Training-based channel estimation for multiple-antennas

Abstract

The burden of designing multiple training sequences for systems having multiple transmit antennas, is drastically reduced by employing a single sequence from which the necessary multiple sequences are developed. The single sequence is selected to create sequences that have an impulse-like autocorrelation function and zero cross correlations. A sequence of any desired length n_t can be realized for an arbitrary number of channel taps, L. The created sequences can be restricted to a standard constellation (that is used in transmitting information symbols) so that a common constellation mapper is used for both the information signals and the training sequence. In some applications a a training sequence may be selected so that it is encoded with the same encoder that is used for encoding information symbols. Both block and trellis coding is possible in embodiments that employ this approach.

Description

RELATED APPLICATION

This application
where S is a convolution matrix of dimension (N_t′−L′+1)×L′. Again, for optimality, the imposed requirement is that

$\begin{array}{cc}{S}^H\left(L^{\prime },N_t^{\prime }\right)S\left(L^{\prime },N_t^{\prime }\right)=\left(N_t^{\prime }-L^{\prime }+1\right)I_{2L},& \left(10\right)\end{array}$
and once the sequence s is found, the task is to create the subsequences s₁ and s₂ from the found sequence s. Preferably, the subsequences s₁ and s₂ can be algorithmically generated from sequence s. Conversely, one may find subsequences s₁ and s₂ that satisfy the requirements of equation (8) and be such that sequence s can be algorithmically generated. This permits the use of a single training signal generator that, through a predetermined algorithm (i.e., coding) develops the subsequences s₁ and s₂. Both approaches lead to embodiment depicted in FIG. 3, where information signals are applied to encoder 13 that generates two streams of symbols that are applied to constellation mapper 14 via switches 15 and 16. Generator 5 creates a training sequence that is applied to encoder 9, and encoder 9 generates the subsequences s₁ and s₂ that are applied to constellation mapper 14 via switches 15 and 16.

Actually, once we realized that the complexity of the training sequence determination problem can be reduced by focusing on the creation of a single sequence from which a plurality of sequences that meet the requirements of equation (8) can be generated, it became apparent that there is no requirement for s to be longer than s₁ and s₂.

FIG. 4 presents one approach for generating optimal subsequences s₁ and s₂ that meet the requirements of equation (8) and that can be generated from a single sequence. In accordance with FIG. 4, generator 5 develops a sequence s of length N_t/2, and encoder 9 develops therefrom the sequences s₁=−s|s and s₂=s|s, where the “|” symbol stands for concatenation; e.g., sequence s₁ comprises sequence −s concatenated with, or followed by, sequence s. Thus, during the training sequence, antenna 11 transmits the sequence −s during the first N_t/2 time periods, and the sequence s during the last N_t/2 time periods. Antenna 12 transmits the sequence s during both the first and last N_t/2 time periods.

In response to the training sequences transmitted by antennas 11 and 12, receiving antenna 21 develops the signal vector y (where the elements of the vector y are the signals received from antennas 11 and 12). Considering the received signal during the first N_t/2 time periods as y₁ and during the last N_t/2 time periods as y₂, and employing only the useful portion of the signal (that is, the portions not corrupted by signals that are not part of the training sequence) one gets

$\begin{array}{cc}\left[\begin{array}{c}{y}_1\\ y_2\end{array}\right]=\left[\begin{array}{cc}-S& S\\ S& S\end{array}\right]\left[\begin{array}{c}{h}_1\\ h_2\end{array}\right]+\left[\begin{array}{c}{z}_1\\ z_2\end{array}\right]& \left(11\right)\end{array}$
where S is a convolution matrix of dimension (N_t−L+1)×L. In accordance with the principles disclosed herein, the FIG. 3 receiver multiplies the received signal in processor 25 with the transpose conjugate matrix S^H, yielding

