Transmitter diversity technique for wireless communications

Abstract

A simple block coding arrangement is created with symbols transmitted over a plurality of transmit channels, in connection with coding that comprises only simple arithmetic operations, such as negation and conjugation. The diversity created by the transmitter utilizes space diversity and either time or frequency diversity. Space diversity is effected by redundantly transmitting over a plurality of antennas, time diversity is effected by redundantly transmitting at different times, and frequency diversity is effected by redundantly transmitting at different frequencies: Illustratively, using two transmit antennas and a single receive antenna, one of the disclosed embodiments provides the same diversity gain as the maximal-ratio receiver combining (MRRC) scheme with one transmit antenna and two receive antennas. The principles of this invention are applicable to arrangements with more than two antennas, and an illustrative embodiment is disclosed using the same space block code with two transmit and two receive antennas.

Claims

1. A receiver comprising: a combiner adapted to receive a block of symbols transmitted with frequency diversity or time diversity, the block of symbols including a first symbol and a second symbol transmitted from a first antenna and a complex conjugate of the first symbol and a negative complex conjugate of the second symbol transmitted from a second antenna, wherein the combiner is configured to combine the block of symbols and supply a first output signal and a second output signal; and a detector coupled to the combiner to receive the first and second output signals and to recover the first symbol and the second symbol.

2. The receiver as recited in claim 1 further comprising a channel estimator coupled to supply the detector with first and second channel estimates corresponding respectively to a first channel between the first antenna and the receiver and a second channel between the second antenna and the receiver, the first and second channel estimates for use in recovering the first symbol and the second symbol.

3. The receiver as recited in claim 2 wherein the channel estimator is coupled to supply the combiner with the first and second channel estimates.

4. The receiver as recited in claim 1 wherein the detector is a maximum likelihood detector.

5. A method comprising: receiving in a combiner a block of symbols transmitted with frequency diversity or time diversity, the block of symbols including first symbol and a complex conjugate of the first symbol and a second symbol and a negative complex conjugate of the second symbol, the first symbol and the complex conjugate of the first symbol transmitted with space diversity using a first antenna and a second antenna, the second symbol and the negative complex conjugate of the second symbol transmitted with space diversity using the first antenna and the second antenna, wherein the combiner combines the block of symbols and supplies a first output signal and a second output signal; and receiving in a detector the first output signal and the second output signal from the combiner and generating a recovered first symbol and a recovered second symbol based on the block of symbols transmitted with frequency diversity or time diversity.

6. The method as recited in claim 5 further comprising: estimating a first channel between the first antenna and the receiver and estimating a second channel between the second antenna and the receiver and generating a first channel estimate and a second channel estimate; and supplying the detector with the first and second channel estimates for use in generating the recovered first symbol and the recovered second symbol.

7. The method as recited in claim 6 further comprising supplying the combiner with the first and second channel estimates.

8. A system comprising: a receiver for receiving wireless communication signals transmitted from a transmitter, the receiver including, a combiner adapted to receive a block of symbols transmitted with frequency diversity or time diversity, the block of symbols including a first symbol and a second symbol respectively transmitted from a first antenna and a second antenna and a complex conjugate of the first symbol and a negative complex conjugate of the second symbol transmitted respectively from the second antenna and the first antenna, wherein the combiner is configured to combine the block of symbols and supply a first output signal and a second output signal; and a detector coupled to the combiner to receive the first and second output signals and to recover the first symbol and the second symbol.

9. The system as recited in claim 8 further comprising: the transmitter, the transmitter including, the first antenna and the second antenna; a coder responsive to receipt of the first symbol and receipt of the second symbol to generate symbols providing redundancy, the symbols providing redundancy including the complex conjugate of the first symbol and the negative complex conjugate of the second symbol; wherein the transmitter is coupled to transmit the first symbol over the first antenna and the second symbol over the second antenna; and wherein the transmitter is coupled to transmit the complex conjugate of the first symbol over the second antenna and the negative complex conjugate of the second symbol over the first antenna.

