United States Patent (19)
`Sousa et al.
`
`54) TRANSMITTER ANTENNA DIVERSITY AND
`EADING-RESISTANT MODULATION FOR
`WIRELESS COMMUNICATION SYSTEMS
`
`75 Inventors: Elvino S. Sousa, 425 Glencairn
`Avenue, North York, Ontario, Canada,
`M5N 1V4; Victor M. DaSilva, Morris
`Plains, N.J.
`73 Assignee: Elvino S. Sousa, North York, Canada
`
`Appl. No.: 721,966
`21
`22 Filed:
`Sep. 27, 1996
`51
`Int. Cl. ............................. H04B 7/10; H04B 11/12;
`H04L27/10; H04L27/04
`52 U.S. Cl. .......................... 375/347; 375/280; 375/281;
`375/299; 455/132
`58 Field of Search ..................................... 375/347, 299,
`375/267, 286, 200, 222, 279-281,308;
`455/101, 132, 277.1, 277.2
`
`56)
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`
`5,048,057 9/1991 Saleh et al. ............................. 375/267
`5,088,113 2/1992 Wei..........
`... 375/280
`5,216,694 6/1993 Wei..................
`... 375/286
`5,289,501
`2/1994 Seshadri et al. .
`... 375/286
`5,636.242 6/1997 Tsujimoto ........
`... 375/200
`5,640,417 6/1997 Barabash et al. ....................... 375/222
`Primary Examiner-Chi H. Pham
`ASSistant Examiner Khai Tran
`
`
`
`USOO5832044A
`Patent Number:
`11
`(45) Date of Patent:
`
`5,832,044
`Nov. 3, 1998
`
`Attorney, Agent, or Firm-Lynn C. Schumacher; Hill &
`Schumacher
`
`57
`ABSTRACT
`The present invention provides abandwidth-efficient fading
`resistant transmission Scheme where a base Station imple
`ments transmitter diversity using L antennas or L carrier
`frequencies or L time slots, regardless of the use of frame
`oriented power control. When the antennas or carriers are
`Spaced Sufficiently far apart, or when a different power is
`used for each power control frame, the transmission from
`each antenna or carrier or time frame undergoes independent
`fading. These transmissions are coordinated to mitigate the
`effects of Rayleigh fading and the mobile receiver can
`recover the entire L-dimensional transmitted vector as long
`as the Signal energy of at least one coordinate is large
`enough. L-dimensional fading-resistant Signal constellations
`are generated by maximizing a figure of merit for the
`Rayleigh fading channel. This Scheme offers a significant
`performance improvement over a conventional Single
`antenna or single-carrier narrowband BPSK Scheme when
`coding is ineffective due to slow fading. When there is
`background white Gaussian noise, the fading-resistant
`Scheme has a significant energy Savings advantage over an
`uncoded BPSK scheme, for a given bit error rate. In the
`forward link of a cellular network, where cochannel inter
`ference is the dominant Source of noise, the fading-resistant
`Scheme results in a significant capacity increase over
`uncoded BPSK, for a given bit error rate. Both coherent and
`differentially coherent Systems are disclosed.
`
`25 Claims, 5 Drawing Sheets
`
`ROTATED CONSTELLATION
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 1 of 18
`
`

`

`U.S. Patent
`
`Nov. 3, 1998
`
`Sheet 1 of 5
`
`5,832,044
`
`
`
`BASE
`STATION
`
`...,m) e C
`
`MINIMUM
`DISTANCE
`DECODER
`
`CHANNEL
`ESTMATOR
`
`FIG. 2
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 2 of 18
`
`

`

`U.S. Patent
`
`Nov. 3, 1998
`
`Sheet 2 of 5
`
`5,832,044
`
`m2 (.325, 1.376)
`
`(-1.376, 325)
`O
`
`(1.376, -.325)
`
`O
`(-325, -1.376)
`ROTATED CONSTELLATION
`
`FIG.3b
`
`m2
`
`(-.447, .341)
`O
`
`
`
`(.341, .447)
`
`O
`(-1.341, - .447)
`
`FIG.3C
`
`O
`(.447-1.341)
`KERPEZ CONSTELLATION
`
`BASELNE CONSTELLATION
`
`FIG.3d
`(PRIOR ART)
`
`
`
`BASELINE CONSTELLATION
`FIG.4d
`(PRIOR ART)
`
`m2
`ROTATED CONSTELLATION
`FIG. Ab
`
`m
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 3 of 18
`
`

