Method and apparatus for improving detection of data bits in a slow frequency hopping communication system

A method and apparatus is provided for improving detection of data bits in data samples (120) of a hop of a slow frequency hopping spread spectrum signal (112). In the detecting process, the carrier to interference (C/l) power ratio of the hop is estimated (124) by using the data samples (120) of the hop. Subsequently, a data bit (130) is detected by using the estimated C/l power ratio (126). The detection process (128) may include utilizing maximum likelihood decoding techniques to derive a data bit (130) from decision metrics and the estimated C/l power ratio (126). The decision metrics correspond to a measurement of the distance of data samples (120) from constellation points within a constellation space representing data samples (120) previously used to generate decision metrics. The detection process (128) also may include utilizing the estimated C/l power ratio (126) in combining data samples (120) of the hop as received from two or more diversity receiver branches.

FIELD OF THE INVENTION 
The present invention relates to communication systems which employ 
spread-spectrum signals and, more particularly, to a method and apparatus 
for improving a soft decision algorithm in a slow frequency hopping spread 
spectrum communication system. 
BACKGROUND OF THE INVENTION 
Communication systems take many forms. In general, the purpose of a 
communication system is to transmit information-bearing signals from a 
source, located at one point, to a user destination, located at another 
point some distance away. A communication system generally consists of 
three basic components: transmitter, channel, and receiver. The 
transmitter has the function of processing the message signal into a form 
suitable for transmission over the channel. This processing of the message 
signal is typically referred to as modulation. The function of the channel 
is to provide a physical connection between the transmitter output and the 
receiver input. The function of the receiver is to process the received 
signal so as to produce an estimate of the original message signal. This 
processing of the received signal is referred to as demodulation. 
Two types of two-way communication channels exist, namely, point-to-point 
channels and point-to-multipoint channels. Examples of point-to-point 
channels include wirelines (e.g., local telephone transmission), microwave 
links, and optical fibers. In contrast, point-to-multipoint channels 
provide a capability where many receiving stations may be reached 
simultaneously from a single transmitter (e.g. cellular radio telephone 
communication systems). These point-to-multipoint systems are also termed 
Multiple Address Systems (MAS). 
Analog and digital transmission methods are used to transmit a message 
signal over a communication channel. The use of digital methods offers 
several operational advantages over analog methods, including but not 
limited to: increased immunity to channel noise and interference, flexible 
operation of the system, common format for the transmission of different 
kinds of message signals, improved security of communication through the 
use of encryption, and increased capacity. 
These advantages are attained at the cost of increased system complexity. 
However, through the use of very large-scale integration (VLSI) 
technology, a cost-effective way of building the hardward has been 
developed. 
To transmit a message signal (either analog or digital) over a band-pass 
communication channel, the message signal must be manipulated into a form 
suitable for efficient transmission over the channel. Modification of the 
message signal is achieved by means of a process termed modulation. This 
process involves varying some parameter of a carrier wave in accordance 
with the message signal in such a way that the spectrum of the modulated 
wave matches the assigned channel bandwidth. Correspondingly, the receiver 
is required to recreate the original message signal from a degraded 
version of the transmitted signal after propagation through the channel. 
The re-creation is accomplished by using a process known as demodulation, 
which is the inverse of the modulation process used in the transmitter. 
In addition to providing efficient transmission, there are other reasons 
for performing modulation. In particular, the use of modulation permits 
multiplexing, that is, the simultaneous transmission of signals from 
several message sources over a common channel. Also, modulation may be 
used to convert the message signal into a form less susceptible to noise 
and interference. 
For multiplexed communication systems, the system typically consists of 
many remote units (i.e. subscriber units) which require active service 
over a communication channel for a short or discrete portion of the 
communication channel resource rather than continuous use of the resources 
on a communication channel. Therefore, communication systems have been 
designed to incorporate the characteristic of communicating with many 
remote units for brief intervals on the same communication channel. These 
systems are termed multiple access communication systems. 
One type of communication system which can be a multiple access system is a 
spread spectrum system. In a spread spectrum system, a modulation 
technique is utilized in which a transmitted signal is spread over a wide 
frequency band within the communication channel. The frequency band is 
much wider than the minimum bandwidth required to transmit the information 
being sent. A voice signal, for example, can be sent with amplitude 
modulation (AM) in a bandwidth only twice that of the information itself. 
Other forms of modulation, such as low deviation frequency modulation (FM) 
or single sideband AM, also permit information to be transmitted in a 
bandwidth comparable to the bandwidth of the information itself. However, 
in a spread spectrum system, the modulation of a signal to be transmitted 
often includes taking a baseband signal (e.g., a voice channel) with a 
bandwidth of only a few kilohertz, and distributing the signal to be 
transmitted over a frequency band that may be many megahertz wide. This is 
accomplished by modulating the signal to be transmitted with the 
information to be sent and with a wideband encoding signal. 
Three general types of spread spectrum communication techniques exist, 
including: 
Direct Sequence 
The modulation of a carrier by a digital code sequence whose bit rate is 
much higher than the information signal bandwidth. Such systems are 
referred to as "direct sequence" modulated systems. 
Hopping 
Carrier frequency shifting in discrete increments in a pattern dictated by 
a code sequence. These systems are called "frequency hoppers." The 
transmitter jumps from frequency to frequency within some predetermined 
set; the order of frequency usage is determined by a code sequence. 