10. The system as recited in claim 9 wherein the first symbol and the complex conjugate of the first symbol are transmitted with frequency diversity and wherein the second symbol and the negative complex conjugate of the second symbol are transmitted with frequency diversity.

11. The system as recited in claim 9 wherein the first symbol and the second symbol are transmitted during a first time interval and the complex conjugate of the first symbol and the negative complex conjugate of the second symbol are transmitted during a second time interval.

12. The system as recited in claim 8 further comprising a channel estimator coupled to supply the detector with first and second channel estimates corresponding respectively to a first channel between the first antenna and the receiver and a second channel between the second antenna and the receiver, the first and second channel estimates for use in recovering the first symbol and the second symbol.

13. The system as recited in claim 12 wherein the channel estimator is coupled to supply the combiner with the first and second channel estimates.

14. The system as recited in claim 8 wherein the detector is a maximum likelihood detector.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a block diagram of a first embodiment in accordance with the principles of this invention;

(2) FIG. 2 presents a block diagram of a second embodiment, where channel estimates are not employed;

(3) FIG. 3 shows a block diagram of a third embodiment, where channel estimates are derived from recovered signals; and

(4) FIG. 4 illustrates an embodiment where two transmitter antennas and two receiver antennas are employed.

DETAILED DESCRIPTION

(5) In accordance with the principles of this invention, effective communication is achieved with encoding of symbols that comprises merely negations and conjugations of symbols (which really is merely negation of the imaginary part) in combination with a transmitter created diversity. Space diversity and either frequency diversity or time diversity are employed.

(6) FIG. 1 presents a block diagram of an arrangement where the two controllable aspects of the transmitter that are used are space and time. That is, the FIG. 1 arrangement includes multiple transmitter antennas (providing space diversity) and employs multiple time intervals. Specifically, transmitter 10 illustratively comprises antennas 11 and 12, and it handles incoming data in blocks of n symbols, where n is the number of transmitter antennas, and in the illustrative embodiment of FIG. 1, it equals 2, and each block takes n symbol intervals to transmit. Also illustratively, the FIG. 1 arrangement includes a receiver 20 that comprises a single antenna 21.

(7) At any given time, a signal sent by a transmitter antenna experiences interference effects of the traversed channel, which consists of the transmit chain, the air-link, and the receive chain. The channel may be modeled by a complex multiplicative distortion factor composed of a magnitude response and a phase response. In the exposition that follows therefore, the channel transfer function from transmit antenna 11 to receive antenna 21 is denoted by h.sub.0, and from transmit antenna 12 to receive antenna 21 is denoted by h.sub.1 where:
h.sub.0=α.sub.0e.sup.jθ.sup.0
h.sub.1=α.sub.1e.sup.jθ.sup.1  (1)
Noise from interference and other sources is added at the two received signals and, therefore, the resulting baseband signal received at any time and outputted by reception and amplification section 25 is
r(t)=α.sub.0e.sup.jθ.sup.0s.sub.i+α.sub.1e.sup.jθ.sup.1s.sub.j+n(t),  (2)
where s.sub.i and s.sub.j are the signals being sent by transmit antenna 11 and 12, respectively.

(8) As indicated above, in the two-antenna embodiment of FIG. 1 each block comprises two symbols and it takes two symbol intervals to transmit those two symbols. More specifically, when symbols s.sub.i and s.sub.j need to be transmitted, at a first time interval the transmitter applies signal s.sub.i to antenna 11 and signal s.sub.j to antenna 12, and at the next time interval the transmitter applies signal −s.sub.j*; to antenna 11 and signal s.sub.i* to antenna 12. This is clearly a very simple encoding process where only negations and conjugations are employed. As demonstrated below, it is as effective as it is simple. Corresponding to the above-described transmissions, in the first time interval the received signal is
r(t)=h.sub.0s.sub.i+h.sub.1s.sub.j+n(t),  (3)
and in the next time interval the received signal is
r(t+T)=−h.sub.0s.sub.j*+h.sub.1s.sub.i*+n(t+T).  (4)

(9) Table 1 illustrates the transmission pattern over the two antennas of the FIG. 1 arrangement for a sequence of signals {s.sub.0, s.sub.1, s.sub.2, s.sub.3, s.sub.4, s.sub.5 . . . }.