`

`U.S. Patent
`
`Nov. 3, 1998
`
`Sheet 3 of 5
`
`5,832,044
`
`
`
`(j)
`X m 1, Ö (t- iT)
`
`S(t)
`
`
`
`DECISION
`DEVICE
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 4 of 18
`
`

`

`U.S. Patent
`
`Nov. 3, 1998
`
`Sheet 4 of 5
`
`5,832,044
`
`O 3 uu
`
`NOISIOECI
`
`BO?AECI
`
`
`
`
`
`** LA
`
`
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 5 of 18
`
`

`

`U.S. Patent
`
`Nov. 3, 1998
`
`Sheet 5 of 5
`
`5,832,044
`
`
`
`(my,...,m) e C
`
`DECISION
`DEVICE
`
`(o',..., ot)
`CHANNEL
`ESTIMATOR
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 6 of 18
`
`

`

`5,832,044
`
`15
`
`25
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`35
`
`40
`
`1
`TRANSMITTER ANTENNA DIVERSITY AND
`EADING-RESISTANT MODULATION FOR
`WIRELESS COMMUNICATION SYSTEMS
`FIELD OF THE INVENTION
`The present invention relates to a method of fading
`resistant modulation for wireleSS communication Systems
`prone to Rayleigh fading. More particularly, the method
`relates to the use of transmitter diversity and the design of
`transmission signal Space constellations used there with
`which are resistant to fading compared to Systems not using
`transmitter diversity. The resulting constellation Symbols are
`represented as vectors in L-dimensional Space and their
`components are transmitted in different antennas, carrier
`frequencies, or time slots which have been designed to
`undergo essentially independent fading. The resulting
`Scheme has a significantly Superior performance to a System
`not using diversity or a System that uses the Standard
`L-dimensional hypercube (with different components being
`transmitted over different antennas, frequencies, or time
`slots) as the Signal constellation.
`BACKGROUND OF THE INVENTION
`A major problem associated with wireleSS communication
`Systems is fading of the transmitted Signal of the type arising
`due to multi-path propagation of the radio signal in which
`the amplitude of the Signal undergoes random fluctuations at
`the receiver. Such random fluctuations are typically mod
`elled by a Rayleigh distributed random variable and the
`resulting fading is typically referred to as Rayleigh fading.
`Examples of Such channels include the mobile radio com
`munications channel where signals are reflected from build
`ings and mountains, indoor wireleSS communication chan
`nels where signals are reflected by walls, furniture, and
`people.
`In a digital communication System information is trans
`mitted as a Sequence of Symbols belonging to Some signal
`ling alphabet. The Signalling alphabet is represented as a Set
`of Q vectors in an L-dimensional vector Space and is referred
`to as the Signalling constellation. These vectors are also
`referred to as points in the Signalling constellation. Each
`transmitted Symbol (vector, or point) carries log-O bits of
`information.
`The problem of Signal fading manifests itself as a distor
`tion of the Signalling constellation where Some of the points
`move closer together. The result is that at the receiver errors
`are made during the detection process (information
`decoding) where a given transmitted constellation point is
`interpreted as a different constellation point as a result of
`channel noise and errors in transmission occur. Techniques
`to reduce the problem of Rayleigh fading include the use of
`frequency, time, and antenna diversity. With frequency
`diversity signals are transmitted over different carrier fre
`quencies, with time diversity Signals are transmitted over
`different time slots, and with antenna diversity the Signal is
`transmitted or received over multiple antennas.
`In typical frequency or time diversity the same signal is
`transmitted over the different carrier frequencies or time
`slots. This results in a decrease of the number of bits per
`Hertz and a consequent loSS in Spectral efficiency. With
`receiver antenna diversity the same signal is received over
`different antennas, there is no loSS in Spectral efficiency, but
`there is a requirement for the use of at least two antennas at
`the receiver with a Sufficient Separation which may be
`difficult to implement in small terminals.
`To maintain a high spectral efficiency frequency or time