$\begin{array}{cc}\left[\begin{array}{c}{r}_1\\ r_2\end{array}\right]=\left[\begin{array}{cc}-S^H& S^H\\ S^H& S^H\end{array}\right]\left[\begin{array}{c}{y}_1\\ y_2\end{array}\right]=\left[\begin{array}{cc}2S^{H}S& 0\\ 0& 2S^{H}S\end{array}\right]\left[\begin{array}{c}{h}_1\\ h_2\end{array}\right]+\left[\begin{array}{c}{\stackrel{\_}{z}}_1\\ {\stackrel{\_}{z}}_2\end{array}\right]& \left(12\right)\\ \mathrm{where}& \\ \left[\begin{array}{c}{\stackrel{\_}{z}}_1\\ {\stackrel{\_}{z}}_2\end{array}\right]=\left[\begin{array}{cc}-S^H& S^H\\ S^H& S^H\end{array}\right]\left[\begin{array}{c}{z}_1\\ z_2\end{array}\right].& \left(13\right)\end{array}$
If the sequence s is such that S^HS=(N_t−L+1)I_L, then

$\begin{array}{cc}\left[\begin{array}{c}{r}_1\\ r_2\end{array}\right]=2\left(N_t-L+1\right)\left[\begin{array}{c}{h}_1\\ h_2\end{array}\right]+\left[\left[\begin{array}{c}{\stackrel{\_}{z}}_1\\ {\stackrel{\_}{z}}_2\end{array}\right]\right].& \left(14\right)\end{array}$
If the noise is white, then the linear processing at the receiver does not color it, and the channel transfer functions correspond to

$\begin{array}{cc}{h}_1=1\text{/}2\left(N_t-L+1\right)r_1& \\ h_2=1\text{/}2\left(N_t-L+1\right)r_2.& \left(15\right)\end{array}$
with a minimum squared error, MSE, that achieves the lower bound expressed in equation (7); to wit,

$\begin{array}{cc}\mathrm{MSE}=\frac{2{\sigma }^{2}L}{\left(N_t-L+1\right)}& \left(16\right)\end{array}$

The above result can be generalized to allow any matrix U to be used to encode the training sequence, s, so that

$\begin{array}{cc}\left[\begin{array}{c}{y}_1\\ y_2\end{array}\right]=U\left[\begin{array}{c}{h}_1\\ h_2\end{array}\right]+\left[\begin{array}{c}{z}_1\\ z_2\end{array}\right]& \left(17\right)\end{array}$
as long as U^HU=2I for a two antennas case, and U^HU=KI for an K antenna case.

Whereas FIG. 4 presents a method for developing sequences s₁ and s₂ of length N_t from a sequence s that is N_t/2 symbols long, FIG. 5 presents a method for developing sequences s₁ and s₂ of length N_t from a sequence s that is 2N_t symbols long, which consists of a sequence d₁=[s(0) s(1) . . . s(N_t−1)] followed by a sequence d₂=[s(0) s(1) . . . s(N_t−1)]. In accordance with this approach, s₁=d₁|−{tilde over (d)}₂* and s₂=d₂|{tilde over (d)}₁*. The sequence {tilde over (d)}₁ corresponds to the sequence d₁ with its elements in reverse order. The symbol {tilde over (d)}₁* operation corresponds to the sequence d₁ with its elements in reverse order and converted to their respective complex conjugates.

The FIG. 5 encoding is very similar to the encoding scheme disclosed by Alamouti in U.S. Pat. No. 6,185,258, issued Feb. 6, 2001, except that (a) the Alamouti scheme is symbols-centric whereas the FIG. 5 encoding is sequence-centric, and (b) the Alamouti scheme does not have the concept of a reverse order of a sequence (e.g., {tilde over (d)}₁*). See also E. Lindskog and A. Paulraj titled “A Transmit Diversity Scheme for Channels With Intersymbol Interference,” ICC, 1:307-311, 2000. An encoder 9 that is created for developing training sequences s₁ and s₂ in accordance with FIG. 5, can be constructed with a control terminal that is set to 1 during transmission of information and set to another value (e.g., 0, or to N_t to indicate the length of the generated block) during transmission of the training sequence, leading to the simplified transmitter realization shown in FIG. 6. More importantly, such an arrangement leads to a simplified receiver because essentially the same decoder is used for both the information signals and the training signals.