(10) TABLE-US-00001 TABLE 1 Time: t t + T t + 2T t + 3T t + 4T t + 5T Antenna 11 s.sub.0 −s.sub.1* s.sub.2 −s.sub.3* s.sub.4 −s.sub.5* . . . Antenna 12 s.sub.1  s.sub.0* s.sub.3  s.sub.2* s.sub.5  s.sub.4* . . .

(11) The received signal is applied to channel estimator 22, which provides signals representing the channel characteristics or, rather, the best estimates thereof. Those signals are applied to combiner 23 and to maximum likelihood detector 24. The estimates developed by channel estimator 22 can be obtained by sending a known training signal that channel estimator 22 recovers, and based on the recovered signal the channel estimates are computed. This is a well known approach.

(12) Combiner 23 receives the signal in the first time interval, buffers it, receives the signal in the next time interval, and combines the two received signals to develop signals
{tilde over (s)}.sub.i={tilde over (h)}.sub.0*r(t)+{tilde over (h)}.sub.1r*(t+T)
{tilde over (s)}.sub.j={tilde over (h)}.sub.1*r(t)−{tilde over (h)}.sub.0r*(t+T)  (5)

(13) Substituting equation (1) into (5) yields
{tilde over (s)}.sub.i=({tilde over (α)}.sub.0.sup.2+{tilde over (α)}.sub.1.sup.2)s.sub.i+{tilde over (h)}.sub.0*n(t)+{tilde over (h)}.sub.1n*(t+T)
{tilde over (s)}.sub.j=({tilde over (α)}.sub.0.sup.2+{tilde over (α)}.sub.1.sup.2)s.sub.j+{tilde over (h)}.sub.0n*(t+T)+{tilde over (h)}.sub.1n*(t+T)  (6)
where {tilde over (α)}.sub.0.sup.2={tilde over (h)}.sub.0{tilde over (h)}.sub.0* and {tilde over (α)}.sub.1.sup.2={tilde over (h)}.sub.1{tilde over (h)}.sub.1*, demonstrating that the signals of equation (6) are, indeed, estimates of the transmitted signals (within a multiplicative factor). Accordingly, the signals of equation (6) are sent to maximum likelihood detector 24.

(14) In attempting to recover s.sub.i, two kinds of signals are considered: the signals actually received at time t and t+T, and the signals that should have been received if s.sub.i were the signal that was sent. As demonstrated below, no assumption is made regarding the value of s.sub.j. That is, a decision is made that s.sub.i=s.sub.x for that value of x for which
d.sup.2[r(t),(h.sub.0s.sub.x+h.sub.1s.sub.j)]+d.sup.2[r(t+T),(−h.sub.1s.sub.j*+h.sub.0s.sub.x*)]
is less than
d.sup.2[r(t),(h.sub.0s.sub.k+h.sub.1s.sub.j)]+d.sup.2[r(t+T),(−h.sub.1s.sub.j*+h.sub.0s.sub.k*)]  (7)
where d.sup.2 (x,y) is the squared Euclidean distance between signals x and y, i.e., d.sup.2(x,y)=|x−y|.sup.2.