Similarly "time hopping" and "time-frequency hopping" have times of 
transmission which are regulated by a code sequence. 
Chirp 
Pulse-FM or "chirp" modulation in which a carrier is swept over a wide band 
during a given pulse interval. 
Information (i.e. the message signal) can be embedded in the spread 
spectrum signal by several methods. One method is to add the information 
to the spreading code before it is used for spreading modulation. This 
technique can be used in direct sequence and frequency hopping systems. It 
will be noted that the information being sent must be in a digital form 
prior to adding it to the spreading code, because the combination of the 
spreading code and the information typically a binary code involves 
module-2 addition. Alternatively, the information or message signal may be 
used to modulate a carrier before spreading it. 
Thus, a spread spectrum system must have two properties: (1) the 
transmitted bandwidth should be much greater than the bandwidth or rate of 
the information being sent and (2) some function other than the 
information being sent is employed to determine the resulting modulated 
channel bandwidth. 
Spread spectrum communication systems can be implemented as multiple access 
systems in a number of different ways. One type of multiple access spread 
spectrum system is a code division multiple access (CDMA) system. CDMA 
spread spectrum systems may use direct sequence (DS-CDMA) or frequency 
hopping (FH-CDMA) spectrum spreading techniques. FH-CDMA systems can 
further be divided into slow frequency hopping (SFH-CDMA) and fast 
frequency hopping (FFH-CDMA) systems. In SFH-CDMA systems several data 
symbols, representing a sequence of data bits which are to be transmitted, 
modulate the carrier wave within a single hop. Whereas, in FFH-CDMA 
systems the carrier wave hops several times per data symbol. 
In a SFH-CDMA system, multiple communication channels are accommodated by 
the assignment of portions of a broad frequency and or time band to each 
particular channel. For example, communication between two communication 
units in a particular communication channel is accomplished by using a 
frequency synthesizer to generate a carrier wave in a particular portion 
of a predetermined broad frequency band for a brief period of time. The 
frequency synthesizer uses an input spreading code to determine the 
particular frequency from within the set of frequencies in the broad 
frequency band at which to generate the carrier wave. Spreading codes are 
input to the frequency synthesizer by a spreading code generator. The 
spreading code generator is periodically clocked or stepped through 
different transitions which causes different or shifted spreading codes to 
be output to the frequency synthesizer. Therefore, as the spreading code 
generator is periodically clocked, then so too is the carrier wave 
frequency hopped or reassigned to different portions of the frequency 
band. In addition to hopping, the carrier wave is modulated by data 
symbols representing a sequence of data bits which are to be transmitted. 
A common type of carrier wave modulation used in SFH-CDMA systems is M-ary 
frequency shift keying (MFSK), where k=log.sub.2 M data symbols are used 
to determined which one of the M frequencies is to be transmitted. 
Multiple communication channels are allocated by using a plurality of 
spreading codes to assign portions of the frequency band to different 
channels during the same time period. As a result, transmitted signals are 
in the same broad frequency band of the communication channel, but within 
unique portions of the broad frequency band assigned by the unique 
spreading codes. These unique spreading codes preferably are orthogonal to 
one another such that the cross-correlation between the spreading codes is 
approximately zero. Particular transmitted signals can be retrieved from 
the communication channel by despreading a signal representative of the 
sum of signals in the communication channel with a spreading code related 
to the particular transmitted signal which is to be retrieved from the 
communication channel. Further, when the spreading codes are orthogonal to 
one another, the received signal can be correlated with a particular 
spreading code such that only the desired signal related to the particular 
spreading code is enhanced while the other signals are not enhanced. 
It will be appreciated by those skilled in the art that several different 
spreading codes exist which can be used to separate data signals from one 
another in a CDMA communication system. These spreading codes include but 
are not limited to pseudonoise (PN) codes and Walsh codes. A Walsh code 
corresponds to a single row or column of the Hadamard matrix. For example, 
in a 64 channel CDMA spread spectrum system, particular mutually 
orthogonal Walsh codes can be selected from the set of 64 Walsh codes 
within a 64 by 64 Hadamard matrix. 
Further it will be appreciated by those skilled in the art that the data 
signals are typically channel coded to improve performance of the 
communication system by enabling transmitted signals to better withstand 
the effects of various channel impairments, such as noise, fading, and 
jamming. Typically, channel coding reduces the probability of bit error, 
and/or reduces the required signal to noise ratio usually expressed as bit 
energy per noise density (E.sub.b N.sub.0), to recover the signal at the 
cost of expending more bandwidth than would otherwise be necessary to 
transmit the data signal. 
A typical spread spectrum transmission involves expanding the bandwidth of 
an information signal, transmitting the expanded signal and recovering the 
desired information signal by remapping the received spread spectrum into 
the original information signals bandwidth. This series of bandwidth 
trades used in spread spectrum signalling techniques allows a 
communication system to deliver a relatively error-free information signal 
in a noisy environment or communication channel. The quality of recovery 
of the transmitted information signal from the communication channel is 
measured by the error rate (i.e., the number of errors in the recovery of 
the transmitted signal over a particular time span or received bit span) 
for some E.sub.b /N.sub.0. As the error rate increases the quality of the 
signal received by the receiving party decreases. As a result, 
communication systems typically are designed to limit the error rate to an 
upper bound or maximum so that the degradation in the quality of the 
received signal is limited. In CDMA spread spectrum communication systems, 
the error rate is related to the noise interference level in the 
communication channel which is directly related to number of simultaneous 
but code divided users within the communication channel. Thus, in order to 
limit the maximum error rate, the number of simultaneous code divided 
users in the communication channel is limited. However, the error rate can 
be reduced by using channel coding schemes. The error rate can also be 
reduced by using diversity combining. Therefore, by using channel coding 
and/or diversity combining schemes the number of simultaneous users in a 
communication channel can be increased while still maintaining the same 
maximum error rate limit. 