With a signal arrangement as shown in FIG. 5, the signal captured at antenna 21 of receiver 20 is

$\begin{array}{cc}\left[\begin{array}{c}{y}_1\\ y_2\end{array}\right]=\left[\begin{array}{cc}-{\tilde{D}}_1^{*}& {\tilde{D}}_1^{*}\\ D_1& D_2\end{array}\right]\left[\begin{array}{c}{h}_1\\ h_2\end{array}\right]+\left[\left[\begin{array}{c}{\stackrel{\_}{z}}_1\\ {\stackrel{\_}{z}}_2\end{array}\right]\right]& \left(18\right)\end{array}$
where the matrices D_i and {tilde over (D)}_i (for i=1, 2) are convolution matrices for d₁ and {tilde over (d)}₁, respectively, of dimension (N_t−L+1)×L. Recalling from equation (8) that MMSE is achieved if and only if D^HD has zeros off the diagonal; i.e.,

$\begin{array}{cc}-{\tilde{D}}_1^T{\tilde{D}}_2^{*}+{\left(D_2^{*}\right)}^T{D}_1=0& \left(19\right)\\ \mathrm{and}& \\ -{\tilde{D}}_2^T{\tilde{D}}_1^{*}+{\left(D_1^{*}\right)}^T{D}_2=0,& \left(20\right)\end{array}$
and identity matrices on the diagonal; i.e.,

$\begin{array}{cc}{\tilde{D}}_2^T{\tilde{D}}_2^{*}+{\left(D_1^{*}\right)}^T{D}_1=2\left(N_t-L+1\right)I_L& \left(21\right)\\ \mathrm{and}& \\ {\tilde{D}}_1^T{\tilde{D}}_1^{*}+{\left(D_2^{*}\right)}^T{D}_2=2\left(N_t-L+1\right)I_L.& \left(22\right)\end{array}$

Various arrangements that interrelate sequences d₁ and d₂ can be found that meet the above requirement. By way of example (and not by way of limitation), a number of simple choices satisfy these conditions follow.

(1) (D₁*)^TD₁=(N_t−L+1)I_L, {tilde over (D)}₁=D₁, and D₂=D₁. To show that equation (21) holds, one may note that {tilde over (D)}₂^T{tilde over (D)}₂* (the first term in the equation) becomes D₁^TD₁*, but if (D₁*)^TD₁ is a diagonal matrix then so is {tilde over (D)}₂^T{tilde over (D)}₂*. Thus, according to this training sequence embodiment, one needs to only identify a sequence d₁ that is symmetric about its center, with an impulse-like autocorrelation function, and set d₂ equal to d₁. This is shown in FIG. 7.
(2) (D₁*)^TD₁=(N_t−L+1)I_L, and {tilde over (D)}₂=D₁. To show that equation (21) holds, one may note that the {tilde over (D)}₂^T{tilde over (D)}₂* first term in the equation also becomes D₁^TD₁*. Thus, according to this training sequence embodiment, one needs to only identify a sequence d₁ with an impulse-like autocorrelation function, and set d₂ equal to {tilde over (d)}₁. This is shown in FIG. 8.
(3) (D₁*)^TD₁=(N_t−L+1)I_L, and {tilde over (D)}₂*=D₁. To show that equation (21) holds, one may note that the {tilde over (D)}₂^T{tilde over (D)}₂* first term in the equation becomes (D₁*)^TD₁. Thus, according to this training sequence embodiment, one needs to only identify a sequence d₁ with an impulse-like autocorrelation function, and set d₂ equal to {tilde over (d)}₁*. This is shown in FIG. 9.
Training Sequences Employing Trellis Coding

Consider a trellis code with m memory elements and outputs from a constellation of size C, over a single channel with memory 2^mC^(L−1)−1. To perform joint equalization and decoding one needs a product trellis with 2^mC^(L−1) states. For a space-time trellis code with m memory elements, n transmit antennas and one receive antenna, over a channel with memory (L−1), one needs a product trellis with 2^mC^n(L−1).

