1820
`Comparison of Diversity Combining Techniques for GSM
`Mika Raitola and Pekka A. Ranta
`Nokia Research Center,
`P.O.Box 45, FIN-0021 1 Helsinki, Finland
`
`ABSTRACT This paper studies diversity combining
`techniques in the GSM based systems. A pre-detection
`maximal-ratio diversity
`receiver
`for GSM'
`is
`presented. It is an optimum diversity demodulator for
`band-limited channels with Gaussian noise and
`intersymbol interference. The performance of diversity
`combining techniques is studied in the GSM data
`channel. The effects of correlation between diversity
`channels is also studied. The best diversity combining
`technique is found to be the presented pre-detection
`maximal-ratio technique.
`
`1. Introduction
`
`The number of users in mobile radio is growing
`rapidly seting tighter requirements for frequency band
`usage. In the development of GSM to the phase 2+ and
`the development of UMTS, the ultimate performance
`of the GSM based systems must be researched. One
`limiting factor in the performance of the GSM radio
`interface is multipath fading. To reduce the effects of
`fading several well known diversity techniques can be
`applied either in the transmitter or the receiver. If the
`diversity branches are with low correlation significant
`performance gains can be achieved. The information in
`diversity signals must be combined as efficiently as
`possible, otherwise some decibels of potential diversity
`gain can be lost.
`
`In this paper we focus on the diversity combining in
`receiver and assume that there are two diversity paths.
`In the uplink these paths can be created by using space
`diversity, which is already used in the GSM base
`stations. In the downlink pure space diversity is not so
`useful as in the uplink, because mobile station antennas
`can not be physically far enough separated. One
`promising
`diversity
`technique
`in mobiles
`is
`polarization diversity.
`
`This paper is organized as follows. First we introduce
`the readers
`to
`the diversity combining and the
`performance of theoretical diversity. Next we present
`an optimal pre-detection diversity combining. Then the
`simulation models in the link level is presented. Next
`we show the simulation results and achieved diversity
`gains. Finally the conclusions are drawn.
`
`'In this presentation GSM refers to any GSM based system,
`e.g. DCS 1800, PCS 1900, etc.
`0-7803-3336-5/96 $5.00 0 1996 IEEE
`
`2. Diversity Combining Techniques
`
`Diversity combining can be done before or after signal
`detection. If diversity combining is done after signal
`detection, it is said to be post-detection combining,
`otherwise it is pre-detection combining. In the case of
`pre-detection combining diversity signals must be co-
`phased before they can be combined.
`
`There are four major techniques to combine the signals
`from diversity paths:
`
`1. Selection combining (Se) means that the best of
`two received signals is selected according some
`quality measurement, which can be e.g. signal
`level, power or signal-to-noise ratio. In the GSM
`based systems the burst-type transmission is used
`and it is best to do diversity selection burst by
`burst.
`
`2.
`
`the
`that one of
`means
`diversity signals is selected, based on a given
`threshold level in one receiver. If one signal above
`some threshold is selected, it is received until the
`signal falls below the threshold level.
`
`3. Maximal-ratio combining (MRC), first proposed
`by Kahn [I], is a weighted sum of the input
`signals. Weighting factor can be signal level,
`power or signal-to-noise ratio. Following figure
`describes the maximal-ratio principle.
`
`v
`
`Figure 1. The principle of a two antenna maximal-
`ratio receiver
`
`4. Equal-gain combining (EGC) means that baseband
`signals are summed. In the equal-gain combining
`there is no signal scaling like in the maximal-ratio
`combining.
`
`If we have L diversity channels which are carrying the
`same
`information and which are
`independently
`Rayleigh fading and corrupted by uncorrelated additive
`zero mean white Gaussian noise, then we can write the
`
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`MM EX1011, Page 1
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`

`

`"=(?) z(
`
`L L - l L - l + k
`
`1821
`
`efficient method to implement the maximum likelihood
`estimation is the Viterbi algorithm. The usage of the
`Viterbi algorithm requires recursive formulation of (5).