(15) Recognizing that {tilde over (h)}.sub.0=h.sub.0+noise that is independent of the transmitted symbol, and that {tilde over (h)}.sub.1=h.sub.1+noise that is independent of the transmitted symbol, equation (7) can be rewritten to yield
(α.sub.0.sup.2+α.sub.1.sup.2)|s.sub.x|.sup.2−{tilde over (s)}.sub.is.sub.x*−{tilde over (s)}.sub.i*s.sub.x≦(α.sub.0.sup.2+α.sub.1.sup.2)|s.sub.k|.sup.2−{tilde over (s)}.sub.is.sub.k*−{tilde over (s)}.sub.i*s.sub.k  (8)
where α.sub.0.sup.2=h.sub.0h.sub.0* and α.sub.1.sup.2=h.sub.1h.sub.1*; or equivalently
(a.sub.0.sup.2+a.sub.1.sup.2−1)|s.sub.x|.sup.2+d.sup.2({tilde over (s)}.sub.i,s.sub.x)≦(a.sub.0.sup.2+a.sub.1.sup.2−1)|s.sub.k|.sup.2+d.sup.2({tilde over (s)}.sub.i,s.sub.k)  (9)

(16) In Phase Shift Keying modulation, all symbols carry the same energy, which means that |s.sub.x|.sup.2=|s.sub.k|.sup.2 and, therefore, the decision rule of equation (9) may be simplified to choose signal
{tilde over (s)}.sub.i=s.sub.xiff d.sup.2({tilde over (s)}.sub.i,s.sub.x)≦d.sup.2({tilde over (s)}.sub.i,s.sub.k).  (10)
Thus, maximum likelihood detector 24 develops the signals s.sub.k for all values of k, with the aid of {tilde over (h)}.sub.0 and {tilde over (h)}.sub.1 from estimator 22, develops the distances d.sup.2({tilde over (s)}.sub.i, s.sub.k), identifies x for which equation (10) holds and concludes that ŝ.sub.i=s.sub.x. A similar process is applied for recovering ŝ.sub.j.

(17) In the above-described embodiment each block of symbols is recovered as a block with the aid of channel estimates {tilde over (h)}.sub.0 and {tilde over (h)}.sub.1. However, other approaches to recovering the transmitted signals can also be employed. Indeed, an embodiment for recovering the transmitted symbols exists where the channel transfer functions need not be estimated at all, provided an initial pair of transmitted signals is known to the receiver (for example, when the initial pair of transmitted signals is prearranged). Such an embodiment is shown in FIG. 2, where maximum likelihood detector 27 is responsive solely to combiner 26. (Elements in FIG. 3 that are referenced by numbers that are the same as reference numbers in FIG. 1 are like elements.) Combiner 26 of receiver 30 develops the signals
r.sub.0=r(t)=h.sub.0s.sub.0+h.sub.1s.sub.1+n.sub.0
r.sub.1=r(t+T)=h.sub.1s.sub.0*−h.sub.0s.sub.1*+n.sub.1
r.sub.2=r(t+2T)=h.sub.0s.sub.2+h.sub.1s.sub.3+n.sub.2
r.sub.3=r(t+3T)=h.sub.1s.sub.2*−h.sub.0s.sub.3*+n.sub.3,  (11)
then develops intermediate signals A and B
A=r.sub.0r.sub.3*−r.sub.2r.sub.1*
B=r.sub.2r.sub.0*−r.sub.1r.sub.3*,  (12)
and finally develops signals
{tilde over (s)}.sub.2=As.sub.1*+Bs.sub.0
{tilde over (s)}.sub.3=As.sub.0*+Bs.sub.1,  (13)
where N.sub.3 and N.sub.4 are noise terms. It may be noted that signal r.sub.2 is actually r.sub.2=h.sub.0ŝ.sub.2+h.sub.1ŝ.sub.3=h.sub.0s.sub.2+h.sub.1s.sub.3+n.sub.2, and similarly for signal r.sub.3. Since the makeup of signals A and B makes them also equal to
A=(α.sub.0.sup.2+α.sub.1.sup.2)(s.sub.2s.sub.1−s.sub.3s.sub.0)+N.sub.1
B=(α.sub.0.sup.2+α.sub.1.sup.2)(s.sub.2s.sub.0*+s.sub.3s.sub.1*)+N.sub.2,  (14)
where N1 and N2 are noise terms, it follows that signals {tilde over (s)}.sub.2 and {tilde over (s)}.sub.3 are equal to
{tilde over (s)}.sub.2=(α.sub.0.sup.2+α.sub.1.sup.2)(|s.sub.0|.sup.2+|s.sub.1|.sup.2)s.sub.2+N.sub.3
{tilde over (s)}.sub.3=(α.sub.0.sup.2+α.sub.1.sup.2)(|s.sub.0|.sup.2+|s.sub.1|.sup.2)s.sub.3+N.sub.4.  (15)