The receiver can incorporate the space-time trellis code structure in the channel model to create an equivalent single-input, single output channel, h_eq, of length m+L. The trellis, in such a case, involves C^(m+L−1) states. The approach disclosed herein uses a single training sequence at the input of the space-time trellis encoder to directly estimate h_eq used by the joint space-time equalizer/decoder. The channel h_eq that incorporates the space-time code structure typically has a longer memory than the channel h₁ and h₂ (in a system where there are two transmitting antennas and one receiving antenna).

To illustrate, assume an encoder 30 as depicted in FIG. 10 that employs an 8-PSK constellation of symbols to encode data from a training sequence generator into a sequence s of symbols taken from the set e^i2πpk/8, p_k=0,1, 2, . . . , 7, where the training sequences s₁ and s₂ are algorithmically derived within encoder 30 from sequence s. Specifically, assume that s₁(k)=s(k), and that s₂(k)=(−1)^pk−1s(k−1), which means that s₂(k)=s(k−1) when s(k−1) is an even member of the constellation (eⁱ⁰, e^iπ/2, e^iπ, and e^i3π/2), and s₂(k)=−s(k−1) when s(k−1) is an odd member of the constellation.

With such an arrangement, the received signal at time k can be expressed as

$\begin{array}{cc}y\left(k\right)=\sum _{i=0}^{L-1}{h}_1\left(i\right)s\left(k-i\right)+\sum _{i=0}^{L-1}{h}_2\left(i,k\right){\left(-1\right)}^{p_{k-i-1}}s\left(k-i-1\right)+z\left(k\right)=\sum _{i=0}^{L-1}{h}_{\mathrm{eq}}\left(i\right)s\left(k-i\right)+z\left(k\right),& \left(23\right)\\ \mathrm{where}& \\ h_{\mathrm{eq}}\left(i,k\right)=\{\begin{array}{cc}{h}_1\left(0\right)& \mathrm{for}i=0\\ h_1\left(i\right)+{\left(-1\right)}^{p_{k-i}}{h}_2\left(i-1\right)& \mathrm{for}0<i<L\\ {\left(-1\right)}^{p_{k-L}}{h}_2\left(L-1\right)& \mathrm{for}i=L.\end{array}& \left(24\right)\end{array}$
A block of received signals (corresponding to the useful portion of the training sequence block) can be expressed in matrix form by
y=Sh_eq+z   (25)
where

$\begin{array}{cc}S=\left[\begin{array}{cccc}s\left(L\right)& s\left(L-1\right)& \cdots & s\left(0\right)\\ s\left(L+1\right)& s\left(L\right)& \cdots & s\left(1\right)\\ ⋮& ⋮& & ⋮\\ s\left(N_t-1\right)& s\left(N_t-2\right)& \cdots & s\left(N_t-L-1\right)\end{array}\right]\left[\begin{array}{c}{h}_{\mathrm{eq}}\left(0,L\right)\\ h_{\mathrm{eq}}\left(1,L+1\right)\\ ⋮\\ h_{\mathrm{eq}}\left(L,N_t-1\right)\end{array}\right]& \left(26\right)\end{array}$
and following the principles disclosed above, it can be realized that when the training sequence is properly selected so that S^HS is a diagonal matrix, i.e., S^HS=(N_t−L)I_L+1, an estimate of h_eq that is, ĥ_eq, is obtained from

$\begin{array}{cc}{\hat{h}}_{\mathrm{eq}}=\frac{S^{H}y}{\left(N_t-L\right)}.& \left(27\right)\end{array}$
If the training sequence were to comprise only the even constellation symbols, e^i2πk/8, k=0, 2, 4, 6, per equation (24), the elements of {tilde over (h)}_eq would correspond to