`For IS1 channels Forney [5] has first derived the
`recursive form of (5). In the following we use the
`alternative metrics
`computation
`defined
`by
`Ungerboeck [3]
`
`bit-error-probability for theoretical diversity. In the
`case of the binary PSK this can be expressed as
`follows [2]
`
`1 + p k
`k )(T) '
`
`(')
`
`where yc represents the average signal-to-noise ratio
`per channel.
`
`2 ~ i ~ ) + u f ) / , - 2 Z / rn U ( ' ) n - m ) ]
`mSn-l
`
`r
`
`7
`
`3. Optimal Pre-detection Diversity
`this section we show the optimum diversity
`In
`demodulator for band-limited channel with Gaussian
`noise and intersymbol interference. This derivation is a
`generalization of the derivation given by Proakis [2].
`The received signal can be written as
`
`r ( t ) = CZ,h(t-nT)+z(t),
`n
`where h(t) represents the response of the channel, z(t)
`represents the additive Gaussian noise and In is the
`information sequence.
`
`(3)
`
`In the following we consider two branch diversity
`receiver, although the result can be generalized to any
`number
`of
`branches.
`Maximum-likelihood
`demodulator maximizes the joint probability function
`p(rdIp) of the random variables r N conditioned by the
`transmitted sequence Ip. In the case of two branch
`diversity receiver, which receives the uncorrelated
`sequences r&*) and rk(2), the joint probability can be
`expressed as
`
`p(ri),rg)llp) = p ( ~ ~ ) ~ ~ p ) p ( ~ ~ ) ~ ~ p )
`
`44)
`The logarithm of the joint probability is proportional to
`the quantity Jo, defined as
`
`J o (Ip) = - 7 ( l ~ ~ ~ ) ( l ) - ~ , n * ( ~ - n ~ ) ( l ) + r(f)(2)-~~nh(f-n~)(2)
`II
`I'>.
`
`-ea
`
`n
`
`n
`
`(5)
`The most probable transmitted sequence is the one
`which maximizes this quantity. A computationally
`
`*
`
`(6)
`where { ak} : s represent the autocorrelation values of
`the channel impulse response and { y k } : ~ are the
`outputs of the channel matched filters. From (6) it is
`evident that an optimum maximum-likelihood diversity
`receiver can be implemented by summing the output
`signals of
`the two channel matched filters and
`summing the autocorrelation values (see fig. 3). This
`implementation has an advantage that the Viterbi
`metrics computation of no-diversity receiver can be
`used.
`
`4. Simulation Model
`
`The performance of diversity combining techniques is
`evaluated by means of bit level simulations of the
`GSM
`full
`rate data channel
`(TCWF9.6). The
`simulation model inclludes blocks for transmitter,
`channel, noise and receiver. The simulation principle is
`the Monte Carlo method and COSSAP simulation tool
`is used. The following basic simplifications are done:
`
`1. Complex envelope: presentation for the radio
`channel and RF parts of the receiver and the
`transmitter.
`
`2. Analog radio signals are presented in digital
`domain.
`
`3. The
`frequency synchronization
`time and
`assumed to be ideal.
`
`is
`
`The used channel propagation model is Typical Urban
`with mobile speed 50 k d h , specified in [4]. There is
`also a possibility to specify correlation between
`diversity channels. Random Gaussian noise is added in
`the both signals after Rayleigh fading channel. The
`carrier frequency l750 MHz and
`are wed.
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`

`1822
`
`v v
`
`s
`
`$1
`
`Data-
`source
`
`trasmitter
`
`-I
`
`Rayleigh-fading
`channel
`
`Rayleigh-fading
`channel
`
`Comparison
`
`I
`
`GSM-
`1 diversity
`receiver
`
`I
`
`Figure 2. The simulation environment
`
`Four different diversity receivers are studied:
`
`1. pre-detection maximal-ratio, defined by (6).