As discussed in Digital Communications: Fundamentals and Applications by 
Bernard Sklar, published by Prentice Hall, Englewood Cliffs, NJ in 1988, 
especially chapters 5 and 6 entitled "Channel Coding" found on pages 
245-380, several of these channel coding and decoding schemes have been 
developed for use in communication systems. Among the decoding schemes 
discussed is using a maximum-likelihood (ML) decoding algorithm. In 
addition to the discussion found in Sklar's book above-mentioned, 
Gottfried Ungerboeck described in general MLSE decoding algorithms in 
"Adaptive Maximum-Likelihood Receiver for Carrier-Modulated 
Data-Transmission Systems", IEEE Transactions on Communications, vol. 
com-22, no. 5, May 1974, p.p. 624-636. However, a need exists for ML 
decoding schemes to be specifically optimized for use in frequency hopping 
spread spectrum communication systems. In optimizing the communication 
system with respect to the ML decoding algorithm, one starting point is 
analyzing the implementation of the ML decoding algorithm to the 
particular environment to which it is to be used. For the purposes of this 
discussion, the environment will include convolutional encoders and ML 
decoding algorithms similar to the Viterbi decoding algorithm. It will be 
appreciated by those skilled in the art that these principles can be 
applied to other encoding techniques such as block encoding and ML 
decoding algorithms other than Viterbi-like algorithms. Through the use of 
these optimized decoding schemes, the number of simultaneous users in a 
communication system can be increased over the number of simultaneous 
users in a communication system using non-optimized decoding algorithms 
while maintaining the same maximum error rate limit. 
Several of diversity combining schemes have been developed for use in 
communication systems. Among the diversity combining schemes is the 
diversity reception technique described in U.S. Pat. No. 5,031,193 
entitled "Method and Apparatus for Diversity Reception of Time-Dispersed 
Signals". This patent describes diversity combining stages which perform 
either bit by bit selection of or maximal ratio combining of signals 
received from several receiver branches. The diversity combined signal may 
optionally be subsequently used in estimating the received sequence. 
Another diversity reception scheme is described in U.S. Pat. No. 4,271,525 
entitled " Adaptive Diversity Receiver For Digital Communications". This 
patent describes an adaptive diversity receiver using an adaptive 
transversal filter for each receiver branch, followed by a decision 
feedback equalizer. The tap gains of the transversal filters are updated 
via feedback from the output of the equalizer, and other points in the 
receiver. However, a need exists for diversity combining schemes to be 
specifically optimized for use in frequency hopping spread spectrum 
communication systems. In optimizing the communication system with respect 
to diversity combining, one starting point is analyzing the implementation 
of diversity combining to the particular environment to which it is to 
used. For the purposes of this discussion, the environment will include at 
least two receiver branches and a signal combining technique of either bit 
by bit selection or maximal ratio combining. It will be appreciated by 
those skilled in the art that these principles can be applied to other 
diversity combining techniques. Through the use of these optimized 
diversity combining schemes, the number of simultaneous users in a 
communication system can be increased over the number of simultaneous 
users in a communication system using non-optimized diversity combining 
techniques while maintaining the same maximum error rate limit. 
SUMMARY OF THE INVENTION 
A method and apparatus is provided for improving detection of data bits in 
data samples of a hop of a slow frequency hopping spread spectrum signal. 
In the detecting process, the carrier to interference (C/I) power ratio of 
the hop is estimated by using the data samples of the hop. Subsequently, a 
data bit is detected by using the estimated C/I power ratio. The detection 
process may include utilizing maximum likelihood decoding techniques to 
derive a data bit from decision metrics and the estimated C/I power ratio. 
The decision metrics correspond to a measurement of the distance of data 
samples from constellation points within a constellation space 
representing data samples previously used to generate decision metrics. 
The detection process also may include utilizing the estimated C/I power 
ratio in combining data samples of the hop as received from two or more 
diversity receiver branches.

DETAILED DESCRIPTION 
Referring now to FIG. 1, a preferred embodiment slow frequency hopping 
(SFH) communication system is shown. In optimizing the communication 
system, one starting point is analyzing the implementation of the ML 
decoding algorithm and diversity combining techniques to the particular 
environment to which it is to be used. For the purposes of this 
discussion, the environment will include convolutional encoding of data 
bits prior to transmission and slow frequency hopping signaling. It will 
be appreciated by those skilled in the art that these principles can be 
applied to other encoding techniques such as block encoding as well as 
other signalling techniques having properties similar to slow frequency 
hopping signalling such as time hopping signalling. 
In order to design either a convolutional decoder to perform optimal ML 
decoding or a diversity combiner to perform optimal diversity combining, 
obtaining knowledge about the received carrier signal power to 
interference signal power ratio (i.e., C/I power ratio) is desirable. 