`diversity should be based on the transmission of different
`
`45
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`
`2
`information symbols over the different frequencies or time
`slots However if we split the information bit stream into a set
`of SubStreams and transmit each Sub-Stream over a different
`frequency or time slot then there is no benefit to using
`diversity. Thus far the use of antenna diversity has been
`relegated mostly to the receiver. Some Schemes of transmit
`ter diversity have been developed where a signal and a
`delayed version of itself have been transmitted on two
`Separate antennas. The effect is to make the channel fre
`quency Selective and to allow for the use of equalizers at the
`receiver. Another approach to implement transmitter diver
`sity is to transmit different bit streams on the different
`antennas and use orthogonal signals So that the transmis
`Sions over the different antennas do not cause mutual inter
`ference. This Scheme then becomes Similar to the Spectrally
`efficient Schemes for frequency and time diversity that we
`have discussed above but also does not achieve the usual
`benefits of diversity.
`If we consider the Spectrally efficient transmitter antenna,
`frequency, and time diversity Schemes where the informa
`tion bit Stream is divided into Sub-Streams and where each
`Sub-Stream is transmitted over a different antenna, a different
`frequency, or a different time slot, then taken jointly the
`transmission of a set of Symbols can be viewed as the
`transmission of a Super symbol where in the case of BPSK
`this Super-Symbol can be represented by a vertex in an
`L-dimensional hyper-cube where L is the number of
`antennas, frequencies, or time slots. The reason for the poor
`performance of this Scheme is that the hypercube Signalling
`constellation is not fading-resistant. The main reason for the
`lack of fading-resistance is that for this constellation, com
`pression of the constellation parallel to any of the coordinate
`axis (as a result of fading on one antenna, one frequency, or
`one time slot) results in points of the constellation coalesc
`ing thereby resulting in errors in the detected information
`bits. It would therefore be very advantageous to devise
`Signalling constellations which achieve a high degree of
`Spectral efficiency and are fading resistant. Such constella
`tions would consist of points in an L-dimensional vector
`Space where L is the number of antennas, carrier
`frequencies, or time slots with relatively independent fading
`Such that Strong fading in one coordinate (one antenna,
`frequency, or time slot) does not cause two of the constel
`lation points to approach each other.
`Further, In present State of the art cellular Systems the
`transmitter power is adjusted once every preselected time
`frame-power control slot, or power control Sub-group. For
`example, power is adjusted every 20 milli-Second time
`frame in the forward link (base to mobile) of the IS-95
`(CDMA) system or every 1.25 milli-second frame (power
`control group) in the reverse link of this system. In State of
`the art mobile radio Systems power control is one of the key
`issues and future Systems will have Smaller and Smaller
`power control frames. The goal of the power control algo
`rithm is to maintain a constant Signal to noise ratio at the
`receiver. However as a result of the required System over
`head to transmit power control bits and the delay incurred in
`transmitting the power control bits there will always be
`(residual) variations in the received power level from frame
`to frame regardless of the rate of power control adjustments.
`AS a result of the power control, the variation in received
`power level (i.e. power control error) will be independent
`from frame-to-frame. This variation in power level is similar
`to the variations that arise due to fading and as in the case
`of diversity discussed above a spectrally efficient coding
`Scheme (signal constellation) is required to mitigate the
`effect of these power variations and consequently reduce the
`probability of error in the channel.
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 7 of 18
`
`