`
`2. post-detection maximal-ratio
`
`3. pre-detection equal-gain
`
`4. selection
`
`and
`In the receivers signals are at the first =-filtered
`A/D-converted. After this channel impulse responses
`are estimated and signals are filtered by the channel
`matched filter and autocorrelation values of
`the
`channel impulse response estimates are calculated. In
`the pre-detection maximal-ratio receiver signals are
`summed at this point and after this combined signal is
`detected in the ML-detector. Pre-detection equal-gain
`receiver
`is similar, except the
`impulse response
`estimates of both channels are forced to have equal
`energy. In the post-detection maximal-ratio receiver
`both signals are detected separately and after this they
`are scaled by the signal-to-noise ratio and then they are
`summed. In the selection receiver both signals are
`detected separately, which is followed by the selection
`of the best signal according the signal-to-noise ratio.
`Fig. 3 illustrates a block diagram of the pre-detection
`maximal-ratio receiver.
`
`5. Simulation Results
`
`Diversity combining is simulated at the first in a single
`path Rayleigh fading channel without channel coding
`and the results are shown in Fig. 4. Also theoretical
`values according (1) are shown. The performance of
`the pre-detection diversity and no-diversity receivers
`are about 2 dB weaker than theoretical results. The
`reason for this is the imperfect channel estimation
`caused by noise and residual intersymbol interference.
`
`Channel-
`estimator
`
`1 correlation
`Auto-
`I
`
`1
`
`conversion
`
`Matched-
`filter
`
`/-
`
`1 conversion I
`h
`[ Matched- L
`
`C h a n n e I -
`estimator
`
`1
`
`correlation
`
`I
`
`Figure 3. Pre-detection maximal-ratio diversity
`receiver
`
`Receiver
`
`Pre-detection maximal-ratio
`maximal-ratio
`Pre-detection equal-gain
`Selection
`
`Diversity
`Gain
`4.8 dB
`4.4 dB
`4.2 dB
`
`I 3.2dB
`
`I
`
`As a next step the performance of diversity combining
`is studied in the GSM 9.6 kbit/s data channel in the
`noise
`limited environment. The best combining
`technique is found to be the pre-detection maximal-
`ratio combining. The results are shown in the Fig. 5
`and the diversity gains of various receivers in the GSM
`specified performance point (BER 0.3%) [4] are shown
`in the Table 1.
`
`Next we study how presented pre-detection maximal-
`ratio receiver perform if there is correlation between
`the diversity channels. The receiver is simulated with
`0.0, 0.3, 0.7 and 1.0 correlation between the diversity
`channels and the results are shown in the Fig. 6. When
`compared to the 0.0 correlation case the correlation of
`0.3 decreases the performance of pre-detection receiver
`0.1 dB and the correlation of 0.7 decreases the
`performance 0.7 dB. When correlation is 1.0 there still
`is 3.0 dB diversity gain left. The reason is that the
`signals are summed coherently and noise is summed
`non-coherently .
`
`IPR2020-00038
`MM EX1011, Page 3
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`

`

`GSM diversity
`
`a Theoretical
`8 Simulated
`
`1823
`
`6 Post-detect MRC
`GSM diversity
`Pre-detect EGC
`TCH/F9 6, TU50, FH and 1750MHz
`D sc
`Correlation betreen ehanni,ls 0 3 0 7 w d I O 0 Without diversity
`
`10-1
`
`10-2
`
`LE w m
`
`"
`
`I
`
`0. 0.
`
`"
`
`
`
`.
`
`,
`10.
`10.
`
` '\\ /
`
`,
`
`I
`
`,
`
`.
`
`I
`
`,
`
`20 20
`
`'. '.
`
`I
`
`
`30 30
`
`Figure 4. Theoretical diversity vs. simulated diversity
`in the single path Rayleigh fading channel.
`
`GSM diversity
`TCH/F9 6. TU50 FH and 1750MHz
`
`\
`
`.