(18) When the power of all signals is constant (and normalized to 1) equation (15) reduces to
{tilde over (s)}.sub.2=(α.sub.0.sup.2+α.sub.1.sup.2+N.sub.3
{tilde over (s)}.sub.3=(α.sub.0.sup.2+α.sub.1.sup.2)s.sub.3+N.sub.4.  (16)

(19) Hence, signals {tilde over (s)}.sub.2 and {tilde over (s)}.sub.3 are, indeed, estimates of the signals s.sub.2 and s.sub.3 (within a multiplicative factor). Line 28 and 29 demonstrate the recursive aspect of equation (13), where signal estimates {tilde over (s)}.sub.2 and {tilde over (s)}.sub.3 are evaluated with the aid of recovered signals s.sub.0 and s.sub.1 that are fed back from the output of the maximum likelihood detector.

(20) Signals {tilde over (s)}.sub.2 and {tilde over (s)}.sub.3 are applied to maximum likelihood detector 24 where recovery is effected with the metric expressed by equation (10) above. As shown in FIG. 2, once signals s.sub.2 and s.sub.3 are recovered, they are used together with received signals r.sub.2, r.sub.3, r.sub.4, and r.sub.5 to recover signals s.sub.4 and s.sub.5, and the process repeats.

(21) FIG. 3 depicts an embodiment that does not require the constellation of the transmitted signals to comprise symbols of equal power. (Elements in FIG. 3 that are referenced by numbers that are the same as reference numbers in FIG. 1 are like elements.) In FIG. 3, channel estimator 43 of receiver 40 is responsive to the output signals of maximum likelihood detector 42. Having access to the recovered signals s.sub.0 and s.sub.1, channel estimator 43 forms the estimates

(22) $\begin{array}{cc}{\tilde{h}}_0=\frac{r_0{s}_0^{*}-r_1{s}_1}{{.Math.s_0.Math.}^2+{.Math.s_1.Math.}^2}=h_0+\frac{s_0^{*}{n}_0+s_1{n}_1}{{.Math.s_0.Math.}^2+{.Math.s_1.Math.}^2}{\tilde{h}}_1=\frac{r_0{s}_1^{*}-r_1{s}_0}{{.Math.s_0.Math.}^2+{.Math.s_1.Math.}^2}=h_1+\frac{s_1^{*}{n}_0+s_0{n}_1}{{.Math.s_0.Math.}^2+{.Math.s_1.Math.}^2}& \left(17\right)\end{array}$
and applies those estimates to combiner 23 and to detector 42. Detector 24 recovers signals s.sub.2 and s.sub.3 by employing the approach used by detector 24 of FIG. 1, except that it does not employ the simplification of equation (9). The recovered signals of detector 42 are fed back to channel estimator 43, which updates the channel estimates in preparation for the next cycle.

(23) The FIGS. 1-3 embodiments illustrate the principles of this invention for arrangements having two transmit antennas and one receive antenna. However, those principles are broad enough to encompass a plurality of transmit antennas and a plurality of receive antennas. To illustrate, FIG. 4 presents an embodiment where two transmit antennas and two receive antennas are used; to wit, transmit antennas 31 and 32, and receive antennas 51 and 52. The signal received by antenna 51 is applied to channel estimator 53 and to combiner 55, and the signal received by antenna 52 is applied to channel estimator 54 and to combiner 55. Estimates of the channel transfer functions h.sub.0, and h.sub.1 are applied by channel estimator 53 to combiner 55 and to maximum likelihood detector 56. Similarly, estimates of the channel transfer functions h.sub.2 and h.sub.3 are applied by channel estimator 54 to combiner 55 and to maximum likelihood detector 56. Table 2 defines the channels between the transmit antennas and the receive antennas, and table 3 defines the notion for the received signals at the two receive antennas.