Measurement of the actual C/I power ratio in SFH communication systems can 
be difficult since the carrier signal hops at discrete time intervals over 
a broad frequency band. The C/I power ratio may change with each hop, 
since the interference in different portions of the broad frequency band 
may vary by the frequency. This variance of the interference at different 
frequencies may be due to signals other than the desired signal being 
transmitted at or near the same frequency as the desired frequency as well 
as from spurious noise bursts from electrical power generators and 
transmission lines, solar flares, atmospheric disturbances and the like. 
Therefore, since actual measurement is difficult, an approximation of the 
C/I power ratio in SFH communication systems is desirable. 
In accordance with a preferred embodiment of the present invention one such 
approximation of the the C/I power ratio is proposed. In this preferred 
embodiment an assumption concerning the communication channel conditions 
has been made. This assumption is that the C/I power ratio remains 
constant over the duration of a single hop. Such an assumption is valid so 
long as the duration of the hop is short enough to be able to reasonably 
assume that the magnitude of the power interference sources in the 
communication channel would be constant over the hop. The preferred 
embodiment approximation or estimate of the C/I power ratio of a hop of a 
SFH spread spectrum signal is measured according to the following equation 
for .PSI.: 
##EQU1## 
In the equation (eq. 1), z represents the phase modulation cancelled forms 
of the data samples of a hop of the SFH signal. The data samples are 
samples of the complex envelope of the hop where the hop has been 
modulated by nth phase shift keying. Cancellation of nth phase shift 
keying modulation of the hop of the slow frequency hopping spread spectrum 
signal can be accomplished by raising the complex envelope of the hop to 
the nth power. As a result, z represents the phase modulation cancelled 
forms of the data samples which comprise samples of the complex envelope 
of the hop raised to the nth power for the nth phase shift keying 
modulated hop of the slow frequency hopping spread spectrum signal. For 
example, a complex envelope of a bi-phase shift key modulated (BPSK) hop 
of a SFH signal is raised to the second power (i.e., squared) in order to 
generate a phase modulation cancelled form of the hop. Similarly, a 
complex envelope of a quadrature phase shift key modulated (QPSK) hop of a 
SFH signal is raised to the fourth power in order to generate a phase 
modulation cancelled form of the hop. 
In addition, in the equation (eq. 1), Ave.sup.2 {Re{z}} is the square of 
the average of the real portion of z over the hop. More precisely, z.sub.k 
represents a single phase modulation cancelled data sample where the data 
sample is represented as a complex number having a real and an imaginary 
portion. In addition, N is the number of data samples of the complex 
envelope of the hop. Thus, Ave.sup.2 {Re{z}} may be computed by squaring 
the result of the following equation: 
##EQU2## 
in which the real portions of each data sample z.sub.i of the hop are 
summed together and subsequently divided by the number of data samples of 
the hop. 
In addition, in the equation (eq. 1), Ave{.vertline.z.vertline..sup.2 } is 
the average of the square of the magnitude of the complex valued z (i.e. 
where z has a real and imaginary portion) over the hop. More precisely, as 
noted above, z.sub.k represents a single phase modulation cancelled data 
sample where the data sample is represented as a complex number having a 
real and an imaginary portion. In addition, N is the number of data 
samples of the complex envelope of the hop. Thus, 
Ave{.vertline.z.vertline..sup.2 } may be computed according to the 
following equation: 
##EQU3## 
in which the square of the absolute value of each data sample z.sub.k is 
summed together and subsequently divided by the number of data samples of 
the hop. 
It will be appreciated by those skilled in the art that any monotonically 
related form of the estimate of the C/I power ratio (.PSI.) may be used 
without departing from the scope of the present invention. For example, an 
estimate maybe formed using .PSI. in which .PSI. is raised to a power 
greater or less than one, .PSI. is multiplied or divided by a constant 
value or variable, and/or .PSI. is added to or subtracted from a constant 
value or variable. Further, it will be appreciated by those skilled in the 
art that this preferred embodiment C/I power ratio estimate (.PSI.) has 
several advantages. These advantages include the ease of calculation of 
the estimate (.PSI.) due to simple arithmetic operations being performed 
on digital values which represent data samples. Another advantage is the 
lack of need for measurements other than those already being done in the 
data bit detecting process. The sampling of the complex envelope of the 
hop is already being done in conjunction with the data bit detecting 
process. Further, measurement of the actual C/I power ratio would involve 
the additional steps of measuring the power of the carrier and 
interference signals over the hop. Yet another advantage is that this 
estimate (.PSI.) does not require any prior knowledge concerning the data 
bits being transmitted within of the hop of the SFH signal. 
This estimate of the C/I ratio (.PSI.) of a hop is a monotonous function of 
the actual C/I power ratio. A derivation of a proof this statement 
follows. Each data sample (x.sub.k) of the complex envelope of the 
received hop of the SFH signal is described by the following equation: 
EQU x.sub.k =P+n.sub.r +jn.sub.i (eq. 4) 
where P is the average amplitude of the received data sample and 
n.sub.r,n.sub.i are the real and imaginary components of the interference. 
Both n.sub.r,n.sub.i are independent, zero mean normal variables, with 
equal variance .sigma..sub.n.sup.2 (i.e. they can be modeled as white, 
Gaussian noise). However, these following derivations can be easily 
extended by one skilled in the art to non-Gaussian noise. The actual C/I 
power ratio can be described as: 
##EQU4## 
When a BPSK modulated SFH signal is used in the communication system, the 
derivation of the proof that the estimated C/I power ratio (.PSI.) of (eq. 