$\begin{array}{cc}{h}_{\mathrm{eq}}^{\mathrm{even}}=\left[h_1\left(0\right),h_1\left(1\right)+h_2\left(0\right),h_1\left(2\right)+h_2\left(1\right),\dots h_1\left(L-1\right)+h_2\left(L-2\right),h_2\left(L-1\right)\right].& \left(28\right)\end{array}$
If the training sequence were to comprise only the odd constellation symbols, e^i2πk/8, k=1, 3, 5, 7, the elements of {tilde over (h)}_eq would correspond to

$\begin{array}{cc}{h}_{\mathrm{eq}}^{\mathrm{odd}}=\left[h_1\left(0\right),h_1\left(1\right)-h_2\left(0\right),h_1\left(2\right)-h_2\left(1\right),\dots h_1\left(L-1\right)-h_2\left(L-2\right),h_2\left(L-1\right)\right].& \left(29\right)\end{array}$
If the training sequence were to comprise a segment of only even constellation symbols followed by only odd constellation symbols (or vice versa), then channel estimator 22 within receiver 20 can determine the h_eq^even coefficients from the segment that transmitted only the even constellation symbols, and can determine the h_eq^odd coefficients from the segment that transmitted only the even constellation symbols. Once both h_eq^even and h_eq^even and h_eq^odd are known, estimator 22 can obtain the coefficients of h₁ from

$\begin{array}{cc}\left[h_1\left(0\right),h_1\left(1\right),h_1\left(2\right),\dots h_1\left(L-1\right)\right]=\frac{h_{\mathrm{eq}}^{\mathrm{even}}+h_{\mathrm{eq}}^{\mathrm{odd}}}{2}& \left(30\right)\end{array}$
and the coefficients of h₂ from

$\begin{array}{cc}\left[h_2\left(0\right),h_2\left(1\right),h_2\left(2\right),\dots h_2\left(L-1\right)\right]=\frac{h_{\mathrm{eq}}^{\mathrm{even}}-h_{\mathrm{eq}}^{\mathrm{odd}}}{2}.& \left(31\right)\end{array}$
What remains, then, is to create a single training sequence s of length N_t where one half of it (the s_even portion) consists of only even constellation symbols (even sub-constellation), and another half of it (the s_odd portion) consists of only odd constellation symbols (odd sub-constellation). The sequences s₁ and s₂ of length N_t are derived from the sequence s by means of the 8-PSK space-time trellis encoder. The sequences s₁ and s₂ must also meet the requirements of equation (8). Once s_even is found, s_odd can simply be
s_odd=αs_even, where α=e^iπk/4 for any k=1,3,5, 7.   (32)
Therefore, the search for sequence s is reduced from a search in the of 8^Nt to a search for s_even in the space 4^(Nt/2) such that, when concatenated with s_odd that is computed from s_even as specified in equation (32), yields a sequence s that has an autocorrelation function that is, or is close to being, impulse-like.

For a training sequence of length N_t=26, with an 8-PSK space-time trellis encoder, we have identified the 12 training sequences specified in Table 1 below.

TABLE 1
sequence #	α	Se
1	exp(i5π/4)	−1 1 1 1 1 −1 −i −1 1 1 −1 1 1
2	exp(i3π/4)	1 1 −1 1 i i 1 −i i −1 −1 −1 1
3	exp(iπ/4)	1 −1 −1 −i i −i 1 1 1 −i −1 1 1
4	exp(iπ/4)	1 −1 −1 −i 1 −1 1 −i −i −i −1 1 1
5	exp(iπ/4)	1 i 1 1 i −1 −1 i 1 −1 1 i 1
6	exp(i3π/4)	1 i 1 i −1 −1 1 −1 −1 i 1 i 1
7	exp(i7π/4)	1 −i 1 1 −i −1 −1 −i 1 −1 1 −i 1
8	exp(i5π/4)	1 −i 1 −1 i 1 −1 −i 1 1 1 −i 1
9	exp(i3π/4)	−1 1 1 1 −1 −1 −i −1 −1 1 −1 1 1
10	exp(i7π/4)	−1 i −1 −i 1 −i i i 1 i 1−i 1
11	exp(iπ/4)	−1 −i −1 i 1 i −i −i 1−i 1 i 1
12	exp(i3π/4)	−1 −i −1 i −1 i −i −i −1 −i 1 i 1

Construction of Training Sequence

While the above-disclosed materials provide a very significant improvement over the prior art, there is still the requirement of selecting a sequence s₁ with an impulse-like autocorrelation function. The following discloses one approach for identifying such a sequence without having to perform an exhaustive search.

