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M-Sequence Generator (MSEQ)

M-Sequence Generator (MSEQ)

Property	Description	Units	Default	Range/Type
L	Length of shift register	None	5	[2, 63]/Integer
N	Period of the m-sequence	None	31	[1, Inf)/Integer
PL	Primitive polynomial (low 32 bits) in decimal	None	37	[1, Inf)/Integer
PH	Primitive polynomial (high 32 bits) in decimal	None	0	[0, Inf)/Integer
SL	Initial state of the shift register (low 32 bits) in decimal	None	1	[0, Inf)/Integer
SH	Initial state of the shift register (high 32 bits) in decimal	None	0	[0, Inf)/Integer
NC	Number of chips	None	0	[0, Inf)/Integer
RC	Chip rate of the m-sequence	Hz	1000	(0, Inf)/Real
T	True output value	None	-1	(-Inf, Inf)/Integer
F	False output value	None	1	(-Inf, Inf)/Integer
ROUT	Output impedance	Ohm	0	[0, Inf)/Real
Ports
Output	Truncated m-sequence (real)

Notes

1. The m-sequence Generator model can be used to generate m-sequence.

2. The m-sequence can be generated using Linear Feedback Shift Register (LFSR) with a primitive polynomial^[2]. For a given primitive polynomial, there are two methods^[2] of implementing LFSR, i.e, Galois feedback generator and Fibonacci feedback generator. Since m-sequence has the maximum possible period for a L-stage LFSR, it is also called maximal length sequence. The maximum period of a L-stage LFSR can be proven to be 2^L-1. The structure of Linear Feedback Shift Register with Fibonacci feedback generator is shown in Fig.1. The primitive polynomials g(D) is given by

(1)

3. Table I shows a list of primitive polynomials for Linear Feedback Shift Register^[2]. In the table, all polynomials are specified by an octal number that defines the coefficients of g(D). The octal number gives the coefficients of g(D) beginning with g_oon the right and proceeding to g_Lin the last nonzero position on the left. For example, a L-tage LFSR uses the entry [367]. Expanding the octal entry 367 into binary form, we obtain

Therefore,

In Table I, each entry in brackets represents one primitive polynomial as a series of octal numbers, explained in the above example. The entries following by an asterisk correspond to circuit implementation with only two feedback connections, which are very useful for high-speed applications. No reciprocal polynomial is listed in Table I. Since the reciprocal polynomial of a primitive polynomial is also primitive, each entry in this table can be used to generate two distinct m-sequences.

Fig. 1 Block diagram of m-sequence Generator (Fibonacci feedback generator)

4. Note that the primitive polynomial in binary is g₀g₁...g_L and the initial state of the shift register in binary is S_L-1S_L-2...S₀ .

5. A list of primitive polynomials is tabulated in the following table:

Degree	Octal Representation of primitive polynomial (g₀on left to g_Lon right)
2	[7]^*
3	[13]^*
4	[23]^*
5	[45]^*, [75], [67]
6	[103]^*, [147], [155]
7	[211]^, [217], [235], [367], [277], [325], [203]^, [313], [345]
8	[435], [551], [747], [453], [545], [537], [703], [543]
9	[1021]^*, [1131], [1461], [1423], [1055], [1167], [1541], [1333], [1605], [1751], [1743], [1617], [1553], [1157]
10	[2011]^*, [2415], [3771], [2157], [3515], [2773], [2033], [2443], [2461], [3023], [3543], [2745], [2431], [3177]
11	[4055]^*, [4445], [4215], [4055], [6015], [7413], [4143], [4563], [4053], [5023], [5623], [4577], [6233], [6673]
12	[10123], [15647], [16533], [16047], [11015], [14127], [17673], [13565], [15341], [15053], [15621], [15321], [11417], [13505]
13	[20033], [23261], [24623], [23517], [30741], [21643], [30171], [21277], [27777], [35051], [34723], [34047], [32535], [31425]
14	[42103], [43333], [51761], [40503], [77141], [62677], [44103], [45145], [76303], [64457], [57231], [64167], [60153], [55753]
15	[100003]^, [102043], [110013], [102067], [104307], [100317], [177775], [103451], [110075], [102061], [114725], [103251], [100021]^, [100201]^*
16	[210013], [234313], [233303], [307107], [307527], [306357], [201735], [272201], [242413], [270155], [302157], [210205], [305667], [236107]
17	[400011]^, [400017], [400431], [525251], [410117], [400731], [411335], [444257], [600013], [403555], [525327], [411077], [400041]^, [400101]^*
18	[1000201]^*, [1000247], [1002241], [1002441], [1100045], [1000407], [1003011], [1020121], [1101005], [1000077], [1001361], [1001567], [1001727], [1002777]
19	[2000047], [2000641], [2001441], [2000107], [2000077], [2000157], [2000175], [2000257], [2000677], [2000737], [2001557], [2001637], [2005775], [2006677]
20	[4000011]^*, [4001051], [4004515], [6006031], [4442235]
21	[10000005]^*, [10040205], [10020045], [10040315], [10000635], [10103075], [10050335], [10002135], [17000075]

Netlist Form

MSEQ:NAME n1 L=val [N =val] [PL=val] [PH =val] [SL=val] [SH =val] NC=val [RC=val] + [T=val] [F =val] [ROUT=val]

Netlist Example

MSEQ:1 1 L = 5 N=31 PL = 41 PH = 0 SL = 31 SH = 0 NC = 124 RC = 1khz T= 1 F= 0

References

1. J. G. Proakis, Digital Communications, McGraw-Hill, 2001.

2. R. L. Peterson, R. E. Ziemer, and D. E. Borth, Introduction to Spread Spectrum Communications. Prentice Hall International Editions, 1995.

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