1) is a monotonous function of the actual C/I power ratio continues as 
follows. 
EQU z.sub.k =x.sub.k.sup.2 =(P+n.sub.r +jn.sub.i).sup.2 =(P+n.sub.r).sup.2 
-n.sub.i.sup.2 +j2(P+n.sub.r)n.sub.i (eq. 6) 
where z.sub.k represents a single phase modulation cancelled data sample 
where the data sample (x.sub.k) is represented as a complex number having 
a real and an imaginary portion and (eq. 4) was substituted into (eq. 6) 
for x.sub.k. 
In addition, in the equation (eq. 1), Ave{Re{z}} is the average of the real 
portion of z over the hop. More precisely, 
##EQU5## 
where the real portion of z.sub.k as defined in (eq. 6) was substituted in 
(eq. 7) and, in accordance with the definition of Gaussian noise model 
given above and the definition of the nth central moment of a Gaussian 
random variable, the average of n.sub.r and n.sub.i (i.e., n.sub.r and 
n.sub.i) each go to zero over the hop and average of n.sub.r.sup.2 and 
n.sub.i.sup.2 (i.e., n.sub.r.sup.2 and n.sub.i.sup.2) each go to 
.sigma..sub.n.sup.2. 
In addition, in the equation (eq. 1), .vertline.z.sub.k .vertline..sup.2 is 
the square of the absolute value of z.sub.k. More precisely, 
##EQU6## 
where the definition of z.sub.k from (eq. 6) was substituted in (eq. 8). 
In addition, in the equation (eq. 1), Ave{.vertline.z.vertline..sup.2 } is 
the average of the square of the magnitude of the real and imaginary 
portions of z over the hop. More precisely, 
##EQU7## 
where the square of the absolute value of z.sub.k as defined in (eq. 8) 
was substituted in (eq. 9). In addition, in accordance with the definition 
of Gaussian noise model given above and the definition of the nth central 
moment of a Gaussian random variable, the average of an odd power of 
n.sub.r and n.sub.i (i.e., n.sub.r and n.sub.i) each go to zero over the 
hop and average of an even power n of n.sub.r and n.sub.i (i.e., n.sub.r 
and n.sub.i) each go to a factor defined as: 
EQU n.sub.r.sup.n =n.sub.i.sup.n 
=1.multidot.3.multidot.5.multidot.(n-1).multidot..sigma..sub.n.sup.n(eq. 
10) 
such that n.sub.r.sup.2 =n.sub.i.sup.2 =.sigma..sub.n.sup.2 and 
n.sub.r.sup.4 =n.sub.i.sup.4 =3.sigma..sub.n.sup.4. 
Thus, (eq. 5), (eq. 7) and (eq. 9) can be substituted into (eq. 1) as 
follows to derive an expression of the estimate of the power ratio (.PSI.) 
in terms of actual C/I power ratio: 
##EQU8## 
which is a monotonic function of C/I since the derivative of the estimate 
(.PSI.) with respect to the actual C/I is greater than zero for all real 
and positive values of C/I. More precisely, 
##EQU9## 
Thus, for a BPSK modulated SFH signal the estimated C/I power ratio 
(.PSI.) of (eq. 1) is a monotonous function of the actual C/I power ratio. 
When a QPSK modulated SFH signal is used in the communication system, the 
derivation of the proof that the estimated C/I power ratio (.PSI.) of (eq. 
1) is a monotonous function of the actual C/I power ratio continues as 
follows. 
EQU z.sub.k =x.sub.k.sup.4 =(P+n.sub.r +jn.sub.i).sup.4 =(P+n.sub.r).sup.4 
-6(P+n.sub.r).sup.2 n.sub.i.sup.2 
EQU +n.sub.i.sup.4 +j4(P+n.sub.r)n.sub.i [(P+n.sub.r).sup.2 -n.sub.i.sup.2 
](eq. 13) 
where z.sub.i represents a single phase modulation cancelled data sample 
where the data sample (x.sub.k) is represented as a complex number having 
a real and an imaginary portion and (eq. 4) was substituted into (eq. 13) 
for x.sub.k. 
In addition, in the equation (eq. 1), Ave{Re{z}} is the average of the real 
portion of z over the hop. More precisely, 
##EQU10## 
where the real portion of z.sub.k as defined in (eq. 13) was substituted 
in (eq. 14) and, in accordance with the definition of Gaussian noise model 
given above and the definition of the nth central moment of a Gaussian 
random variable, the average of an odd power of n.sub.r and n.sub.i (i.e., 
n.sub.r and n.sub.i) each go to zero over the hop and average of an even 
power n of n.sub.r and n.sub.i (i.e., n.sub.r and n.sub.i) each go to a 
factor defined in (eq. 10) such that n.sub.r.sup.2 =n.sub.i.sup.2 
=.sigma..sub.n.sup.2 and n.sub.r.sup.4 =n.sub.i.sup.4 
=3.sigma..sub.n.sup.4. 
In addition, in the equation (eq. 1), .vertline.z.sub.k .vertline..sup.2 is 
the square of the absolute value of z.sub.k. More precisely, 
##EQU11## 
where the definition of z.sub.k from (eq. 13) was substituted in (eq. 15). 