(24) TABLE-US-00002 TABLE 2 Antenna 51 Antenna 52 Antenna 31 h.sub.0 h.sub.2 Antenna 32 h.sub.1 h.sub.3

(25) TABLE-US-00003 TABLE 3 Antenna 51 Antenna 52 Time t r.sub.0 r.sub.2 Time t + T r.sub.1 r.sub.3

(26) Based on the above, it can be shown that the received signals are
r.sub.0=h.sub.0s.sub.0+h.sub.1s.sub.1+n.sub.0
r.sub.1=−h.sub.0s.sub.1*+h.sub.1s.sub.0*+n.sub.1
r.sub.2=h.sub.2s.sub.0+h.sub.3s.sub.1+n.sub.2
r.sub.3=−h.sub.2s.sub.1*+h.sub.3s.sub.0*+n.sub.3  (18)
where n.sub.0, n.sub.1, n.sub.2, and n.sub.3 are complex random variables representing receiver thermal noise, interferences, etc.

(27) In the FIG. 4 arrangement, combiner 55 develops the following two signals that are sent to the maximum likelihood detector:
{tilde over (s)}.sub.0=h.sub.0*r.sub.0+h.sub.1r.sub.1*+h.sub.2*r.sub.2+h.sub.3r.sub.3*
{tilde over (s)}.sub.1=h.sub.1*r.sub.0−h.sub.0r.sub.1*+h.sub.3*r.sub.2−h.sub.2r.sub.3*.  (19)

(28) Substituting the appropriate equations results in
{tilde over (s)}.sub.0=(a.sub.0.sup.2+a.sub.1.sup.2+a.sub.2.sup.2+a.sub.3.sup.2)s.sub.0+h.sub.0*n.sub.0+h.sub.1n.sub.1*+h.sub.2*n.sub.2+h.sub.3n.sub.3*
{tilde over (s)}.sub.1=(a.sub.0.sup.2+a.sub.1.sup.2+a.sub.2.sup.2+a.sub.3.sup.2)s.sub.1+h.sub.1*n.sub.0−h.sub.0n.sub.1*+h.sub.3*n.sub.2−h.sub.2n.sub.3*  (20)
which demonstrates that the signal {tilde over (s)}.sub.0 and {tilde over (s)}.sub.i are indeed estimates of the signals s.sub.0 and s.sub.1. Accordingly, signals {tilde over (s)}.sub.0 and {tilde over (s)}.sub.1 are sent to maximum likelihood decoder 56, which uses the decision rule of equation (10) to recover the signals ŝ.sub.0 and ŝ.sub.1.

(29) As disclosed above, the principles of this invention rely on the transmitter to force a diversity in the signals received by a receiver, and that diversity can be effected in a number of ways. The illustrated embodiments rely on space diversity—effected through a multiplicity of transmitter antennas, and time diversity—effected through use of two time intervals for transmitting the encoded symbols. It should be realized that two different transmission frequencies could be used instead of two time intervals. Such an embodiment would double the transmission speed, but it would also increase the hardware in the receiver, because two different frequencies need to be received and processed simultaneously.

(30) The above illustrated embodiments are, obviously, merely illustrative implementations of the principles of the invention, and various modifications and enhancements can be introduced by artisans without departing from the spirit and scope of this invention, which is embodied in the following claims. For example, all of the disclosed embodiments are illustrated for a space-time diversity choice, but as explained above, one could choose the space-frequency pair. Such a choice would have a direct effect on the construction of the receivers.