A root-of-unity sequence with alphabet size N has complex roots of unity elements of the form

$e^{\frac{\mathrm{i2\pi }k}{N}},k=1,2,\dots \left(N-1\right).$
As indicated above, the prior art has shown that perfect roots-of-unity sequences (PRUS) can be found for any training sequence of length N_t, as long as no constraint is imposed on the value of N. As also indicated above, however, it is considered disadvantageous to not limit N to a power of 2. Table 2 presents the number of PRUSs that were found to exist (through exhaustive search) for different sequence lengths when the N is restricted to 2 (BPSK), 4 (QPSK), or 8 (8-PSK). Cell entries in Table 2 with “-” indicate that sequence does not exist, and blank cells indicate that an exhaustive search for a sequence was not performed.

TABLE 2
	Nt =
	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
BPSK	—	—	8	—	—	—	—	—	—	—	—	—	—	—	—	—	—
QPSK	8	—	32	—	—	—	128	—	—	—	—	—	—	—	6144	—	—
8-PSK	16	—	128	—	—	—	512	—	—	—	—	—

A sequence s of length N_t is called L-perfect if the corresponding training matrix S of dimension (N_t−L+1)×L satisfies equation (8). Thus, an L-perfect sequence of length N_t is optimal for a channel with L taps. It can be shown that the length N_t of an L-perfect sequence from a 2^p-alphabet can only be equal to

$\begin{array}{cc}{N}_t=\left\{\begin{array}{cc}2\left(L+i\right)& \mathrm{for}L=\mathrm{odd}\\ 2\left(L+i\right)-1& \mathrm{for}L=\mathrm{even}\end{array}\right\}\mathrm{for}i=0,1,\dots ,& \left(33\right)\end{array}$
which is a necessary, but not sufficient, condition for L-perfect sequences of length N_t. Table 3 shows the minimum necessary N_t for L=2, 3, . . . 10, the size of the corresponding matrix S, and the results of an exhaustive search for L-perfect sequences (indicating the number of such sequences that were found). Cell entries marked “x” indicate that sequences exist, but number of such sequences it is not known.

TABLE 3
	L
	2	3	4	5	6	7	8	9	10
Nt	3	6	7	10	11	14	15	18	19
S	2 × 2	4 × 3	4 × 4	6 × 5	6 × 6	8 × 7	8 × 8	10 × 9	10 × 10
BPSK	4	8	8	—	—	—	—	—	—
QPSK	16	64	64	—	—	128		x
8-PSK	64	512	512			x		x

It is known that with a PRUS of a given length, N_PRUS, one can estimate up to L=N_PRUS unknowns. It can be shown that a training sequence of length N_t is also an L-perfect training sequence if
N_t=kN_PRUS+L−1 and k≧1.   (34)
Accordingly, an L-perfect sequence of length kN_PRUS+L−1 can be constructed by selecting an N_PRUSsequence, repeating it k times, and circularly extending it by L−1 symbols. Restated and amplified somewhat, for a selected PRUS of a given N_PRUS, i.e.,

$\begin{array}{cc}{s}_p\left(N_{\mathrm{PRUS}}\right)=\left[s_p\left(0\right)s_p\left(1\right)\dots s_p\left(N_{\mathrm{PRUS}}-1\right)\right],& \left(35\right)\end{array}$
the L-perfect sequence of length kN_PRUS+L−1 is created from a concatenation of k s_p(N_PRUS) sequences followed by the first L−1 symbols of s_p(N_PRUS), or from a concatenation of the last L−1 symbols of s_p(N_PRUS) followed by k s_p(N_PRUS) sequences.