In addition, in the equation (eq. 1), Ave{.vertline.z.vertline..sup.2 } is 
the average of the square of the magnitude of the real and imaginary 
portions of z over the hop. More precisely, 
##EQU12## 
The above expression can be simplified by eliminating the terms which go 
to zero (i.e. those terms having n.sub.r or n.sub.i raised to an odd 
power) results in the following expression: 
##EQU13## 
where the square of the absolute value of z.sub.k as defined in (eq. 8) 
was substituted in (eq. 9). In addition,, in accordance with the 
definition of Gaussian noise model given above and the definition of the 
nth central moment of a Gaussian random variable, the average of an odd 
power of n.sub.r and n.sub.i (i.e., n.sub.r.sup.n and n.sub.i.sup.n) each 
go to zero over the hop and average of an even power n of n.sub.r and 
n.sub.i (i.e., n.sub.r.sup.n and n.sub.i.sup.n) each go to a factor 
defined in (eq. 10) such that n.sub.r.sup.2 =n.sub.i.sup.2 
=.sigma..sub.n.sup.2, n.sub.r.sup.4 =n.sub.i.sup.4 =3.sigma..sub.n.sup.4, 
n.sub.r.sup.6 =n.sub.i.sup.6 =15.sigma..sub.n.sup.6, and n.sub.r.sup.8 
=n.sub.i.sup.8 =105.sigma..sub.n.sup.8. 
Thus, (eq. 5), (eq. 14) and (eq. 16) can be substituted into (eq. 1) as 
follows to derive an expression of the estimate of the power ratio (.PSI.) 
in terms of actual C/I power ratio: 
##EQU14## 
which is a monotonic function of C/I since the derivative of the estimate 
(.PSI.) with respect to the actual C/I is greater than zero for all real 
and positive values of C/I. More precisely, 
##EQU15## 
Thus, for a QPSK modulated SFH signal the estimated C/I power ratio 
(.PSI.) of (eq. 1) is a monotonous function of the actual C/I power ratio. 
It will be appreciated by those skilled in the art that the above 
derivations can be extended to any nth phase shift keying modulated SFH 
signal to prove that the estimated C/I power ratio (.PSI.) of (eq. 1) is a 
monotonous function of the actual C/I power ratio for any nth phase shift 
keying modulated SFH signal. 
Since this estimate of each hop's C/I power ratio (.PSI.) of (eq. 1) is a 
monotonous function of the actual C/I power ratio, this estimate of each 
hop's C/I power ratio (.PSI.) may preferably be used to determine a level 
of confidence that a particular hop was detected properly by a receiving 
station. The number of levels of confidence which may be determined can be 
varied depending on the particular use for the level of confidence. For 
example, two levels of confidence may be determined for use in a hard 
decision environment. The two levels of confidence include: (1) full 
confidence which corresponds to the estimated C/I power ratio being at or 
above a particular threshold and (2) no confidence which corresponds to 
the estimated C/I power ratio being below the particular threshold. In 
another example, several levels of confidence may be determined for use in 
a soft decision environment. These several levels of confidence correspond 
to increasing confidence as the estimated C/I power ratio increases in 
value. 
A description of a preferred embodiment communication system, shown in FIG. 
1, which incorporates the above mentioned optimizing principles for a data 
bit detection in a SFH signal follows. In the encoding portion 102 of the 
communication system, traffic channel data bits 100 are input to an 
encoder 102 at a particular bit rate. The input traffic channel data bits 
can include either voice converted to data by a vocoder, pure data, or a 
combination of the two types of data. Encoder 102 preferrably encodes the 
input data bits 100 into data symbols 104 at a fixed encoding rate with an 
encoding algorithm which facilitates subsequent maximum likelihood 
decoding of the data symbols into data bits (e.g. convolutional or block 
coding algorithms). 
The data symbols 104 may optionally then be interleaved by the encoding 
portion 102. Typically, interleaving increases the output distance between 
the consecutively input non-interleaved data symbols. This interleaving of 
data symbols causes burst of errors to be spread out in time and thus to 
be handled by the data bit detector as if they were random errors. This 
interleaving thereby allows random-error-correcting coding (e.g. 
convolutional coding) to be useful in a bursty noise communication channel 
(e.g. radio frequency communication channels). The interleaving preferably 
is limited to a predetermined size of the block of data symbols. The block 
size preferably is derived from the maximum number of data symbols, 
representing input data bits 100, which can be transmitted at a 
predetermined chip rate within a predetermined length transmission block. 
Subsequently, the interleaved data symbols 104 are output from the 
encoding portion 102. It will be appreciated by those skilled in the art 
that several different variations of interleaving could be implemented 
without departing from the scope of the present invention. For example, 
several different techniques can be used to interleave the data symbols 
(e.g., convolutional or block interleaving). In addition, the size of the 
interleaving block could be altered to accommodate different transmission 
lengths or rates. Also, the dimensions of the matrix could be altered to 
increase or decrease the interleaved distance between consecutively input 
groups of data symbols. 
The interleaved data symbols 104 are then input to a transmitting portion 
106 of the communication system. It will be appreciated by those skilled 
in the art that additional coding of the data symbols 104 may be done in 
the transmitting portion 106 to enable multiple access by several users to 
the same communication channel. Such encoding may include coding which 
ensures orthogonality of an individual users encoded traffic channel bits 
from other users encoded traffic channel bits. However, this additional 
coding typically depends upon the specific implementation of the SFH 
communication system. Further, this additional coding typically will not 
interfere with the implementation of the teachings of the present 
invention as described herein as long as the additional encoding is done 
after the initial encoding and the additional decoding is done prior to 
the preferred embodiment data bit detection process. The interleaved data 
symbols 104 are prepared for transmission over a communication channel as 
a SFH signal by a modulator 106. Subsequently, the modulated sequence is 
provided to an antenna 110 for transmission over the communication channel 
112. 