`

`5,832,044
`
`15
`
`25
`
`35
`
`40
`
`3
`SUMMARY OF THE INVENTION
`The present invention provides a method for fading
`resistant modulation for wireleSS communication Systems
`and addresses the problem of transmitting information with
`propagating Signals through random or fading communica
`tion channels in a spectrally efficient manner. The invention
`provides a method for the use of transmitter antenna,
`frequency, or time diversity, to attain a significant perfor
`mance increase over Systems not utilizing diversity and at
`the Same time avoid the loSS in Spectral efficiency that is
`characteristic of typical transmitter diversity Schemes,
`through the design of transmission Signal Space constella
`tions which are resistant to fading in the Sense that the fading
`of the total received signal is significantly improved in
`comparison to Similar Systems which do not use transmitter
`diversity, or use transmitter diversity with the Standard
`L-dimensional hypercube as the Signal constellation.
`The technique uses transmitter diversity and can be used
`in Systems that employ either of the three types of trans
`mitter diversity: antenna diversity, frequency diversity, or
`time diversity. These diversity techniques consist of the
`Simultaneous transmission of data modulated Signals over a
`Set of L different antennas, L different carrier frequencies, or
`L different time slots, in a coordinated (jointly encoded)
`manner. The waveforms transmitted on the L different
`antennas are designed to be orthogonal. These waveforms
`are also inherently orthogonal in the case of the use of L
`carrier frequencies or L time slots.
`The L different antennas, L different carrier frequencies,
`or L different time slots, are chosen So that the Signal fading
`is essentially independent among them. Ideally the Signal
`fading over these different diversity paths would be inde
`pendent. AS in typical digital modulation Schemes the trans
`mitter transmits a sequence of Symbols (waveforms) from
`Some fixed symbol alphabet. Each waveform may be rep
`resented as a vector in an L-dimensional vector Space. The
`Signaling alphabet can be represented as a set of vectors
`which is typically called the Signaling constellation. Each of
`these vectorS has L components. In the current invention
`each of the L components of a constellation vector is
`transmitted in a different antenna (case of antenna diversity),
`a different carrier frequency (case of frequency diversity), or
`a different time slot or time frame (case of time diversity).
`If the constellation is chosen as the Set of Vertices of a
`hyper-cube then the transmitter diversity System just
`described would have the same performance as a System
`with the parameter L=1, i.e. no transmitter diversity. How
`ever in the current invention we describe methods to make
`the diversity System have a performance that is significantly
`Superior to that of the non-diversity System by changing the
`Signaling constellation to a new constellation which is
`obtained by maximizing a fading-resistance measure. This
`measure has the characteristics that under the effect of
`Rayleigh fading the points in the Signal constellation main
`tain a large Separation. In particular, this fading resistance
`measure has the characteristics that the resulting derived
`constellation has the property that none of the points of the
`constellation are Superimposed by collapsing the constella
`tion parallel to any of the coordinate axes.
`In a preferred embodiment of the method the points of the
`Signalling constellation are obtained by Starting with the
`L-dimensional hypercube and transforming it by applying an
`orthogonal transformation (a set of rotations and reflections)
`in L-dimensional Space. More generally, the fading resistant
`constellation is obtained from the L-dimensional hyper-cube
`constellation by representing the hypercube constellation as
`
`45
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`65
`
`4
`a matrix, with rows equal to the signaling vectors (vertices
`of the hyper-cube), and multiplying this matrix by an LXL
`orthogonal matrix. A procedure to find good orthogonal
`transformation matrices is given and Some good Sets of
`rotation matrices (orthogonal transformation matrices) for
`the 2,3,4,5 dimensional cases are specified.
`We also realize that there are other constellations, which
`are not obtained from the L-dimensional hyper-cube by an
`orthogonal transformation, which would have a high degree
`of fading-resistance. One Such example is the KerpeZ con
`Stellation which was designed for transmitting Signals on
`wireline channels with non-symmetric noise characteristics.
`In another embodiment of the method of the present
`invention the Signals transmitted in each antenna, carrier
`frequency, or time slot, which correspond to particular
`components of the Signaling vectors, are differentially
`encoded. AS for the previous case (the case of coherent
`detection) the use of the L-dimensional hypercube as a
`Signaling constellation offers no advantage for the transmit
`ter diversity System over the case L=1. However, a trans
`formed constellation (different orthogonal matrix than
`above) offers significant improvements. This differential
`Scheme can also be used in Systems with either of the three
`types of diversity: antenna, frequency, or time.
`In this disclosure we give the approach to find good
`orthogonal transformations (generalized rotation matrices)
`by factoring the orthogonal matrix into a product of Givens
`matrices and doing a computer Search for optimum rotation
`angles. Minor modifications to this approach and other
`approaches will produce other rotation matrices which have
`Similar fading resistance and are significantly better than the
`Standard hypercube constellation.
`The method disclosed herein is advantageous in Systems
`which Suffer from the So-called frequency non-Selective
`fading (also called flat fading) and where it is difficult to
`implement receiver antenna diversity. In Such a System it is
`typically desirable to implement transmitter antenna diver
`sity Since the receiver terminal is Small and does not have the
`required dimensions to allow the installation of multiple
`antennas with Sufficient inter-antenna Spacing. The base
`Station to mobile terminal link of a cellular System is a prime
`example of this application, especially in cases where the
`transmitted Signal bandwidth is not significantly greater than
`the coherence bandwidth of the channel.
`In a digital cellular System Such as those Standardized in
`IS-136, IS-95, GSM, information bits are transmitted in
`blocks (slots, time frames). In these systems the transmitter
`power is typically controlled (adjusted) So as to attempt to
`maintain a constant power (or Signal to noise ratio) at the
`receiver. In the case of IS-95 the power is controlled
`(adjusted) once every 20 milli-Second time frame in the
`forward channel and once every 1.25 milli-second time
`frame in the reverse channel. However when the terminal is
`in motion even after the control of power there is still a
`residual variation in the power of the received signal within
`the power control time frame. This variation is Similar to
`Signal fading. The method disclosed herein can be used to
`encode the transmitted Signal in Such a way that different
`components of each Signal constellation vector are trans
`mitted in different time slots and hence undergo different
`variations in received power level. The rotated constella
`tions presented (whether for the case of coherent detection
`or differential detection) will have significant performance
`gains over the Standard hypercube constellations which in
`this case correspond to transmitting all the components of
`each constellation point Sequentially in the Same time frame.
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 8 of 18
`
`