To illustrate, assume that the number of channel “taps” that need to be estimated, L, is 5, and that a QPSK alphabet is desired to be used. From the above it is known that N_PRUS must be equal to or greater than 5, and from Table 2 it is known that the smallest N_PRUS that can be found for QSPK that is larger than 5 is N_PRUS=8. Employing equation (34) yields

$\begin{array}{cc}\begin{array}{c}{N}_t={\mathrm{kN}}_{\mathrm{PRUS}}+L-1\\ =k·8+5-1\\ =12,20,28,\dots \end{array}& \left(36\right)\\ \mathrm{for}k=1,2,3,\dots & \end{array}$

While an L-perfect training sequence cannot be constructed from PRUS sequences for values of N_t other than values derived by operation of equation (34), it is known that, nevertheless, L-perfect sequences may exist. The only problem is that it may be prohibitively difficult to find them. However, in accordance with the approach disclosed below, sub-optimal solutions are possible to create quite easily.

If it is given that the training sequence is N_t long, one can express this length by
N_t=kN_PRUS+L−1+M, where M>0   (37)
In accord with our approach, select a value of N_PRUS≧L that minimizes M, create a sequence of length kN_PRUS+L−1 as disclosed above, and then extend that sequence by adding M symbols. The M added symbols can be found by selecting, through an exhaustive search, the symbols that lead to the lowest estimation MSE. Alternatively, select a value of N_PRUS≧L that minimizes M′ in the equation,
N_t=kN_PRUS+L−1−M′, where M′>0   (38)
create a sequence of length kN_PRUS+L−1 as disclosed above, and then drop the last (or first) M′ symbols.

The receiver shown in FIG. 2 includes the channel estimator 22, which takes the received signal and multiplies it S^H as appropriate; see equation (12), above.

Claims

1. A space-time diversity transmitter that includes (a) n transmitting antennas, where n is greater than one, (b) first encoder responsive to an applied information bit stream, said encoder developing n symbol streams, and (c) a constellation mapper responsive to said n symbol streams, for mapping symbols of each of said n symbol streams into a standard signal constellation to create a corresponding mapped stream, said constellation mapper applying each of the created n mapped streams to a different one of said n antennas in blocks of n_t mapped symbols that are synchronized in time to each other, the improvement comprising:

a training generator for generating either n sequences of signals or a sequence of signals that contains n subsequences of signal;

a second encoder for creating n training symbol sequences from said signals created by said training generator, each containing n_t symbols, where n_t represents a training sequence length; and

said constellation mapper is configured to map said n training symbol sequences onto a standard constellation to develop n mapped training sequences, and to apply the n mapped training sequences to said n antennas at times when said constellation mapper stops applying said n mapped stream to said n antennas;

where said n training symbol sequences have an impulse-like autocorrelation function and zero cross correlation.

2. The transmitter of claim 1 where said n training symbol sequences are selected to enable a receiver that receives said n training symbol sequences to determine characteristics of a medium through which said n antennas communicate to said receiver.

3. The transmitter of claim 2 where said n training sequences have a common length n_t that is related to transmitted symbols memory, L−1, of said medium, n_t being at least equal to 2L−1.

4. The transmitter of claim 1 where said constellation mapper employs a constellation taken from a set that includes binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), and 8-point phase shift keying (8-PSK).

5. The transmitter of claim 1 where n=2, said generator creates a sequence s composed of sequence d₁ followed by sequence d₂, and said second encoder creates a first training sequence that is −d₁ concatenated with {tilde over (d)}₂*, and a second sequence that is d₂ concatenated with d₁* where {tilde over (d)}₂* corresponds to the sequence d₂ with its elements in reverse order and converted to their respective complex conjugates, and the sequence d₁* corresponds to the sequence d₁ with its elements converted to their complex conjugate values.

6. The transmitter of claim 5 where said sequence d₁ and said sequence d₂ contain n_t/2 n_t symbols each, where n_t is related to number of channel parameters, L, that a receiver which seeks to receive signals from an antenna of said transmitter estimates.