A receiving portion 114 of the communication system receives the 
transmitted SFH spread spectrum signal from over the communication channel 
112 through antenna 116. Each hop of the received SFH signal preferably is 
sampled into data samples 120 by demodulator 118. Subsequently, the data 
samples 120 are output to the detector 122 of the communication system. 
If the encoder 102 of the communication has interleaved the data symbols, 
then the detector 122 deinterleaves the data samples by using a technique 
which is substantially inverse to the interleaving technique used in the 
encoder 102. After, if necessary, such deinterleaving, the detector 122 of 
the communication system inputs the data samples 120 into a an estimator 
124 which preferably generates an estimate of the C/I power ratio (.PSI.) 
126 for each hop in accordance with the algorithm described above as (eq. 
1) and reproduced below: 
##EQU16## 
The symbol z preferrably represents the phase modulation cancelled forms 
of the data samples of a hop of the SFH signal. The data samples 
preferrably are samples of the complex envelope of the hop where the hop 
has been modulated by nth phase shift keying. Cancellation of nth phase 
shift keying modulation of the hop of the slow frequency hopping spread 
spectrum signal preferably is accomplished by raising the complex envelope 
of the hop to the nth power. As a result, z represents the phase 
modulation cancelled forms of the data samples which comprise samples of 
the complex envelope of the hop raised to the nth power for the nth phase 
shift keying modulated hop of the slow frequency hopping spread spectrum 
signal. It will be appreciated by those skilled in the art that any 
monotonically related form of the estimate of the C/I power ratio (.PSI.) 
may be used without departing from the scope of the present invention. 
The detector 122 of the communication system also inputs the data samples 
120 into the detecting portion 128 which detects data bits 130 in the data 
samples 128 of each particular hop by using the estimated C/I power ratio 
126 for that particular hop which was generated by the estimator 124. 
The preferred embodiment described in reference to FIG. 1 may be further 
extended into a more specific use in the detection process of the C/I 
power ratio estimate 126 to the decoding process as shown in FIG. 2. In 
FIG. 2, the detector 122 input the data samples 120 associated with each 
hop into a decision metric generator 132 of the detecting portion 128. The 
decision metric generator 132 uses the input data samples 120 to generate 
decision metrics 134 associated with each hop which correspond to a 
distance of an input data sample from a constellation point within a 
constellation space representing previously input data samples 120. These 
decision metric 134 correspond to possible transitions within a maximum 
likelihood decoding trellis which decoder 140 will subsequently be 
determining. 
The estimator 124 inputs the estimate of the C/I power ratio (.PSI.) 126 
associated with each hop into the detecting portion 128. The detecting 
portion 128 provides the C/I power ratio estimates (.PSI.) 126 to a 
confidence measure generator 136. The confidence measure generator 136 
also receives the decision metric 134 associated with each hop from the 
decision metric generator. The confidence measure generator 136 uses the 
C/I power ratio estimate (.PSI.) 126 associated with a particular hop to 
determine a level of confidence 138 in the accuracy of the decision 
metrics 134 associated with the particular hop (i.e., accurately or 
actually relate to the transmitted encoded data bits 100). For example, if 
the C/I power ratio estimate (.PSI.) 126 for the hop is below a 
predetermined threshold, then the probability that the data samples 120 of 
that hop actually represent the transmitted encoded data bits 100 is low. 
As a result the decision metrics 134 are probably not actually related to 
the transmitted encoded data bits 100, because the data samples 120 of the 
hop probably do not correspond to the transmitted encoded data bits 100. 
The number of different levels of confidence 138 which may be determined 
for a particular hop can be varied depending on the particular use for the 
level of confidence 138. For example, two levels of confidence in the 
decision metrics 134 of each hop may be determined for use in a hard 
decision environment. The two levels of confidence include: (1) full 
confidence which corresponds to the estimated C/I power ratio being at or 
above a particular threshold and (2) no confidence which corresponds to 
the estimated C/I power ratio being below the particular threshold. In 
response to a full confidence measure 138, the associated decision metrics 
134 for the hop would be used by the decoder 140. However, in response to 
a no confidence measure 138, the associated decision metrics 134 for the 
hop would not be used by the decoder 140. In another example, several 
levels of confidence in the decision metrics 134 of each hop may be 
determined for use in a soft decision environment. These several levels of 
confidence correspond to increasing confidence as the estimated C/I power 
ratio 138 increases in value. In response to the increasing level of 
confidence measure 138, the associated decision metrics 134 for the hop 
would be given greater weight by decoder 140. Such a weighting system of 
the decision metrics 134 by a decoder 140 is often termed using side 
information about the decision metrics 134. 
The decoder 140 preferably generates estimated data bits 130 by utilizing 
maximum likelihood decoding technques to derive the estimated traffic 
channel data bits 130 from the decision metrics 134 of each hop and the 
associated confidence measures 138 which are input to the decoder 140. 