`

`5,832,044
`
`6
`FIG. 3c is a Kerpez constellation (L=2) which when used
`according to the present invention provides increased fading
`resistance;
`FIG. 4a prior art baseline constellation for L=3;
`FIG. 4b is a rotated constellation (L=3) constructed
`according to the present invention;
`FIG. 5 is a block diagram of a multi-frequency transmitter
`for a base Station;
`FIG. 6 is a block diagram of a multi-frequency receiver
`for receiving transmissions from the transmitter of FIG. 5;
`FIG. 7 illustrates a power control frame with 8 signalling
`intervals with the Signalling vector L=2;
`FIG. 8 is a block diagram of a differentially coherent
`receiver used in the method of the present invention; and
`FIG. 9 is a block diagram of a differentially coherent
`multi-frequency receiver with L demodulators used in the
`case where transmitter diversity is implemented using multi
`frequency transmission in which the mobile receiver does
`not track the carrier phases of the L transmissions.
`DETAILED DESCRIPTION OF THE
`INVENTION
`
`1O
`
`15
`
`S
`The present method provides for the joint encoding of
`Signals transmitted over a set of L-antennas using transfor
`mations of the basic hypercube Signal constellation. The
`invention contemplates joint encoding along time as well as
`acroSS Signals transmitted by different antennas. Such meth
`ods can be realized using trellis codes, convolutional codes,
`or block codes, where each code symbol is a point in the
`constellations disclosed herein and where the different com
`ponents of each constellation point (each trellis code
`Symbol, or convolutional code Symbol, or block code
`symbol) are transmitted in the different antennas (or differ
`ent frequencies, or different time slots).
`In another application a radio System may use L carrier
`frequencies that have a Sufficiently large frequency spacing
`So that the fading is independent over the different frequen
`cies. The case L=2 would be sufficient to result in a
`Significant improvement with our Scheme. In this case we
`design signal constellations which can be represented as Sets
`of points (vectors) in a 2-dimensional space (the plane). In
`this case the hypercube constellation is the well known
`QPSK constellation (except that the two axes correspond to
`two different carrier frequencies and not the two different
`phases-cos and Sin) and applying the method of the present
`invention the orthogonal transformation corresponds to a
`rotation in the plane and provides an optimum rotation angle
`of approximately 31.7 degrees.
`The present invention provides a method of fading
`resistant modulation for wireleSS communication Systems
`using transmitter antenna diversity. The method comprises
`providing an L-dimensional Signalling constellation com
`prising Q points, wherein each point represents a vector in
`a vector Space, the vector Space comprising L orthogonal
`coordinate axes, and the constellation points being Such that
`any two of them are vectors which differ in a plurality of
`their components. The method includes transmitting each of
`Said L components of Said Signalling constellation over one
`of either L different antennas, L different carrier frequencies
`and L different time slots.
`In another aspect the invention provides method of
`fading-resistant modulation for wireleSS communication
`Systems. The method comprises providing an L-dimensional
`Signalling constellation comprising L orthogonal coordinate
`axes and 2 constellation points wherein each of said 2.
`points represent a vector in a vector Space, and the constel
`lation points being Such that any two of them are vectors
`which differ in a plurality of their components. The method
`includes transmitting each of Said L components of Said
`transformed Signalling constellation over one of either L
`different antennas, L different carrier frequencies and L
`different time slots.
`50
`BRIEF DESCRIPTION OF THE DRAWINGS
`The method of fading-resistant modulation for wireless
`communication Systems in accordance with the present
`invention will now be discussed, by way of example only,
`reference being had to the accompanying drawings, in
`which:
`FIG. 1 is a diagrammatic representation of a forward link
`channel model;
`FIG. 2 is a Schematic block diagram of a receiver for
`receiving L orthogonal transmissions,
`FIG. 3a is a prior art baseline constellation for L=2 with
`Q-9;
`FIG. 3b is a rotated constellation (L=2) constructed
`according to the method of the present invention providing
`increased fading resistance in a wireleSS communication
`system over the constellation of FIG. 3a;
`
`25
`
`FADING-RESISTANT MODULATION
`Channel Model 1:Multi-Antenna Transmitter Diversity
`The forward link channel (base station to mobile terminal)
`model is depicted in FIG. 1. The base station has L trans
`mitter antennas, the mobile receiver has a Single antenna,
`and each of the L links has a different fading amplitude. The
`received signal is given by:
`
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`65
`
`L
`
`(1.1)
`
`r(t) =
`Climi's(t)cos(cot + 0) + n(t), Osts T
`The signal from the transmitter's i' antenna is a pulse
`amplitude modulated (PAM) signal and m, is the signal
`amplitude, S(t) is the pulse shape, C is the fading amplitude
`of link l, and n(t) is a white Gaussian noise process with
`power spectral density N/2. It is assumed that the fading
`amplitude for a given link is constant over the Signalling
`interval O.T and that the receiver uses coherent detection.
`The signals S(t), S(t), ii, are assumed to be orthogonal and
`all of the energy of S(t), 1s is L., is contained in O.T. AS
`an example, the Signals may be spread spectrum or code
`division multiple access (CDMA) signals.
`The optimum receiver consists of a bank of L correlators,
`as shown in FIG. 2. The output of the i' correlator is:
`
`T
`
`is the pulse energy and
`
`1sisL, are uncorrelated Zero-mean Gaussian random vari
`ables with variance NoE. The received vector y=(y,y, . .
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 9 of 18
`
`

