link , 12th IEEE International Symposium on Personal, In-

door and Mobile Radio Communications, 2001

[40] Q. M. Rahman, A. B. Sesay: Non-coherent MT-CDMA system with diversity

combining, Canadian Conference on Electrical and Computer Engineering,

2001.

[41] S. Hara, R. Prasad: DS-CDMA, MC-CDMA and MT-CDMA for mobile

multi-media communications, IEEE 46th Vehicular Technology Conference,

1996

[42] Qualcomm, QUALCOMM CDMA Technologies Announces 1xEV High-

Speed Data Chipset and System Software for Handsets, Press Release, Oct.2000

[43] Qualcomm, QUALCOMM Demonstrates its UMTS and HSDPA Solutions

for Global Wireless Market at 3GSM World Congress, Press Release, Feb.

2006

[44] G. Faria, Mobile DVB-T Using Antenna Diversity Receivers, Harris Broad-

cast Communications, Feb. 2001

[45] J. Lorincz, D. Begusic, Physical layer analysis of emerging IEEE 802.11n

WLAN standard , The 8th International Conference on Advanced Communi-cation Technology, 2006

[46] IEEE Std 802.16-2004, IEEE Standard for Local and Metropolitan Area

Networks Part 16: Air Interface for Fixed Broadband Wireless Access Sys-

tems, Oct. 2004

[47] IEEE Std 802.16e-2005 and IEEE Std 802.16-2004/Cor 1-2005, Amendment

2 and Corrigendum 1 to IEEE Std 802.16-2004, Feb. 2005

24



[48] J. Hämäläinen, R. Wichman: Closed-Loop Transmit Diversity for FDD

WCDMA Systems, The Thirty-Fourth Asilomar Conference on Signals, Sys-

tems and Computers, 2000.

[49] Evolved Universal Terrestrial Radio Access (E-UTRA); Long Term Evolu-tion (LTE) physical layer; General description, Approved Report of 3GPP

TSG RAN WG1 #46bis, Nov. 2006

[50] Evolved Universal Terrestrial Radio Access (E-UTRA); Long Term Evolu-

tion (LTE) physical layer; General description , (Draft1) Report of the 35th

3GPP TSG RAN meeting, Mar. 2007

[51] Evolved Universal Terrestrial Radio Access (E-UTRA); Long Term Evolu-

tion (LTE) physical layer; General description, Draft Report of 3GPP TSG

RAN WG1 #49b v0.1.0, Aug. 2007

[52] T. Haselton: A need for speed: 802.11n router roundup, Aug.

2007 [Available online: http://arstechnica.com/reviews/hardware/802-11n-

router-roundup.ars]

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