When the traffic channel data bits 100 have been convolutionally encoded, 
the maximum likelihood decoding techniques which are used may based upon 
the Viterbi decoding algorithm. 
The preferred embodiment described in reference to FIG. 1 may be further 
extended into a more specific use in the detection process of the C/I 
power ratio estimate 126 to the diversity combining process as shown in 
FIG. 3. In FIG. 3, the receiving portion 114 of the communication system 
receives the transmitted SFH spread spectrum signal from over the 
communication channel 112 through antenna structure 116. The antenna 
structure 116 preferrably includes at least a first receiving antenna 142 
and a second receiving antenna 144. The first receiving antenna 142 is 
preferrably geographically displaced from the second receiving antenna 144 
such that a diversity antenna structure is formed. Each hop of the SFH 
signal as received by the first and second antennae 142 and 144 is 
preferrably input to the demodulator 118. Demodulator 118 includes a first 
and second receiver branch 146 and 148, respectively. The first receiver 
branch 146 is coupled to the first antenna 142 in order to demodulate and 
sample each hop of the SFH signal 122 received by the first antenna 142 
into a first data sample set 150. Similarly, the second receiver branch 
148 is coupled to the second antenna 144 in order to demodulate and sample 
each hop of the SFH signal 122 received by the second antenna 144 into a 
second data sample set 152. Subsequently, the sets of data samples 150 and 
152 (collectively described as data samples 120) are output to the 
detector 122 of the communication system. The data samples 120 may 
preferrably be coupled to detector 122 on a data bus having each of the 
data sample sets 150 and 152 thereon or by a set of individual data signal 
couplers for each data samples set 150 and 152. 
The detector 122 of the communication system inputs the sets of data 
samples 120 into an estimator 124 which preferrably generates a first and 
a second estimate of the C/I power ratio (.PSI.) 158 and 160 (collectively 
described as C/I power ratio estimate 126) for each hop corresponding to 
the first and second set of data samples 150 and 152, respectively, in 
accordance with the algorithm described above as (eq. 1). These C/I power 
ratio estimates 126 are output to the detecting portion 128. 
Similarly, the detector 122 of the communication system inputs the sets of 
data samples 120 (i.e. first and second sets 150 and 152, respectively) 
into the detecting portion 128. The detecting portion provides the first 
and second data sample sets 150 and 152 to a diversity combiner 154. The 
diversity combiner 154 combines the first and second sets of data samples 
150 and 152, respectively, into a single combined set of data samples 156. 
The diversity combining is accomplished by using weighting coefficients 
for the first and second sets of input data samples 150 and 152 of each 
hop which are derived from the associated first and second C/I power ratio 
estimate 158 and 160 input. 
The diversity combiner 154 uses the first and second C/I power ratio 
estimate (.PSI.) 158 and 160, respectively, associated with a particular 
hop to determine a level of confidence in the accuracy of the reception of 
the first and second set of data samples 150 and 152, respectively 
associated with the particular hop by the receiving portion 114. For 
example, if the first C/I power ratio estimate (.PSI.) 158 for the hop is 
below a predetermined threshold, then the probability that the first set 
of data samples 150 of that hop actually represent the transmitted encoded 
data bits 100 is nominal. The number of different levels of confidence in 
the accuracy of reception which may be determined for a particular hop can 
be varied depending on the particular use for the level of confidence. For 
example, two levels of confidence of each hop may be determined for use in 
a hard decision environment. The two levels of confidence include: (1) 
full confidence which corresponds to the estimated C/I power ratio being 
at or above a particular threshold and (2) no confidence which corresponds 
to the estimated C/I power ratio being below the particular threshold. In 
response to a full confidence measure, the associated set of data samples 
for the hop would be used by the diversity combiner 154 in generating the 
single combined set of data samples 156 for the hop. However, in response 
to a no confidence measure, the associated set of data samples for the hop 
would not be used by the diversity combiner 154 in generating the single 
combined set of data samples 156 for the hop. In another example, several 
levels of confidence in the accuracy of reception of each hop may be 
determined for use in a soft decision environment. These several levels of 
confidence correspond to increasing confidence as the estimated C/I power 
ratio 126 increases in value. In response to the increasing level of 
confidence, the associated set of data samples for the hop would be 
assigned greater weighting coefficients by the diversity combiner 154. It 
will be appreciated by those skilled in the art that these diversity 
combining techniques can be extended to combining a plurality of sets of 
data samples received on a corresponding plurality of receiver branches. 
Subsequently, single combined set of data samples 156 preferrably is used 
by the detecting portion 128 to detect data bits 130 in the data samples. 
Such detection may be accomplished by using a decoding technique similar 
to the one described above in reference to FIG. 2. However, other types of 
detection of data bits in the combined set of data samples 156 could be 
used without departing from the spirit and scope of preferred embodiment 
diversity combining invention as claimed. 
Although the invention has been described and illustrated with a certain 
degree of particularly, it is understood that the present disclosure of 
embodiments has been made by way of example only and that numerous changes 
in the arrangement and combination of parts as well as steps may be 
resorted to by those skilled in the art without departing from the spirit 
and scope of the invention as claimed. For example, the modulator, 
antennas and demodulator portions of the preferred embodiment 
communication system as described were directed to CDMA spread spectrum 
signals transmitted over a radio communication channel. However, as will 
be understood by those skilled in the art, the communication channel could 
alternatively be an electronic data bus, wireline, optical fiber link, or 
any other type of communication channel.