`

`5,832,044
`
`8
`
`7
`..y.) is fed into a decision device which estimates the
`transmitted vector m=(m,m,...,m). It is assumed that the
`receiver can estimate the fading amplitudes C. The receiver
`finds the L-dimensional constellation point in C, with coor
`dinates Suitably amplified, that has the closest Euclidean
`distance to the received vectory. That is, the receiver pickS
`the Symbol rih=(rihriha, . . . .in)e C that minimizes
`
`5
`
`, (yi/Es Clim)2.
`
`L
`
`=
`
`a.
`
`A Symbol detection error occurs when rinzm.
`It is noted that the transmission bit rate can be increased
`with no loSS in performance and without using more band
`width by transmitting two carriers that are in phase
`quadrature from each antenna. The received signal becomes:
`
`15
`
`O s s t is T,
`where m and m, are the Signal levels corresponding to the
`two orthogonal carriers transmitted on the i' antenna.
`25
`Orthogonality among S(t), 1s is L., ensures that the 2L
`signals do not interfere with one another. Similarly, QPSK
`has the same performance as BPSK and the bandwidth
`efficiency is twice as high.
`The communication links shown in FIG. 1 are not nec
`essarily line-of-Sight. In a multipath environment, where
`there is no line-of-Sight component, a Rayleigh fading
`model is normally assumed. If the channel delay spread is
`Small relative to the Symbol period, orthogonality between
`the L linkS is still possible. The fading amplitudes C, are
`modelled as independent and identically distributed Ray
`leigh random variables with probability density function
`
`35
`
`f...(c)-2ce, C.20.
`
`(1,4)
`
`40
`
`45
`
`50
`
`The assumption of independent fading is valid if the trans
`mitter antennas are spaced Sufficiently far apart, which is
`relatively easy to do when the transmitter is the base Station.
`The fading-resistant transmission Schemes discussed
`hereinafter forming the present invention assume that the
`receiver is capable of estimating the fading amplitude of
`each link This is possible if the fading amplitudes vary
`Slowly over time. If the fading amplitudes vary quickly over
`time, the performance of the receiver will degrade due to
`estimation errors.
`Baseline Scheme: Independent BPSK Signals
`The baseline Scheme consists of a transmitter with L
`antennas which sends either a+1 or -1 bit on each antenna,
`55
`independently of the rest, and the output of the i' correlator
`is given by (1.2) with me{1,-1}. This corresponds to
`Sending independent BPSK Signals on each antenna. There
`is an L-fold expansion in bandwidth over the L=1 case in
`order to have Lorthogonal transmissions but the overall data
`rate also increases by a factor of L. So that there is no
`bandwidth penalty.
`For optimal detection, the correlator output y is fed into
`a threshold device which outputs a 1 if the input is positive,
`and a-1 otherwise. The probability of bit erroris (e.g. see J.
`Proakis, Digital Communications, 2nd edition, McGraw
`Hill Book Company, N.Y., 1989., p. 717)
`
`60
`
`65
`
`(1.5)
`
`1.
`
`Ef No
`P
`1.
`- EN 1
`(error) = -
`where E=CE.2=E/2 is the average received bit energy.
`Eq. (1.5) applies to each of the L links, and So the overall bit
`error rate is also given by (1.5). For this scheme the overall
`bit error rate is independent of L and there is no advantage
`over single-antenna BPSK.
`Construction of Fading-Resistant Constellations
`The ideal figure of merit in the design of Signaling
`constellations is that of the probability of symbol error.
`However, it is an untractable problem in mathematics to
`construct signaling constellations that minimize the prob