`
`
`
`8 Pre-detect MRC
`a Post-detect MRC
`,st-detect MRC
`e-detect EGC
`Pre-detect EGC
`
`I 0 Without diversity U sc 0 Without diversity
`
`-2.5
`
`0.0
`
`2.5
`
`5.0
`
`7.5
`
`Ec/No
`
`[dBl
`1 6 . 1 1 . 1 9 9 5 U i k ~ R d b h INRC)
`
`Figure 5. The BER performance of diversity receivers
`in the noise limited GSM 9.6 kbit/s data channel
`(TCH/F9.6).
`
`a Pre-detect MRC
`GSM diversity
`TCH/F9.6. TU50. FH and 1750MHz 0 Without diversity
`
`10-2 -
`
`10-3 -
`
`m
`
`10-4 -
`
`-2 5
`
`0 0
`
`2 5
`
`5 0
`
`I
`
`
`I I
`
`7 5 7.5
`
`Ec/No
`
`[dBl
`90.7.1998 W&m RPntolo INRC)
`
`Figure 6. The BER performance of the pre-detection
`maximal-ratio receiver when correlation between
`diversity branches is 0.0, 0.3, 0.7 and 1.0.
`
`10
`
`10-2 7
`
`m w
`m
`
`IO+ -
`
`-2 0
`
`'
`
`,
`0 0
`Ec/No
`
`I
`2 0
`
`
`
`I
`4 0
`
`I
`6 0
`[dBl
`19 a 199B M.ka R d & h I#RC
`
`Figure 7. The BER pqformance of the post-detection
`maximal-ratio, pre-detection equal-gain and selection
`receiver when correlation between diversity branches
`is 0.3, 0.7 and 1.0.
`
`Finally we study how other three diversity receivers
`perform if there is correlation of 0.3, 0.7 and 1.0
`between the diversity channels. The results are show in
`the Fig. 7. Post-detection maximal-ratio and pre-
`detection equal-gain receivers have almost the same
`performance when correlation is 0.3 or 0.7, but when
`correlation is 1 .O post-detection combining gives 2.3
`dB diversity gain and pre-detection 3.0 dB gain.
`
`6. Summary
`
`In this study we have done a comparison between four
`diversity combining
`techniques. A pre-detection
`maximal-ratio diversity receiver for GSM has been
`presented.
`
`The performance of different diversity combining
`techniques is studied by Monte Carlo simulations in
`the GSM data channel. The best diversity combining
`technique is found to be the pre-detection maximal-
`ratio combining which gives 4.8 dB diversity gain. The
`post-detection maximal-ratio and the pre-detection
`equal-gain receivers have diversity gains of 4.4 dB and
`4.2 dB. The selection receiver is the weakest.
`
`A small amount of correlation (0.3) between diversity
`branches has only a slight effect to the performance of
`diversity. When diversity signals are totally correlated
`post-detection combining gives 2.3 dB gain. In this
`case pre-detection combining sums signals coherently
`and noise non-coherently and thus gives theoretical 3.0
`dB diversity gain.
`
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`1824
`
`7. References
`[l] L. R. Kahn, Ratio Squarer, Proc. IRE, Vol. 42, pp.
`1704, Nov. 1954
`[2] J. G. Proakis, Digital Communications, McGraw-
`Hill, 1989
`[3] G. Ungerboeck, Adaptive Maximum-Likelihood
`Receiver for Carrier-Modulated Data-transmission
`Systems, IEEE Trans. Com., Vol. 22, No. 5, pp.
`624-636, May. 1974
`[4] GSM 5.05, Radio Transmission and Reception,
`ETSI, March. 1995
`[5] G. D. Fomey, Maximum-Likelihood Sequence
`Estimation of Digital Sequences in the Presence of
`Intersymbol Interference, IEEE Trans. Inform.
`Theory, Vol. 18, pp. 363-378, May. 1972
`
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