7. The transmitter of claim 1 where n=2, said generator creates a sequence d, and said second encoder creates a first training sequence that is −d concatenated with {tilde over (d)}*, and a second sequence that is d concatenated with d*, where the sequence d* corresponds to the sequence d with its elements converted to their complex conjugate values and the sequence {tilde over (d)}* corresponds to the sequence d with its elements in reverse order and converted to their respective complex conjugate values.

8. The transmitter of claim 1 where n2 n=2, said generator creates a sequence d, and said second encoder creates a first training sequence that is −d concatenated with {tilde over (d)}*, and a second sequence that is {tilde over (d)} concatenated with d*, where the sequence d* corresponds to the sequence d with its elements converted to their complex conjugate values and the sequence {tilde over (d)}* corresponds to the sequence d with its elements in reverse order and converted to their respective complex conjugate values.

9. The transmitter of claim 1 where n=2, said generator creates a sequence d, and said second encoder creates a first training sequence that is −d concatenated with d, and a second sequence that is {tilde over (d)}* concatenated with d*, where the sequence d* corresponds to the sequence d with its elements converted to their complex conjugate values and the sequence {tilde over (d)}* corresponds to the sequence d with its elements in reverse order and converted to their respective complex conjugate values.

10. The transmitter of claim 1 where said first encoder and said second encoder embodied in a single module that creates either said n symbol streams or said n training symbol sequences.

11. The transmitter of claim 1 where said second encoder is a trellis encoder.

12. The transmitter of claim 11 where

(a) said n training sequences are selected to enable a receiver that receives said n training sequences to determine characteristics of a transmission medium between said transmitter and said receiver, and

(b) said generator develops said symbols sequence to comprise n_t+(n−2)L+m symbols long, where L is the number of channel parameters that describe a channel within said transmission medium from one of said n transmitter antennas to a receiving antenna of said receiver, m is number of symbols stored in a memory of said trellis encoder, and n_t is not less than 2L−1.

13. The transmitter of claim 11 where said training sequence mapper employs symbols from a set composed of elements e^i2πpk/8, p_k=0,1,2, . . . , 7.

14. The transmitter of claim 13 where said generator develops a symbols sequence s(k), and said second encoder develops a first sequence s₁ (k)=s(k), and a second sequence s₂(k)=(−1)^pk−1s(k−1).

15. The transmitter of claim 14 where said sequence s(k) is composed of a first segment, s_even, that comprises symbols from a set composed of e^i2πpk/8, p_k=0, 2, 4, 6, and a second segment, s_odd, where s_odd=αs_even, and α=e^iπk/4 for any k=1, 3, 5, 7.

16. The transmitter of claim 15 where said s_even, and a corresponding α are any one of the following:

17. A space-time diversity transmitter that includes (a) n transmitting antennas, where n is greater than one, (b) first encoder responsive to an applied information bit stream, said encoder developing n symbol streams, and (c) a constellation mapper responsive to said n symbol streams, for mapping symbols of each of said n symbol streams into a standard signal constellation to create a corresponding mapped stream, said constellation mapper applying each of the created n mapped streams to a different one of said n antennas in blocks of n_t mapped symbols that are synchronized in time to each other, the improvement comprising:

a training generator for generating either n sequences of signals or a sequence of signals that contains n subsequences of signal;

a second encoder for creating n training symbol sequences from said signals created by said training generator, each containing n_t symbols, where n_t represents a training sequence length; and

said constellation mapper is configured to map said n training sequences onto a standard constellation to develop n mapped training sequences, and to apply the n mapped training sequences to said n antennas at times when said constellation mapper stops applying said n mapped stream to said n antennas;

where said n training sequences have an impulse-like autocorrelation function and zero cross correlation, and where n2 n=2, said generator creates a sequence s, and said second encoder creates a first training sequence that is equal to −s concatenated with s, and a second training sequence that is equal to s concatenated with s.

18. The transmitter of claim 17 where said sequence s contains n_t/2 symbols, where n_t is related to number of channel parameters, L, that a receiver which seeks to receive signals from an antenna of said transmitter estimates.