`ability of error in Rayleigh fading channels. AS Such we will
`use a Sub-optimal figure of merit. Other Similar figures of
`merit will yield good Signaling constellations. The funda
`mental property of a good Signaling constellation is that the
`encoding of the information bits to the transmitted wave
`forms should be Such that a given information bit has an
`effect on the Signals on a multiple number of coordinates of
`the constellation points. In this respect the L-dimensional
`hypercube, with the edges of the cube being aligned with the
`coordinate axes, is the worst constellation Since in this case
`each information bit affects the Signal in only one
`coordinate, and with fading in that coordinate the bit is lost.
`In other words any two points of the Signaling constellation
`should have a large number of components which differ
`Significantly.
`The following quantity, hereinafter the constellation fig
`ure of merit for the Rayleigh fading channel, gives an
`indication of the performance of a Signal constellation at
`high SNR,
`
`(1.6)
`
`L
`
`(m; - mi)/E
`
`CFMRaleig, (C) = min
`m, meC i=1
`in z in n1zni
`where E is the average Symbol energy of the constellation C.
`Note that (1.6) is scale-invariant, that is, CFM
`(aC)
`=CFM.,(C), where a is a Scalar. We describe a method
`for constructing L-dimensional fading-resistant constella
`tions which have a large CFM. We are interested only
`in constellations where mizrin, 1sis L.
`Given an L-dimensional constellation of Q points, there is
`applied a transformation to the constellation which preserves
`the Euclidean distances between points but improves the
`constellation's resistance to fading. We impose the restric
`tion that the transformation preserve Euclidean distances
`and norms because we do not want to degrade the perfor
`mance of the constellation in the AWGN channel. Such
`transformations are called isometries.
`The original constellation is represented as a CL matrix
`C, where each row of the matrix corresponds to a point in the
`L-dimensional constellation. One example of a distance
`preserving transformation is to multiply this matrix by an
`orthogonal LXL matrix A. The optimal matrix A maximizes
`the fading-resistance of the transformed constellation CA,
`that is, it maximizes CFMr.(CA).
`In Appendix A it is shown how an LXL orthogonal matrix
`A can be written as the product of
`
`()
`
`rotation matrices and a reflection matrix. From (A.5), we see
`that multiplication of the constellation matrix C by an
`
`ERICSSON v. UNILOC
`Ex. 1010 / Page 10 of 18
`
`

`

`5,832,044
`
`10
`For the same bit rate and AWGN channel performance as
`the baseline Scheme, we start off with the L-cube, which is
`the constellation for the baseline Scheme. (This also corre
`sponds to a single energy shell of the Z lattice.) For
`example, when L=2, the baseline constellation matrix is
`
`arbitrary Orthogonal matrix A has the following geometrical
`interpretation. The constellation is rotated with respect to the
`(i,j)-plane by an amount 0, 1s is L-1, i+1 sisL, and there
`ii
`
`()
`
`Such rotations. Then the constellation is reflected in the ith
`axis, where the matrix I has (i,i) entry equal to -1, and the
`number of Such reflections is equal to the number of -1
`elements on the main diagonal of I. Writing A=QI, where Q
`is the product of
`
`()
`
`1O
`
`15
`
`rotation matrices in (A.5), we see that
`
`(1 .7)
`CFMyleigh (CA)=CFMyleigh (CQi) =CFMyleigh (CQ)
`where the second identity in (1.7) follows because the matrix
`CQi is the matrix CQ with several of its columns negated,
`and negati